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Neverov VD, Lukyanov AE, Krasavin AV, Vagov A, Lvov BG, Croitoru MD. Exploring disorder correlations in superconducting systems: spectroscopic insights and matrix element effects. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2024; 15:199-206. [PMID: 38379929 PMCID: PMC10877080 DOI: 10.3762/bjnano.15.19] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Accepted: 01/25/2024] [Indexed: 02/22/2024]
Abstract
Understanding the intricate interplay between disorder and superconductivity has become a key area of research in condensed matter physics, with profound implications for materials science. Recent studies have shown that spatial correlations of disorder potential can improve superconductivity, prompting a re-evaluation of some theoretical models. This paper explores the influence of disorder correlations on the fundamental properties of superconducting systems, going beyond the traditional assumption of spatially uncorrelated disorder. In particular, we investigate the influence of disorder correlations on key spectroscopic superconductor properties, including the density of states, as well as on the matrix elements of the superconducting coupling constant and their impact on the localization length. Our findings offer valuable insights into the role of disorder correlations in shaping the behavior of superconducting materials.
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Affiliation(s)
- Vyacheslav D Neverov
- National Research Nuclear University MEPhI, Moscow 115409, Russian Federation
- National Research University Higher School of Economics, 101000 Moscow, Russian Federation
| | - Alexander E Lukyanov
- National Research Nuclear University MEPhI, Moscow 115409, Russian Federation
- National Research University Higher School of Economics, 101000 Moscow, Russian Federation
| | - Andrey V Krasavin
- National Research Nuclear University MEPhI, Moscow 115409, Russian Federation
- National Research University Higher School of Economics, 101000 Moscow, Russian Federation
| | - Alexei Vagov
- National Research University Higher School of Economics, 101000 Moscow, Russian Federation
| | - Boris G Lvov
- National Research University Higher School of Economics, 101000 Moscow, Russian Federation
| | - Mihail D Croitoru
- National Research University Higher School of Economics, 101000 Moscow, Russian Federation
- Departamento de Física, Centro de Ciências Exatas e da Natureza,Universidade Federal de Pernambuco, Recife, Pernambuco, 50740-560, Brasil
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2
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Weitzel A, Pfaffinger L, Maccari I, Kronfeldner K, Huber T, Fuchs L, Mallord J, Linzen S, Il'ichev E, Paradiso N, Strunk C. Sharpness of the Berezinskii-Kosterlitz-Thouless Transition in Disordered NbN Films. PHYSICAL REVIEW LETTERS 2023; 131:186002. [PMID: 37977616 DOI: 10.1103/physrevlett.131.186002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2023] [Accepted: 09/21/2023] [Indexed: 11/19/2023]
Abstract
We present a comprehensive investigation of the Berezinskii-Kosterlitz-Thouless transition in ultrathin strongly disordered NbN films. Measurements of resistance, current-voltage characteristics, and kinetic inductance on the very same device reveal a consistent picture of a sharp unbinding transition of vortex-antivortex pairs that fit standard renormalization group theory without extra assumptions in terms of inhomogeneity. Our experiments demonstrate that the previously observed broadening of the transition is not an intrinsic feature of strongly disordered superconductors and provide a clean starting point for the study of dynamical effects at the Berezinskii-Kosterlitz-Thouless transition.
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Affiliation(s)
- Alexander Weitzel
- Institute for Experimental and Applied Physics, University of Regensburg, D-93040 Regensburg, Germany
| | - Lea Pfaffinger
- Institute for Experimental and Applied Physics, University of Regensburg, D-93040 Regensburg, Germany
| | - Ilaria Maccari
- Department of Physics, Stockholm University, SE-10691 Stockholm, Sweden
| | - Klaus Kronfeldner
- Institute for Experimental and Applied Physics, University of Regensburg, D-93040 Regensburg, Germany
| | - Thomas Huber
- Institute for Experimental and Applied Physics, University of Regensburg, D-93040 Regensburg, Germany
| | - Lorenz Fuchs
- Institute for Experimental and Applied Physics, University of Regensburg, D-93040 Regensburg, Germany
| | - James Mallord
- Institute for Experimental and Applied Physics, University of Regensburg, D-93040 Regensburg, Germany
| | - Sven Linzen
- Leibniz Institute of Photonic Technology, D-07745 Jena, Germany
| | - Evgeni Il'ichev
- Leibniz Institute of Photonic Technology, D-07745 Jena, Germany
| | - Nicola Paradiso
- Institute for Experimental and Applied Physics, University of Regensburg, D-93040 Regensburg, Germany
| | - Christoph Strunk
- Institute for Experimental and Applied Physics, University of Regensburg, D-93040 Regensburg, Germany
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3
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Caldas H, Rufo S, Griffith MAR. Non-homogeneous pairing in disordered two-orbital s-wave superconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 36:055601. [PMID: 37820641 DOI: 10.1088/1361-648x/ad0275] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Accepted: 10/11/2023] [Indexed: 10/13/2023]
Abstract
We investigate the effects of non-magnetic disorder in a hybridized two-dimensional two-orbital s-wave superconductor (SC) model. The situation in which electronic orbitals overlap such that the hybridizationVi,jamong them is antisymmetric, under inversion symmetry, was taken into account. The on-site disorder is given by a random impurity potentialW. We find that while the random disorder acts to the detriment of superconductivity, hybridization proceeds to favor it. Accordingly, hybridization plays an important role in two-orbital models of superconductivity, in order to hold the long-range order against the increase of disorder. This makes the present model eligible to describe real materials, since the hybridization may be induced by pressure or doping. In addition, the regime from moderate to strong disorder reveals that the system is broken into SC islands with correlated local order parameters. These correlations persist to distances of several order lattice spacing which corresponds to the size of the SC-Islands.
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Affiliation(s)
- Heron Caldas
- Departamento de Ciências Naturais, Universidade Federal de São João Del Rei, Praça Dom Helvécio 74, 36301-160 São João Del Rei, MG, Brazil
| | - S Rufo
- Beijing Computational Science Research Center, Building 9, East Zone, No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, People's Republic of China
- CeFEMA, Instituto Superior técnico, Universidade de Lisboa, Av. Rovisco Pais, No. 1, 1049-001 Lisboa, Portugal
| | - M A R Griffith
- Beijing Computational Science Research Center, Building 9, East Zone, No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, People's Republic of China
- CeFEMA, Instituto Superior técnico, Universidade de Lisboa, Av. Rovisco Pais, No. 1, 1049-001 Lisboa, Portugal
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4
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Mallik S, Ménard GC, Saïz G, Witt H, Lesueur J, Gloter A, Benfatto L, Bibes M, Bergeal N. Superfluid stiffness of a KTaO 3-based two-dimensional electron gas. Nat Commun 2022; 13:4625. [PMID: 35941153 PMCID: PMC9360446 DOI: 10.1038/s41467-022-32242-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 07/21/2022] [Indexed: 11/09/2022] Open
Abstract
After almost twenty years of intense work on the celebrated LaAlO3/SrTiO3system, the recent discovery of a superconducting two-dimensional electron gas (2-DEG) in (111)-oriented KTaO3-based heterostructures injects new momentum to the field of oxides interface. However, while both interfaces share common properties, experiments also suggest important differences between the two systems. Here, we report gate tunable superconductivity in 2-DEGs generated at the surface of a (111)-oriented KTaO3 crystal by the simple sputtering of a thin Al layer. We extract the superfluid stiffness of the 2-DEGs and show that its temperature dependence is consistent with a node-less superconducting order parameter having a gap value larger than expected within a simple BCS weak-coupling limit model. The superconducting transition follows the Berezinskii-Kosterlitz-Thouless scenario, which was not reported on SrTiO3-based interfaces. Our finding offers innovative perspectives for fundamental science but also for device applications in a variety of fields such as spin-orbitronics and topological electronics.
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Affiliation(s)
- S Mallik
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, 1 Avenue Augustin Fresnel, 91767, Palaiseau, France
| | - G C Ménard
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, PSL University, CNRS, Sorbonne Université, Paris, France
| | - G Saïz
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, PSL University, CNRS, Sorbonne Université, Paris, France
| | - H Witt
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, 1 Avenue Augustin Fresnel, 91767, Palaiseau, France.,Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, PSL University, CNRS, Sorbonne Université, Paris, France
| | - J Lesueur
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, PSL University, CNRS, Sorbonne Université, Paris, France
| | - A Gloter
- Laboratoire de Physique des Solides, Université Paris-Saclay, CNRS UMR 8502, 91405, Orsay, France
| | - L Benfatto
- Department of Physics and ISC-CNR, Sapienza University of Rome, Rome, Italy
| | - M Bibes
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, 1 Avenue Augustin Fresnel, 91767, Palaiseau, France
| | - N Bergeal
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, PSL University, CNRS, Sorbonne Université, Paris, France.
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5
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Dutta S, Raychaudhuri P, Mandal SS, Ramakrishnan TV. Superfluid density in conventional superconductors: from clean to strongly disordered. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:335601. [PMID: 35675804 DOI: 10.1088/1361-648x/ac76fd] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2022] [Accepted: 06/08/2022] [Indexed: 06/15/2023]
Abstract
The highly convergent form of superfluid density in disordered conventional superconductors available in the literature and independently obtained by us following the approach of an earlier paper (Mandal and Ramakrishnan 2020Phys. Rev.B102024514) has been reformulated to separate out the generally used so-called 'dirty-limit' term and an additional term. We use this new expression for making an extensive comparison with previously published experimental data and show that the former, generally used, term isnotsufficient for analyzing these results. We point out that consequently, there is a large regime (disordered superconductors with moderate to no disorder) where theoretical predictions need to be confronted with experiment.
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Affiliation(s)
- Surajit Dutta
- Tata Institute of Fundamental Research, Mumbai 400005, India
| | | | - Sudhansu S Mandal
- Department of Physics, Indian Institute of Technology, Kharagpur 721302, India
| | - T V Ramakrishnan
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
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6
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Raychaudhuri P, Dutta S. Phase fluctuations in conventional superconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:083001. [PMID: 34731851 DOI: 10.1088/1361-648x/ac360b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 11/03/2021] [Indexed: 06/13/2023]
Abstract
Within the Bardeen-Cooper-Schrieffer (BCS) theory, superconductivity is entirely governed by the pairing energy scale, which gives rise to the superconducting energy gap, Δ. However, another important energy scale, the superfluid phase stiffness,J, which determines the resilience of the superconductor to phase-fluctuations is normally ignored. The spectacular success of BCS theory owes to the fact that in conventional superconductorsJis normally several orders of magnitude larger than Δ and thus an irrelevant energy scale. However, in certain situations such as in the presence of low carrier density, strong disorder, at low-dimensions or in granular superconductors,Jcan drastically come down and even become smaller than Δ. In such situations, the temperature and magnetic field evolution of superconducting properties is governed by phase fluctuations, which gives rise to novel electronic states where signatures of electronic pairing continue to exist even when the zero resistance state is destroyed. In this article, we will review the recent experimental developments on the study of phase fluctuations in conventional superconductors.
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Affiliation(s)
- Pratap Raychaudhuri
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Surajit Dutta
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
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7
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Liu M, Nam H, Kim J, Fiete GA, Shih CK. Influence of Nanosize Hole Defects and their Geometric Arrangements on the Superfluid Density in Atomically Thin Single Crystals of Indium Superconductor. PHYSICAL REVIEW LETTERS 2021; 127:127003. [PMID: 34597098 DOI: 10.1103/physrevlett.127.127003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Revised: 05/11/2021] [Accepted: 08/04/2021] [Indexed: 06/13/2023]
Abstract
Using Indium sqrt[7]×sqrt[3] on Si(111) as an atomically thin superconductor platform, and by systematically controlling the density of nanohole defects (nanometer size voids), we reveal the impacts of defect density and defect geometric arrangements on superconductivity at macroscopic and microscopic length scales. When nanohole defects are uniformly dispersed in the atomic layer, the superfluid density monotonically decreases as a function of defect density (from 0.7% to 5% of the surface area) with minor change in the transition temperature T_{C}, measured both microscopically and macroscopically. With a slight increase in the defect density from 5% to 6%, these point defects are organized into defect chains that enclose individual two-dimensional patches. This new geometric arrangement of defects dramatically impacts the superconductivity, leading to the total disappearance of macroscopic superfluid density and the collapse of the microscopic superconducting gap. This study sheds new light on the understanding of how local defects and their geometric arrangements impact superconductivity in the two-dimensional limit.
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Affiliation(s)
- Mengke Liu
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Hyoungdo Nam
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Jungdae Kim
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
- Department of Physics and EHSRC, University of Ulsan, Ulsan 680-749, South Korea
| | - Gregory A Fiete
- Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Chih-Kang Shih
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
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8
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Lakhno VD. Pseudogap Isotope Effect as a Probe of Bipolaron Mechanism in High Temperature Superconductors. MATERIALS (BASEL, SWITZERLAND) 2021; 14:4973. [PMID: 34501062 PMCID: PMC8434434 DOI: 10.3390/ma14174973] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Revised: 08/05/2021] [Accepted: 08/28/2021] [Indexed: 11/17/2022]
Abstract
A theory of a pseudogap phase of high-temperature superconductors where current carriers are translation invariant bipolarons is developed. A temperature T* of a transition from a pseudogap phase to a normal one is calculated. For the temperature of a transition to the pseudogap phase, the isotope coefficient is found. It is shown that the results obtained, in particular, the possibility of negative values of the isotope coefficient, are consistent with the experiment. New experiments on the influence of the magnetic field on the isotope coefficient are proposed.
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Affiliation(s)
- Victor D Lakhno
- Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, 125047 Moscow, Russia
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9
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Signatures of two-dimensional superconductivity emerging within a three-dimensional host superconductor. Proc Natl Acad Sci U S A 2021; 118:2017810118. [PMID: 33846248 DOI: 10.1073/pnas.2017810118] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Spatial disorder has been shown to drive two-dimensional (2D) superconductors to an insulating phase through a superconductor-insulator transition (SIT). Numerical calculations predict that with increasing disorder, emergent electronic granularity is expected in these materials-a phenomenon where superconducting (SC) domains on the scale of the material's coherence length are embedded in an insulating matrix and coherently coupled by Josephson tunneling. Here, we present spatially resolved scanning tunneling spectroscopy (STS) measurements of the three-dimensional (3D) superconductor BaPb1-x Bi x O3 (BPBO), which surprisingly demonstrate three key signatures of emergent electronic granularity, having only been previously conjectured and observed in 2D thin-film systems. These signatures include the observation of emergent SC domains on the scale of the coherence length, finite energy gap over all space, and strong enhancement of spatial anticorrelation between pairing amplitude and gap magnitude as the SIT is approached. These observations are suggestive of 2D SC behavior embedded within a conventional 3D s-wave host, an intriguing but still unexplained interdimensional phenomenon, which has been hinted at by previous experiments in which critical scaling exponents in the vicinity of a putative 3D quantum phase transition are consistent only with dimensionality d = 2.
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10
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Zaytseva I, Abaloszew A, Camargo BC, Syryanyy Y, Cieplak MZ. Upper critical field and superconductor-metal transition in ultrathin niobium films. Sci Rep 2020; 10:19062. [PMID: 33149161 PMCID: PMC7642399 DOI: 10.1038/s41598-020-75968-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2020] [Accepted: 10/20/2020] [Indexed: 11/09/2022] Open
Abstract
Recent studies suggest that in disordered ultrathin films superconducting (SC) state may be intrinsically inhomogeneous. Here we investigate the nature of SC state in ultrathin Nb films, of thickness d ranging from 1.2 to 20 nm, which undergo a transition from amorphous to polycrystalline structure at the thickness [Formula: see text] nm. We show that the properties of SC state are very different in polycrystalline and amorphous films. The upper critical field ([Formula: see text]) is orbitally limited in the first case, and paramagnetically limited in the latter. The magnetic field induced superconductor-metal transition is observed, with the critical field approximately constant or decreasing as a power-law with the film conductance in polycrystalline or amorphous films, respectively. The scaling analysis indicates distinct scaling exponents in these two types of films. Negative contribution of the SC fluctuations to conductivity exists above [Formula: see text], particularly pronounced in amorphous films, signaling the presence of fluctuating Cooper pairs. These observations suggest the development of local inhomogeneities in the amorphous films, in the form of proximity-coupled SC islands. An usual evolution of SC correlations on cooling is observed in amorphous films, likely related to the effect of quantum fluctuations on the proximity-induced phase coherence.
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Affiliation(s)
- Iryna Zaytseva
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02668, Warsaw, Poland.
| | - Aleksander Abaloszew
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02668, Warsaw, Poland
| | - Bruno C Camargo
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02668, Warsaw, Poland
| | - Yevgen Syryanyy
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02668, Warsaw, Poland
| | - Marta Z Cieplak
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02668, Warsaw, Poland.
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11
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Gupta C, Parab P, Bose S. Superfluid density from magnetic penetration depth measurements in Nb-Cu 3D nano-composite films. Sci Rep 2020; 10:18331. [PMID: 33110107 PMCID: PMC7591886 DOI: 10.1038/s41598-020-75351-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Accepted: 09/21/2020] [Indexed: 11/20/2022] Open
Abstract
Superconductivity in 3D Nb–Cu nanocomposite granular films have been studied with varying thickness for two different compositions, Nb rich with 88 at% of Nb and Cu rich with 46 at% of Nb. For both compositions, the superconducting transition temperature (Tc) decreases with decreasing film thickness. For any thickness, doubling the Cu content in the films decreases the Tc by about 2 K. To explore if phase fluctuations play any role in superconductivity in these 3D films, the superfluid stiffness (JS) of the films was measured using low frequency two-coil mutual inductance (M) technique. Interestingly, the measurement of M in magnetic fields showed two peaks in the imaginary component of M for both Nb rich and Cu rich films. The two peaks were associated with the pair-breaking effect of the magnetic field on the intra and inter-granular coupling in these films consisting of random network of superconductor (S) and normal metal (N) nano-particles. Furthermore, JS was seen to decrease with decreasing film thickness and increasing Cu content. However, for all films studied JS remained higher than the superconducting energy gap (∆) indicating that phase fluctuations do not play any role in superconductivity in the film thickness and composition range investigated. Our results indicate that an interplay of quantum size effects (QSE) and superconducting proximity effect (SPE) controls the Tc with composition in these 3D nano-composite films.
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Affiliation(s)
- Chandan Gupta
- School of Physical Sciences, UM-DAE Center for Excellence in Basic Sciences, University of Mumbai, Kalina Campus, Mumbai, 400098, India
| | - Pradnya Parab
- School of Physical Sciences, UM-DAE Center for Excellence in Basic Sciences, University of Mumbai, Kalina Campus, Mumbai, 400098, India
| | - Sangita Bose
- School of Physical Sciences, UM-DAE Center for Excellence in Basic Sciences, University of Mumbai, Kalina Campus, Mumbai, 400098, India.
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12
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Rubio-Verdú C, Garcı A-Garcı A AM, Ryu H, Choi DJ, Zaldı Var J, Tang S, Fan B, Shen ZX, Mo SK, Pascual JI, Ugeda MM. Visualization of Multifractal Superconductivity in a Two-Dimensional Transition Metal Dichalcogenide in the Weak-Disorder Regime. NANO LETTERS 2020; 20:5111-5118. [PMID: 32463696 DOI: 10.1021/acs.nanolett.0c01288] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Eigenstate multifractality is a distinctive feature of noninteracting disordered metals close to a metal-insulator transition, whose properties are expected to extend to superconductivity. While multifractality in three dimensions (3D) only develops near the critical point for specific strong-disorder strengths, multifractality in 2D systems is expected to be observable even for weak disorder. Here we provide evidence for multifractal features in the superconducting state of an intrinsic, weakly disordered single-layer NbSe2 by means of low-temperature scanning tunneling microscopy/spectroscopy. The superconducting gap, characterized by its width, depth, and coherence peaks' amplitude, shows a characteristic spatial modulation coincident with the periodicity of the quasiparticle interference pattern. The strong spatial inhomogeneity of the superconducting gap width, proportional to the local order parameter in the weak-disorder regime, follows a log-normal statistical distribution as well as a power-law decay of the two-point correlation function, in agreement with our theoretical model. Furthermore, the experimental singularity spectrum f(α) shows anomalous scaling behavior typical from 2D weakly disordered systems.
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Affiliation(s)
| | - Antonio M Garcı A-Garcı A
- Shanghai Center for Complex Physics, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Hyejin Ryu
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Center for Spintronics, Korean Institute of Science and Technology, Seoul 02792, Korea
| | - Deung-Jang Choi
- CIC nanoGUNE, 20018 Donostia-San Sebastián, Spain
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), 20018 San Sebastián, Spain
- Donostia International Physics Center (DIPC), 20018 San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
| | | | - Shujie Tang
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
| | - Bo Fan
- Shanghai Center for Complex Physics, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Zhi-Xun Shen
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
- Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305, United States
| | - Sung-Kwan Mo
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - José Ignacio Pascual
- CIC nanoGUNE, 20018 Donostia-San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
| | - Miguel M Ugeda
- CIC nanoGUNE, 20018 Donostia-San Sebastián, Spain
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), 20018 San Sebastián, Spain
- Donostia International Physics Center (DIPC), 20018 San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
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13
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Mahmood F, He X, Božović I, Armitage NP. Locating the Missing Superconducting Electrons in the Overdoped Cuprates La_{2-x}Sr_{x}CuO_{4}. PHYSICAL REVIEW LETTERS 2019; 122:027003. [PMID: 30720319 DOI: 10.1103/physrevlett.122.027003] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2018] [Revised: 12/11/2018] [Indexed: 06/09/2023]
Abstract
Overdoped high-temperature cuprate superconductors have often been understood within the standard BCS framework of superconductivity. However, measurements in a variety of overdoped cuprates indicate that the superfluid density is much smaller than expected from BCS theory and decreases smoothly to zero as the doping is increased. Here, we combine time-domain THz spectroscopy with kHz range mutual inductance measurements on the same overdoped La_{2-x}Sr_{x}CuO_{4} films to determine the total, superfluid, and uncondensed spectral weight as a function of doping. A significant fraction of the carriers remains uncondensed in a wide Drude-like peak as T→0, while the superfluid density remains linear in temperature. These observations are seemingly inconsistent with existing, realistic theories of impurity scattering suppressing the superfluid density in a BCS-like d-wave superconductor. Our large measurement frequency range gives us a unique look at the low frequency spectral weight distribution, which may suggest the presence of quantum phase fluctuations as the critical doping is approached.
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Affiliation(s)
- Fahad Mahmood
- The Institute for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218 USA
| | - Xi He
- Brookhaven National Laboratory, Upton, New York 11973, USA
- Applied Physics Department, Yale University, New Haven, Connecticut 06520, USA
| | - Ivan Božović
- Brookhaven National Laboratory, Upton, New York 11973, USA
- Applied Physics Department, Yale University, New Haven, Connecticut 06520, USA
| | - N P Armitage
- The Institute for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218 USA
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14
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Kremen A, Khan H, Loh YL, Baturina TI, Trivedi N, Frydman A, Kalisky B. Imaging quantum fluctuations near criticality. NATURE PHYSICS 2018; 14:1205-1210. [PMID: 30555522 PMCID: PMC6287708 DOI: 10.1038/s41567-018-0264-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/16/2017] [Accepted: 07/23/2018] [Indexed: 06/09/2023]
Abstract
A quantum phase transition (QPT) occurs between two competing phases of matter at zero temperature, driven by quantum fluctuations. Though the presence of these fluctuations is well established, they have not been locally imaged in space and their local dynamics has not been studied so far. We use a scanning superconducting quantum interference device to image quantum fluctuations in the vicinity of the QPT from a superconductor to an insulator. We find fluctuations of the diamagnetic response in both space and time that survive well below the transition temperature, demonstrating their quantum nature. The fluctuations appear as telegraph-like noise with a range of characteristic times and a non-monotonic temperature dependence, revealing unexpected quantum granularity. The lateral dimension of these fluctuations grows towards criticality, offering a new measurable length scale. Our results provide physical insight about the reorganization of phases across a QPT, with implications for any theoretical description. This paves a new route for future quantum information applications.
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Affiliation(s)
- A Kremen
- Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar Ilan University Ramat Gan, Israel
| | - H Khan
- Department of Physics, The Ohio State University, Columbus, OH 43210, USA
| | - Y L Loh
- Department of Physics and Astrophysics, University of North Dakota, Grand Forks, ND 58202, USA
| | - T I Baturina
- Institute of Semiconductor Physics, 630090, Novosibirsk, Russia
- Novosibirsk State University, Pirogova str. 2, Novosibirsk 630090, Russia
- Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar Ilan University Ramat Gan, Israel
| | - N Trivedi
- Department of Physics, The Ohio State University, Columbus, OH 43210, USA
| | - A Frydman
- Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar Ilan University Ramat Gan, Israel
| | - B Kalisky
- Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar Ilan University Ramat Gan, Israel
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15
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Roy A, Shimshoni E, Frydman A. Quantum Criticality at the Superconductor-Insulator Transition Probed by the Nernst Effect. PHYSICAL REVIEW LETTERS 2018; 121:047003. [PMID: 30095933 DOI: 10.1103/physrevlett.121.047003] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Indexed: 06/08/2023]
Abstract
The superconductor-insulator transition (SIT) is an excellent example of a quantum phase transition at zero temperature, dominated by quantum fluctuations. These are expected to be very prominent close to the quantum critical point. So far, most of the experimental studies of the SIT have concentrated on transport properties and tunneling experiments that provide indirect information on criticality close to the transition. Here we present an experiment uniquely designed to study the evolution of quantum fluctuations through the quantum critical point. We utilize the Nernst effect, which has been shown to be effective in probing superconducting fluctuation. We measure the Nernst coefficient in amorphous indium oxide films tuned through the SIT and find a large signal on both the superconducting and the insulating sides, which peaks close to the critical point. The transverse Peltier coefficient α_{xy}, which is the thermodynamic quantity extracted from these measurements, follows quantum critical scaling with critical exponents ν∼0.7 and z∼1. These exponents are consistent with a clean X-Y model in 2+1 dimensions.
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Affiliation(s)
- A Roy
- Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel
| | - E Shimshoni
- Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel
| | - A Frydman
- Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel
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16
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Abstract
The correct detection of the Berezinskii-Kosterlitz-Thouless (BKT) transition in quasi-two-dimensional superconductors still remains a controversial issue. Its main signatures, indeed, are often at odds with the theoretical expectations. In a recent work (Maccari, I.; Benfatto, L.; Castellani, C. Phys. Rev. B 2017, 96, 060508), we have shown that the presence of spatially correlated disorder plays a key role in this sense because it is the reason underlying the experimentally-observed smearing of the universal superfluid-density jump. In the present paper we closely investigate the effects of correlated disorder on the BKT transition, specifically addressing the issue of whether or not it changes the BKT universality class.
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17
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Makise K, Ichikawa F, Asano T, Shinozaki B. Field-tuned superconductor-insulator transitions and Hall resistance in thin polycrystalline MoN films. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:065402. [PMID: 29186006 DOI: 10.1088/1361-648x/aa9e2e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We report on the superconductor-insulator transitions (SITs) of disordered molybdenum nitride (MoN) thin films on (1 0 0) MgO substrates as a function of the film thickness and magnetic fields. The T c of the superconducting MoN films, which exhibit a sharp superconducting transition, monotonically decreases as the normal state R sq increases with a decreasing film thickness. For several films with different thicknesses, we estimate the critical field H c and the product zν ≃ 0.6 of the dynamical exponent z and the correlation length exponent ν using a finite scaling analysis. The value of this product can be explained by the (2 + 1) XY model. We found that the Hall resistance ΔR xy (H) is maximized when the magnetic field satisfies H HP(T) [Formula: see text] |1 - T/T C0| in the superconducting state and also in the normal states owning to the superconducting fluctuation corresponding to the ghost critical magnetic field. We measured the Hall conductivity δσ xy (H) = σ xy (H) - [Formula: see text] and fit the Gaussian approximation theory for δσ xy (H) to the experimental data. Agreement between the data and the theory beyond H c suggests the survival of the Cooper pair in the insulating region of the SIT.
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Affiliation(s)
- Kazumasa Makise
- National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
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18
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Singh G, Jouan A, Benfatto L, Couëdo F, Kumar P, Dogra A, Budhani RC, Caprara S, Grilli M, Lesne E, Barthélémy A, Bibes M, Feuillet-Palma C, Lesueur J, Bergeal N. Competition between electron pairing and phase coherence in superconducting interfaces. Nat Commun 2018; 9:407. [PMID: 29379023 PMCID: PMC5789063 DOI: 10.1038/s41467-018-02907-8] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2017] [Accepted: 01/08/2018] [Indexed: 11/29/2022] Open
Abstract
In LaAlO3/SrTiO3 heterostructures, a gate tunable superconducting electron gas is confined in a quantum well at the interface between two insulating oxides. Remarkably, the gas coexists with both magnetism and strong Rashba spin-orbit coupling. However, both the origin of superconductivity and the nature of the transition to the normal state over the whole doping range remain elusive. Here we use resonant microwave transport to extract the superfluid stiffness and the superconducting gap energy of the LaAlO3/SrTiO3 interface as a function of carrier density. We show that the superconducting phase diagram of this system is controlled by the competition between electron pairing and phase coherence. The analysis of the superfluid density reveals that only a very small fraction of the electrons condenses into the superconducting state. We propose that this corresponds to the weak filling of high-energy dxz/dyz bands in the quantum well, more apt to host superconductivity.
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Affiliation(s)
- G Singh
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, PSL Research University, CNRS, 10 Rue Vauquelin, 75005, Paris, France
- Université Pierre and Marie Curie, Sorbonne-Universités, 75005, Paris, France
| | - A Jouan
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, PSL Research University, CNRS, 10 Rue Vauquelin, 75005, Paris, France
- Université Pierre and Marie Curie, Sorbonne-Universités, 75005, Paris, France
| | - L Benfatto
- Institute for Complex Systems (ISC-CNR), UOS Sapienza, Piazzale A. Moro 5, 00185, Roma, Italy.
- Dipartimento di Fisica Università di Roma "La Sapienza", Piazzale A. Moro 5, 00185, Roma, Italy.
| | - F Couëdo
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, PSL Research University, CNRS, 10 Rue Vauquelin, 75005, Paris, France
- Université Pierre and Marie Curie, Sorbonne-Universités, 75005, Paris, France
| | - P Kumar
- National Physical Laboratory, Council of Scientific and Industrial Research (CSIR), Dr. K.S. Krishnan Marg, New Delhi, 110012, India
| | - A Dogra
- National Physical Laboratory, Council of Scientific and Industrial Research (CSIR), Dr. K.S. Krishnan Marg, New Delhi, 110012, India
| | - R C Budhani
- Condensed Matter Low Dimensional Systems Laboratory, Department of Physics, Indian Institute of Technology, Kanpur, 208016, India
| | - S Caprara
- Institute for Complex Systems (ISC-CNR), UOS Sapienza, Piazzale A. Moro 5, 00185, Roma, Italy
- Dipartimento di Fisica Università di Roma "La Sapienza", Piazzale A. Moro 5, 00185, Roma, Italy
| | - M Grilli
- Institute for Complex Systems (ISC-CNR), UOS Sapienza, Piazzale A. Moro 5, 00185, Roma, Italy
- Dipartimento di Fisica Università di Roma "La Sapienza", Piazzale A. Moro 5, 00185, Roma, Italy
| | - E Lesne
- Unité Mixte de Physique CNRS-Thales, 1 Av. A. Fresnel, 91767, Palaiseau, France
| | - A Barthélémy
- Unité Mixte de Physique CNRS-Thales, 1 Av. A. Fresnel, 91767, Palaiseau, France
| | - M Bibes
- Unité Mixte de Physique CNRS-Thales, 1 Av. A. Fresnel, 91767, Palaiseau, France
| | - C Feuillet-Palma
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, PSL Research University, CNRS, 10 Rue Vauquelin, 75005, Paris, France
- Université Pierre and Marie Curie, Sorbonne-Universités, 75005, Paris, France
| | - J Lesueur
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, PSL Research University, CNRS, 10 Rue Vauquelin, 75005, Paris, France
- Université Pierre and Marie Curie, Sorbonne-Universités, 75005, Paris, France
| | - N Bergeal
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, PSL Research University, CNRS, 10 Rue Vauquelin, 75005, Paris, France.
- Université Pierre and Marie Curie, Sorbonne-Universités, 75005, Paris, France.
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19
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Patil S, Medicherla VRR, Ali K, Singh RS, Manfrinetti P, Wrubl F, Dhar SK, Maiti K. Observation of pseudogap in MgB 2. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:465504. [PMID: 29086758 DOI: 10.1088/1361-648x/aa8aa2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We investigate the electronic structure of a specially prepared highly dense conventional high temperature superconductor, MgB2, employing high resolution photoemission spectroscopy. The spectral evolution close to the Fermi energy is commensurate to BCS descriptions as expected. However, the spectra in the wider energy range reveal the emergence of a pseudogap much above the superconducting transition temperature indicating an apparent departure from the BCS scenario. The energy scale of the pseudogap is comparable to the energy of the [Formula: see text] phonon mode responsible for superconductivity in MgB2 and the pseudogap can be attributed to the effect of electron-phonon coupling on the electronic structure. These results reveal a scenario of the emergence of the superconducting gap within an electron-phonon coupling induced pseudogap and have significant implications in the study of high temperature superconductors.
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Affiliation(s)
- S Patil
- Department of Condensed Matter Physics and Materials' Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai-400005, India. Department of Physics, Indian Institute of Technology (Banaras Hindu University), Varanasi-221005, India
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20
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Poran S, Nguyen-Duc T, Auerbach A, Dupuis N, Frydman A, Bourgeois O. Quantum criticality at the superconductor-insulator transition revealed by specific heat measurements. Nat Commun 2017; 8:14464. [PMID: 28224994 PMCID: PMC5322500 DOI: 10.1038/ncomms14464] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2016] [Accepted: 01/03/2017] [Indexed: 11/09/2022] Open
Abstract
The superconductor–insulator transition (SIT) is considered an excellent example of a quantum phase transition that is driven by quantum fluctuations at zero temperature. The quantum critical point is characterized by a diverging correlation length and a vanishing energy scale. Low-energy fluctuations near quantum criticality may be experimentally detected by specific heat, cp, measurements. Here we use a unique highly sensitive experiment to measure cp of two-dimensional granular Pb films through the SIT. The specific heat shows the usual jump at the mean field superconducting transition temperature marking the onset of Cooper pairs formation. As the film thickness is tuned towards the SIT, is relatively unchanged, while the magnitude of the jump and low-temperature specific heat increase significantly. This behaviour is taken as the thermodynamic fingerprint of quantum criticality in the vicinity of a quantum phase transition. To detect thermodynamic signatures of quantum fluctuations for quantum phase transitions is challenging. Here, Poran et al. report a significant increase in the specific heat when the thickness of granular Pb films approaches a superconductor-insulator transition.
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Affiliation(s)
- S Poran
- Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel.,Institut NÉEL, CNRS, 25 avenue des Martyrs, F-38042 Grenoble, France
| | - T Nguyen-Duc
- Institut NÉEL, CNRS, 25 avenue des Martyrs, F-38042 Grenoble, France.,Univ. Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France
| | - A Auerbach
- Department of Physics, Technion, 32000 Haifa, Israel.,Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, UPMC-Sorbonne Universités, 4 Place Jussieu, 75252 Paris, France
| | - N Dupuis
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, UPMC-Sorbonne Universités, 4 Place Jussieu, 75252 Paris, France
| | - A Frydman
- Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel.,Institut NÉEL, CNRS, 25 avenue des Martyrs, F-38042 Grenoble, France.,Univ. Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France
| | - Olivier Bourgeois
- Institut NÉEL, CNRS, 25 avenue des Martyrs, F-38042 Grenoble, France.,Univ. Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France
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21
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Aslam M, Paul A, Thakur GS, Gayen S, Kumar R, Singh A, Das S, Ganguli AK, Waghmare UV, Sheet G. Evidence of a pseudogap driven by competing orders of multi-band origin in the ferromagnetic superconductor Sr0.5Ce0.5FBiS2. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:195701. [PMID: 27089948 DOI: 10.1088/0953-8984/28/19/195701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
From temperature and magnetic field dependent point-contact spectroscopy on the ferromagnetic superconductor Sr0.5Ce0.5FBiS2 (bulk superconducting [Formula: see text] K) we observe (a) a pseudogap in the normal state that sustains to a remarkably high temperature of 40 K and (b) two-fold enhancement of T c upto 5 K in the point-contact geometry. In addition, Andreev reflection spectroscopy reveals a superconducting gap of 6 meV for certain point-contacts suggesting that the mean field T c of this system could be approximately 40 K, the onset temperature of pseudo-gap. Our results suggest that quantum fluctuations originating from other competing orders in Sr0.5Ce0.5FBiS2 forbid a global phase coherence at high temperatures thereby suppressing T c. Apart from the known ordering to a ferromagnetic state, our first-principles calculations reveal nesting of a multi-band Fermi surface and a significant electron-phonon coupling that could result in charge density wave-like instabilities.
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Affiliation(s)
- Mohammad Aslam
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, S. A. S. Nagar, Manauli, PO 140306, India
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22
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Cea T, Castellani C, Seibold G, Benfatto L. Nonrelativistic Dynamics of the Amplitude (Higgs) Mode in Superconductors. PHYSICAL REVIEW LETTERS 2015; 115:157002. [PMID: 26550746 DOI: 10.1103/physrevlett.115.157002] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2015] [Indexed: 06/05/2023]
Abstract
Despite the formal analogy with the Higgs particle, the amplitude fluctuations of the order parameter in weakly coupled superconductors do not identify a real mode with a Lorentz-invariant dynamics. Indeed, its resonance occurs at 2Δ_{0}, which coincides with the threshold 2E_{gap} for quasiparticle excitations that spoil any relativistic dynamics. Here we investigate the fate of the Higgs mode in the unconventional case where 2E_{gap} becomes larger than 2Δ_{0}, as due to strong coupling or strong disorder. We show that also in this situation, the amplitude fluctuations never identify a real mode at 2Δ_{0}, since such a "bosonic" limit is always reached via strong mixing with the phase fluctuations, which dominate the low-energy part of the spectrum. Our results have direct implications for the interpretation of the subgap optical absorption in disordered superconductors.
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Affiliation(s)
- T Cea
- ISC-CNR and Department of Physics, "Sapienza" University of Rome, P.le A. Moro 5, 00185 Rome, Italy
| | - C Castellani
- ISC-CNR and Department of Physics, "Sapienza" University of Rome, P.le A. Moro 5, 00185 Rome, Italy
| | - G Seibold
- Institut Für Physik, BTU Cottbus-Senftenberg, P.O. Box 101344, 03013 Cottbus, Germany
| | - L Benfatto
- ISC-CNR and Department of Physics, "Sapienza" University of Rome, P.le A. Moro 5, 00185 Rome, Italy
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23
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Loh YL, Dhakal R, Neis JF, Moen EM. Divergence of dynamical conductivity at certain percolative superconductor-insulator transitions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:505702. [PMID: 25420003 DOI: 10.1088/0953-8984/26/50/505702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Random inductor–capacitor (LC) networks can exhibit percolative superconductor-insulator transitions (SITs). We use a simple and efficient algorithm to compute the dynamicalconductivity σ(ω,p) of one type of LC network on large (4000 × 4000) square lattices, where δ = p − p(c) is the tuning parameter for the SIT. We confirm that the conductivity obeys a scaling form, so that the characteristic frequency scales as∝|δ|(νz) with νz ≈ 1.91, the superfluid stiffness scales as ϒ∝|δ|(t) with t ≈ 1.3, and the electric susceptibility scales as χE∝|δ|(−s) with s = 2νz − t ≈ 2.52. In the insulating state, the low-frequency dissipative conductivity is exponentially small, whereas in the superconductor, it is linear in frequency.The sign of Im σ(ω) at small ω changes across the SIT. Most importantly, we find that right at the SIT Re σ(ω) ∝ ω(t/νz−1)∝ω(−0.32), so that the conductivity diverges in the DC limit, in contrast with most other classical and quantum models of SITs.
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24
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Poran S, Molina-Ruiz M, Gérardin A, Frydman A, Bourgeois O. Specific heat measurement set-up for quench condensed thin superconducting films. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2014; 85:053903. [PMID: 24880383 DOI: 10.1063/1.4875590] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We present a set-up designed for the measurement of specific heat of very thin or ultra-thin quench condensed superconducting films. In an ultra-high vacuum chamber, materials of interest can be thermally evaporated directly on a silicon membrane regulated in temperature from 1.4 K to 10 K. On this membrane, a heater and a thermometer are lithographically fabricated, allowing the measurement of heat capacity of the quench condensed layers. This apparatus permits the simultaneous thermal and electrical characterization of successively deposited layers in situ without exposing the deposited materials to room temperature or atmospheric conditions, both being irreversibly harmful to the samples. This system can be used to study specific heat signatures of phase transitions through the superconductor to insulator transition of quench condensed films.
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Affiliation(s)
- Shachaf Poran
- Institut NÉEL, CNRS, 25 Avenue des Martyrs, F-38042 Grenoble, France
| | - Manel Molina-Ruiz
- Institut NÉEL, CNRS, 25 Avenue des Martyrs, F-38042 Grenoble, France
| | - Anne Gérardin
- Institut NÉEL, CNRS, 25 Avenue des Martyrs, F-38042 Grenoble, France
| | - Aviad Frydman
- Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel
| | - Olivier Bourgeois
- Institut NÉEL, CNRS, 25 Avenue des Martyrs, F-38042 Grenoble, France
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25
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Kamar NA, Vidhyadhiraja NS. Site-disorder driven superconductor-insulator transition: a dynamical mean field study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:095701. [PMID: 24525620 DOI: 10.1088/0953-8984/26/9/095701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We investigate the effect of site disorder on the superconducting state in the attractive Hubbard model within the framework of dynamical mean field theory. For a fixed interaction strength (U), the superconducting order parameter decreases monotonically with increasing disorder (x), while the single-particle spectral gap decreases for small x, reaches a minimum and keeps increasing for larger x. Thus, the system remains gapped beyond the destruction of the superconducting state, indicating a disorder-driven superconductor-insulator transition. We investigate this transition in depth considering the effects of weak and strong disorder for a range of interaction strengths. In the clean case, the order parameter is known to increase monotonically with increasing interaction, saturating at a finite value asymptotically for U→∞. The presence of disorder results in destruction of superconductivity at large U, thus drastically modifying the clean case behaviour. A physical understanding of our findings is obtained by invoking particle-hole asymmetry and the probability distributions of the order parameter and spectral gap.
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Affiliation(s)
- Naushad Ahmad Kamar
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560 064, India
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26
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Ghosh S, Mandal SS. Amplitude fluctuations driven by the density of electron pairs within nanosize granular structures inside strongly disordered superconductors: evidence for a shell-like effect. PHYSICAL REVIEW LETTERS 2013; 111:207004. [PMID: 24289705 DOI: 10.1103/physrevlett.111.207004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2013] [Indexed: 06/02/2023]
Abstract
Motivated by the recent observation of the shell effect in a nanoscale pure superconductor by Bose et al. [Nat. Mater. 9, 550 (2010)], we explore the possible shell-like effect in a strongly disordered superconductor as it is known to produce nanosize superconducting puddles (SPs). We find a remarkable change in the texture of the pairing amplitudes that is responsible for forming the SP, upon monotonic tuning of the average electron density, <n>, and keeping the disorder landscape unaltered. Both the spatially averaged pairing amplitude and the quasiparticle excitation gap oscillate with <n>. This oscillation is due to a rapid change in the low-lying quasiparticle energy spectra and thereby a change in the shapes and positions of the SPs. We establish a correlation between the formation of SPs and the shell-like effect. The experimental consequences of our theory are also discussed.
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Affiliation(s)
- Sanjib Ghosh
- Department of Theoretical Physics, Indian Association for the Cultivation of Science, Kolkata 700 032, India
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27
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Kamlapure A, Das T, Ganguli SC, Parmar JB, Bhattacharyya S, Raychaudhuri P. Emergence of nanoscale inhomogeneity in the superconducting state of a homogeneously disordered conventional superconductor. Sci Rep 2013; 3:2979. [PMID: 24132046 PMCID: PMC3797984 DOI: 10.1038/srep02979] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2013] [Accepted: 10/02/2013] [Indexed: 11/09/2022] Open
Abstract
The notion of spontaneous formation of an inhomogeneous superconducting state is at the heart of most theories attempting to understand the superconducting state in the presence of strong disorder. Using scanning tunneling spectroscopy and high resolution scanning transmission electron microscopy, we experimentally demonstrate that under the competing effects of strong homogeneous disorder and superconducting correlations, the superconducting state of a conventional superconductor, NbN, spontaneously segregates into domains. Tracking these domains as a function of temperature we observe that the superconducting domains persist across the bulk superconducting transition, Tc, and disappear close to the pseudogap temperature, T*, where signatures of superconducting correlations disappear from the tunneling spectrum and the superfluid response of the system.
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Affiliation(s)
- Anand Kamlapure
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
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28
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Mondal M, Kamlapure A, Ganguli SC, Jesudasan J, Bagwe V, Benfatto L, Raychaudhuri P. Enhancement of the finite-frequency superfluid response in the pseudogap regime of strongly disordered superconducting films. Sci Rep 2013; 3:1357. [PMID: 23446946 PMCID: PMC3584313 DOI: 10.1038/srep01357] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2012] [Accepted: 02/18/2013] [Indexed: 11/30/2022] Open
Abstract
The persistence of a soft gap in the density of states above the superconducting transition temperature Tc, the pseudogap, has long been thought to be a hallmark of unconventional high-temperature superconductors. However, in the last few years this paradigm has been strongly revised by increasing experimental evidence for the emergence of a pseudogap state in strongly-disordered conventional superconductors. Nonetheless, the nature of this state, probed primarily through scanning tunneling spectroscopy (STS) measurements, remains partly elusive. Here we show that the dynamic response above Tc, obtained from the complex ac conductivity, is highly modified in the pseudogap regime of strongly disordered NbN films. Below the pseudogap temperature, T*, the superfluid stiffness acquires a strong frequency dependence associated with a marked slowing down of critical fluctuations. When translated into the length-scale of fluctuations, our results suggest a scenario of thermal phase fluctuations between superconducting domains in a strongly disordered s-wave superconductor.
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Affiliation(s)
- Mintu Mondal
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Anand Kamlapure
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | | | - John Jesudasan
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Vivas Bagwe
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Lara Benfatto
- ISC-CNR and Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185, Rome, Italy
| | - Pratap Raychaudhuri
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
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29
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Driessen EFC, Coumou PCJJ, Tromp RR, de Visser PJ, Klapwijk TM. Strongly disordered TiN and NbTiN s-wave superconductors probed by microwave electrodynamics. PHYSICAL REVIEW LETTERS 2012; 109:107003. [PMID: 23005319 DOI: 10.1103/physrevlett.109.107003] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2012] [Indexed: 06/01/2023]
Abstract
We probe the effects of strong disorder (2.4<k(F)l<8.6) on superconductivity in thin films of niobium titanium nitride and titanium nitride by measuring the microwave electrodynamics in coplanar waveguide resonators. We find a gradual evolution of the electromagnetic response with disorder, deviating from BCS theory, for both materials. This result can be understood as due to changes in the quasiparticle density of states, induced by the short elastic scattering length. The observations are consistent with a model using an effective pair breaker, dependent on the level of disorder.
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Affiliation(s)
- E F C Driessen
- Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands.
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30
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Seibold G, Benfatto L, Castellani C, Lorenzana J. Superfluid density and phase relaxation in superconductors with strong disorder. PHYSICAL REVIEW LETTERS 2012; 108:207004. [PMID: 23003178 DOI: 10.1103/physrevlett.108.207004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2011] [Revised: 02/18/2012] [Indexed: 06/01/2023]
Abstract
We consider the attractive Hubbard model with on-site disorder as a prototype of a disordered superconductor. We solve the Bogoliubov-de Gennes equations on two-dimensional finite clusters at zero temperature and evaluate the electromagnetic response to a vector potential. We find that the standard decoupling between transverse and longitudinal response does not apply in the presence of disorder. Moreover, the superfluid density is strongly reduced by the relaxation of the phase of the order parameter already at mean-field level when disorder is large. We also find that the anharmonicity of the phase fluctuations is strongly enhanced by disorder. Beyond mean field, this provides an enhancement of quantum fluctuations inducing a zero-temperature transition to a nonsuperconducting phase of disordered preformed pairs. Finally, the connection of our findings with the glassy physics for extreme dirty superconductors is discussed.
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Affiliation(s)
- G Seibold
- Institut Für Physik, BTU Cottbus, PostBox 101344, 03013 Cottbus, Germany
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31
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Sherman D, Kopnov G, Shahar D, Frydman A. Measurement of a superconducting energy gap in a homogeneously amorphous insulator. PHYSICAL REVIEW LETTERS 2012; 108:177006. [PMID: 22680898 DOI: 10.1103/physrevlett.108.177006] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2011] [Indexed: 06/01/2023]
Abstract
We present tunneling spectroscopy measurements that directly reveal the existence of a superconducting gap in the insulating state of homogenously disordered amorphous indium oxide films. Two films on both sides of the disorder induced superconductor to insulator transition show the same energy gap scale. This energy gap persists up to relatively high magnetic fields and is observed across the magnetoresistance peak typical of disordered superconductors. The results provide useful information for understanding the nature of the insulating state in the disorder induced superconductor to insulator transition.
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Affiliation(s)
- D Sherman
- The Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel
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32
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Hongisto TT, Zorin AB. Single-charge transistor based on the charge-phase duality of a superconducting nanowire circuit. PHYSICAL REVIEW LETTERS 2012; 108:097001. [PMID: 22463659 DOI: 10.1103/physrevlett.108.097001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2011] [Indexed: 05/31/2023]
Abstract
We propose a transistorlike circuit including two serially connected segments of a narrow superconducting nanowire joint by a wider segment with a capacitively coupled gate in between. This circuit is made of amorphous NbSi film and embedded in a network of on-chip Cr microresistors ensuring a sufficiently high external electromagnetic impedance. Assuming a virtual regime of quantum phase slips (QPS) in two narrow segments of the wire, leading to quantum interference of voltages on these segments, this circuit is dual to the dc SQUID. Our samples demonstrated appreciable Coulomb blockade voltage (analog of critical current of the SQUIDs) and periodic modulation of this blockade by an electrostatic gate (analog of flux modulation in the SQUIDs). The model of this QPS transistor is discussed.
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Affiliation(s)
- T T Hongisto
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
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33
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Mondal M, Kumar S, Chand M, Kamlapure A, Saraswat G, Seibold G, Benfatto L, Raychaudhuri P. Role of the vortex-core energy on the Berezinskii-Kosterlitz-Thouless transition in thin films of NbN. PHYSICAL REVIEW LETTERS 2011; 107:217003. [PMID: 22181915 DOI: 10.1103/physrevlett.107.217003] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2011] [Indexed: 05/31/2023]
Abstract
We analyze the occurrence of the Berezinskii-Kosterlitz-Thouless (BKT) transition in thin films of NbN at various film thickness, by probing the effect of vortex fluctuations on the temperature dependence of the superfluid density below T(BKT) and of the resistivity above T(BKT). By direct comparison between the experimental data and the theory, we show the crucial role played by the vortex-core energy in determining the characteristic signatures of the BKT physics, and we estimate its dependence on the disorder level. Our work provides a paradigmatic example of BKT physics in a quasi-two-dimensional superconductor.
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Affiliation(s)
- Mintu Mondal
- Tata Institute of Fundamental Research, Colaba, Mumbai, India
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