Evidence for two superconducting energy gaps in MgB(2) by point-contact spectroscopy

The Superconducting Mechanism in BiS2-Based Superconductors: A Comprehensive Review with Focus on Point-Contact Spectroscopy

The family of BiS2-based superconductors has attracted considerable attention since their discovery in 2012 due to the unique structural and electronic properties of these materials. Several experimental and theoretical studies have been performed to explore the basic properties and the underlying mechanism for superconductivity. In this review, we discuss the current understanding of pairing symmetry in BiS2-based superconductors and particularly the role of point-contact spectroscopy in unravelling the mechanism underlying the superconducting state. We also review experimental results obtained with different techniques including angle-resolved photoemission spectroscopy, scanning tunnelling spectroscopy, specific heat measurements, and nuclear magnetic resonance spectroscopy. The integration of experimental results and theoretical predictions sheds light on the complex interplay between electronic correlations, spin fluctuations, and Fermi surface topology in determining the coupling mechanism. Finally, we highlight recent advances and future directions in the field of BiS2-based superconductors, underlining the potential technological applications.

Table-top laser-based terahertz high harmonic generation spectroscopy under magnetic fields and low temperatures

We have developed a terahertz (THz) nonlinear spectrometer at low temperatures (1.5-300 K) and under high magnetic fields (up to 10 T) by combining the laser-driven table-top intense THz source with a superconducting magnet. The strong-field THz pump pulse was generated from LiNbO3 crystal using the tilted-pulse-front technique and tightly focused into the center of the magnet by an off-axis parabolic mirror and a THz lens. The electric fields at the focus can achieve 500 kV/cm with a monocycle waveform and 30 kV/cm with a multicycle waveform at 0.5 THz. The sample was mounted on a low-temperature motorized rotation stage, which enables performing the polarization dependent measurements of the third harmonic generation (THG) intensity without rotating the incident THz pulses. The magnetic field direction can be rotated using a mechanical rotator, allowing for a convenient switch between Faraday and Voigt geometry. We demonstrate the excellent performance of our instrument by conducting THG measurements in the two-band superconductor MgB2 as a function of temperature, sample azimuth angle, as well as in-plane and out-of-plane magnetic fields. The successful combination of the strong field THz source with magnetic fields enables us to study a variety of materials with magnetic-field-dependent properties of interest.

Two-gap topological superconductor LaB2 with high Tc = 30 K

Since two gap superconductivity was discovered in MgB2, research on multigap superconductors has attracted increasing attention because of its intriguing fundamental physics. In MgB2, the Mg atom donates two electrons to the borophene layer, resulting in a stronger gap from the σ band and a weaker gap from the π bond. First-principles calculations demonstrate that the two gap anisotropic superconductivity strongly enhances the transition temperature of MgB2 in comparison with that given by the isotropic model. In this work, we report a three-band (B-σ, B-π, and La-d) two-gap superconductor LaB2 with very high Tc = 30 K by solving the fully anisotropic Migdal-Eliashberg equation. Because of the σ and π-d hybridization on the Fermi surface, the electron-phonon coupling constant λ = 1.5 is significantly larger than the λ = 0.7 of MgB2. Our work paves a new route to enhance the electron-phonon coupling strength of multigap superconductors with d orbitals. On the other hand, our analysis reveals that LaB2 belongs to the weak topological semimetal category, leading to a possible topological superconductor with the highest Tc to date. Moreover, upon applying pressure and/or doping, the topology is tunable between weak and strong with Tc varying from 15 to 30 K, opening up a flexible platform for manipulating topological superconductors.

Point-Contact Spectroscopy in Bulk Samples of Electron-Doped Cuprate Superconductors

Point-contact spectroscopy was performed on bulk samples of electron-doped high temperature superconductor Nd2-xCexCuO4-δ. The samples were characterized using X-ray diffraction and scanning electron microscopy equipped with a wavelength-dispersive spectrometer and an electron backscatter diffraction detector. Samples with Ce content x = 0.15 showed the absence of spurious phases and randomly oriented grains, most of which had dimensions of approximately 220 µm2. The low-bias spectra in the tunneling regime, i.e., high-transparency interface, exhibited a gap feature at about ±5 meV and no zero-bias conductance, despite the random oriented grains investigated within our bulk samples, consistent with most of the literature data on oriented samples. High-bias conductance was also measured in order to obtain information on the properties of the barrier. A V-shape was observed in some cases, instead of the parabolic behavior expected for tunnel junctions.

Possible Eliashberg-Type Superconductivity Enhancement Effects in a Two-Band Superconductor MgB_{2} Driven by Narrow-Band THz Pulses

We study THz-driven condensate dynamics in epitaxial thin films of MgB_{2}, a prototype two-band superconductor (SC) with weak interband coupling. The temperature and excitation density dependent dynamics follow the behavior predicted by the phenomenological bottleneck model for the single-gap SC, implying adiabatic coupling between the two condensates on the ps timescale. The amplitude of the THz-driven suppression of condensate density reveals an unexpected decrease in pair-breaking efficiency with increasing temperature-unlike in the case of optical excitation. The reduced pair-breaking efficiency of narrow-band THz pulses, displaying minimum near ≈0.7  T_{c}, is attributed to THz-driven, long-lived, nonthermal quasiparticle distribution, resulting in Eliashberg-type enhancement of superconductivity, competing with pair breaking.

Non-homogeneous pairing in disordered two-orbital s-wave superconductors

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.

D-Wave Superconducting Gap Symmetry as a Model for Nb1−xMoxB2 (x = 0.25; 1.0) and WB2 Diborides

Recently, Pei et al. (National Science Review2023, nwad034, 10.1093/nsr/nwad034) reported that ambient pressure β-MoB2 (space group: R3¯m) exhibits a phase transition to α-MoB2 (space group: P6/mmm) at pressure P~70 GPa, which is a high-temperature superconductor exhibiting Tc=32 K at P~110 GPa. Although α-MoB2 has the same crystalline structure as ambient-pressure MgB2 and the superconducting critical temperatures of α-MoB2 and MgB2 are very close, the first-principles calculations show that in α-MoB2, the states near the Fermi level, εF, are dominated by the d-electrons of Mo atoms, while in MgB2, the p-orbitals of boron atomic sheets dominantly contribute to the states near the εF. Recently, Hire et al. (Phys. Rev. B2022, 106, 174515) reported that the P6/mmm-phase can be stabilized at ambient pressure in Nb1−xMoxB2 solid solutions, and that these ternary alloys exhibit Tc~8 K. Additionally, Pei et al. (Sci. China-Phys. Mech. Astron. 2022, 65, 287412) showed that compressed WB2 exhibited Tc~15 K at P~121 GPa. Here, we aimed to reveal primary differences/similarities in superconducting state in MgB2 and in its recently discovered diboride counterparts, Nb1−xMoxB2 and highly-compressed WB2. By analyzing experimental data reported for P6/mmm-phases of Nb1−xMoxB2 (x = 0.25; 1.0) and highly compressed WB2, we showed that these three phases exhibit d-wave superconductivity. We deduced 2Δm(0)kBTc=4.1±0.2 for α-MoB2, 2Δm(0)kBTc=5.3±0.1 for Nb0.75Mo0.25B2, and 2Δm(0)kBTc=4.9±0.2 for WB2. We also found that Nb0.75Mo0.25B2 exhibited high strength of nonadiabaticity, which was quantified by the ratio of TθTF=3.5, whereas MgB2, α-MoB2, and WB2 exhibited TθTF~0.3, which is similar to the TθTF in pnictides, A15 alloys, Heusler alloys, Laves phase compounds, cuprates, and highly compressed hydrides.

Prediction ofπ-electrons mediated high-temperature superconductivity in monolayer LiC12

Prediction and synthesis of two-dimensional high transition temperature (T_C) superconductors is an area of extensive research. Based on calculations of the electronic structures and lattice dynamics, we predict that graphene-like layered monolayer LiC₁₂is aπ-electrons mediated Bardeen-Cooper-Schrieffer-type superconductor. Monolayer LiC₁₂is theoretically stable and expected to be synthesized experimentally. From the band structures and the phonon dispersion spectrum, it is found that the saddle point ofπ-bonding bands induces large density of states at the Fermi energy level. There is strongly coupled between the vibration mode in the in-plane direction of the lithium atoms and theπ-electrons of carbon atoms, which induces the high-T_Csuperconductivity in LiC₁₂. TheT_Ccan reach to 41 K under an applied 10% biaxial tensile strain based on the anisotropic Eliashberg equation. Our results show that monolayer LiC₁₂is a good candidate asπ-electrons mediated electron-phonon coupling high-T_Csuperconductor.

Measurements of Surface Impedance in MgB2 in DC Magnetic Fields: Insights in Flux-Flow Resistivity

We present the multifrequency measurements of the surface resistance of spark-plasma-sintered MgB2 performed through a dielectric loaded resonator operating at 16.5 and 26.7 GHz. By normally applying magnetic fields ≤1.2 T to the sample surface, we drove it in the mixed state. By means of data-rooted analysis, we found that the sample vortex dynamics could be fully described within a single-component approach. Pinning phenomena were present and characterized by a depinning frequency smaller than the measurement ones. The multiband nature of the superconductor emerged in the flux-flow resistivity, whose field dependence could be interpreted well within theoretical models. By exploiting them, the upper critical field was extracted in the low-temperature range, which exhibited a consistent temperature trend with the values obtained at the onset of the resistive transition near Tc, and was well in line with literature data on other polycrystalline samples.

Recent Development of Ultrafast Optical Characterizations for Quantum Materials

The advent of intense ultrashort optical pulses spanning a frequency range from terahertz to the visible has opened a new era in the experimental investigation and manipulation of quantum materials. The generation of strong optical field in an ultrashort time scale enables the steering of quantum materials nonadiabatically, inducing novel phenomenon or creating new phases which may not have an equilibrium counterpart. Ultrafast time-resolved optical techniques have provided rich information and played an important role in characterization of the nonequilibrium and nonlinear properties of solid systems. Here, some of the recent progress of ultrafast optical techniques and their applications to the detection and manipulation of physical properties in selected quantum materials are reviewed. Specifically, the new development in the detection of the Higgs mode and photoinduced nonequilibrium response in the study of superconductors by time-resolved terahertz spectroscopy are discussed.

Antimicrobial Activity of MgB2 Powders Produced via Reactive Liquid Infiltration Method

We report for the first time on the antimicrobial activity of MgB2 powders produced via the Reactive Liquid Infiltration (RLI) process. Samples with MgB2 wt.% ranging from 2% to 99% were obtained and characterized, observing different levels of grain aggregation and of impurity phases. Their antimicrobial activity was tested against Staphylococcus aureus ATCC BAA 1026, Enterococcus faecalis ATCC 29212, Escherichia coli ATCC 25922, Pseudomonas aeruginosa ATCC 27853, and Candida albicans ATCC 10231. A general correlation is observed between the antibacterial activity and the MgB2 wt.%, but the sample microstructure also appears to be very important. RLI-MgB2 powders show better performances compared to commercial powders against microbial strains in the planktonic form, and their activity against biofilms is also very similar.

2D Materials and Heterostructures at Extreme Pressure

2D materials possess wide-tuning properties ranging from semiconducting and metallization to superconducting, etc., which are determined by their structure, empowering them to be appealing in optoelectronic and photovoltaic applications. Pressure is an effective and clean tool that allows modifications of the electronic structure, crystal structure, morphologies, and compositions of 2D materials through van der Waals (vdW) interaction engineering. This enables an insightful understanding of the variable vdW interaction induced structural changes, structure-property relations as well as contributes to the versatile implications of 2D materials. Here, the recent progress of high-pressure research toward 2D materials and heterostructures, involving graphene, boron nitride, transition metal dichalcogenides, 2D perovskites, black phosphorene, MXene, and covalent-organic frameworks, using diamond anvil cell is summarized. A detailed analysis of pressurized structure, phonon dynamics, superconducting, metallization, doping together with optical property is performed. Further, the pressure-induced optimized properties and potential applications as well as the vision of engineering the vdW interactions in heterostructures are highlighted. Finally, conclusions and outlook are presented on the way forward.

Multiband superconductors with degenerate excitation gaps

There is a tacit assumption that multiband superconductors are essentially the same as multigap superconductors. More precisely, it is usually assumed that the number of excitation gaps in the single-particle energy spectrum of a uniform superconductor (i.e. number of peaks in the density of states of the superconducting electrons) determines the number of contributing bands in the corresponding superconducting model. Here we demonstrate that contrary to this widely accepted viewpoint, the superconducting magnetic properties are sensitive to the number of contributing bands even when the spectral gaps are degenerate and cannot be distinguished. In particular, we find that the crossover between superconductivity types I and II-the intertype regime-is strongly affected by the difference between characteristic lengths of multiple contributing condensates. The reason for this is that condensates with diverse characteristic lengths, when coexisting in one system, interfere constructively or destructively, which results in multi-condensate magnetic phenomena regardless of the presence/absence of the multigap spectrum of a superconducting multiband material.

Spectroscopic signature of two superconducting gaps and their unusual field dependence in RuB2

Recently RuB2was shown to be a possible two-gap, type-I superconductor. Temperature dependent heat capacity measurements revealed a two-gap superconducting ground state, while magnetic field dependent magnetization measurements indicated surprizing type-I superconductivity with a very low experimental critical field (Hc) ∼120 Oe. In this paper, we report direct spectroscopic evidence of two superconducting energy gaps in RuB2. We have measured scanning tunnelling spectra exhibiting signature of two gaps on different grains of polycrystalline RuB2, possibly originating from multiple bands. Analysis of the temperature dependent tunnelling spectra revealed that the gaps from different bands evolve differently with temperature before disappearing simultaneously at a singleTc. Interestingly, our experiments also reveal that the gaps in quasiparticle density of states survive up to magnetic fields much higher than the bulkHcand they evolve smoothly with field, unlike what is expected for a type-I superconductor, indicating the existence of a 'mixed state'.

Single-gap superconductivity in Mo8Ga41

In this paper, the potential existence of two-gap superconductivity in Mo₈Ga₄₁ is addressed in detail by means of thermodynamic and spectroscopic measurements. A combination of highly sensitive bulk and surface probes, specifically ac-calorimetry and scanning tunneling spectroscopy (STS), are utilized on the same piece of crystal and reveal the presence of only one intrinsic gap in the system featuring strong electron-phonon coupling. Minute traces of additional superconducting phases detected by STS and also in the heat capacity measured in high magnetic fields on a high-quality and seemingly single-phase crystal might mimic the multigap superconductivity of Mo₈Ga₄₁ suggested recently in several studies.

Superconductivity in Pristine 2H_{a}-MoS_{2} at Ultrahigh Pressure

As a follow-up of our previous work on pressure-induced metallization of the 2H_{c}-MoS_{2} [Chi et al., Phys. Rev. Lett. 113, 036802 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.036802], here we extend pressure beyond the megabar range to seek after superconductivity via electrical transport measurements. We found that superconductivity emerges in the 2H_{a}-MoS_{2} with an onset critical temperature T_{c} of ca. 3 K at ca. 90 GPa. Upon further increasing the pressure, T_{c} is rapidly enhanced beyond 10 K and stabilized at ca. 12 K over a wide pressure range up to 220 GPa. Synchrotron x-ray diffraction measurements evidenced no further structural phase transition, decomposition, and amorphization up to 155 GPa, implying an intrinsic superconductivity in the 2H_{a}-MoS_{2}. DFT calculations suggest that the emergence of pressure-induced superconductivity is intimately linked to the emergence of a new flat Fermi pocket in the electronic structure. Our finding represents an alternative strategy for achieving superconductivity in 2H-MoS_{2} in addition to chemical intercalation and electrostatic gating.

Revisiting optical properties of MgB2 with a high-quality sample prepared by a HPCVD method

We investigated a high-quality MgB2 thin film with a thickness of ~1000 nm on an Al2O3 substrate using optical spectroscopy. We measured the reflectance spectra of the film at various temperatures both below, and above, the superconducting transition temperature, T c   [Formula: see text] 40 K. An earlier study showed that when the sample surface is exposed to air the optical properties of the surface change immediately, however, the saturated change is negligibly small in the far-infrared region. The optical conductivity spectrum in the normal state shows two (narrow and broad) Drude modes, with the narrow Drude mode being dominant in the low frequency region below 1000 cm-1. Our study, which uses a good-quality sample, provides more reliable data on the optical properties of MgB2, in a similar spectral range. The optical data is analyzed further using an extended Drude model, and the electron-phonon spectral density function, α 2 F(ω), is extracted. The spectral density function α 2 F(ω) features two peaks: a small one near 114 cm-1, and a strong peak around the 550 cm-1 where the B-B bond stretching phonon exists. Our data in the superconducting state does not show the expected energy shift of the onset of scattering associated with the α 2 F(ω) peaks.

Point contact tunneling spectroscopy apparatus for large scale mapping of surface superconducting properties

We describe the design and testing of a point contact tunneling spectroscopy device that can measure material surface superconducting properties (i.e., the superconducting gap Δ and the critical temperature T(C)) and density of states over large surface areas with size up to mm(2). The tip lateral (X,Y) motion, mounted on a (X,Y,Z) piezo-stage, was calibrated on a patterned substrate consisting of Nb lines sputtered on a gold film using both normal (Al) and superconducting (PbSn) tips at 1.5 K. The tip vertical (Z) motion control enables some adjustment of the tip-sample junction resistance that can be measured over 7 orders of magnitudes from a quasi-ohmic regime (few hundred Ω) to the tunnel regime (from tens of kΩ up to few GΩ). The low noise electronic and LabVIEW program interface are also presented. The point contact regime and the large-scale motion capabilities are of particular interest for mapping and testing the superconducting properties of macroscopic scale superconductor-based devices.

A new simple method for point contact Andreev reflection (PCAR) using a self-aligned atomic filament in transition-metal oxides

Point contact Andreev reflection (PCAR) has become a standard method for measuring the spin polarization (P) of spintronic materials due to its unique simplicity and the firm physical ground, but it is still challenging to achieve a clean point contact between a superconductor (SC) and a metal (N) for implementing PCAR. In this work, we suggest a much simpler method for PCAR measurement, where a point contact between SC and N is provided by a metallic filament in a transition-metal oxide generated by electrical bias. This method has been successfully demonstrated using a structure composed of Nb/NiO/Pt, where P of the Ni filament was estimated to be about 40%, consistent with the known value of the bulk Ni. In addition, we investigated the dependence of the conductance spectrum on the measurement temperature and the magnetic field. We found that the superconductivity is not fully suppressed until 9 T far above the critical field of Nb, which is associated with the nm-sized constriction of our SC/N junction, much smaller than the coherence length of the SC.

Multi-channel Andreev reflection in Co-W nanocontacts fabricated using focused electron/ion beam induced deposition

We report multi-channel electron transport in nano-contacts fabricated using focused electron beam induced deposited (FEBID) cobalt and focused ion beam induced deposited (FIBID) tungsten. Anomalous Andreev reflection (AR) effect is observed to which the conventional Blonder-Tinkham-Klapwijk (BTK) fit cannot be applied. In specific, we have observed multiple number of shoulders near the AR peak, whose origin is unknown in literature. We explain this effect based on a simple model that takes into account the material properties of the FIBID grown W superconductor, as well as the specific interface properties that are an outcome of using FEBID/FIBID as a fabrication technique. We show that numerical calculations using the BTK approximation based on the consideration of multiple channels generate similar shoulders as we observed in the AR experiments. Electrical measurements and x-ray photoemission spectroscopy carried out on FIBID W deposits puts additional evidence towards multi-channel current transport occuring at the interface of the nanocontacts.

Ground state, collective mode, phase soliton and vortex in multiband superconductors

This article reviews theoretical and experimental work on the novel physics in multiband superconductors. Multiband superconductors are characterized by multiple superconducting energy gaps in different bands with interaction between Cooper pairs in these bands. The discovery of prominent multiband superconductors MgB2 and later iron-based superconductors, has triggered enormous interest in multiband superconductors. The most recently discovered superconductors exhibit multiband features. The multiband superconductors possess novel properties that are not shared with their single-band counterpart. Examples include: the time-reversal symmetry broken state in multiband superconductors with frustrated interband couplings; the collective oscillation of number of Cooper pairs between different bands, known as the Leggett mode; and the phase soliton and fractional vortex, which are the main focus of this review. This review presents a survey of a wide range of theoretical exploratory and experimental investigations of novel physics in multiband superconductors. A vast amount of information derived from these studies is shown to highlight unusual and unique properties of multiband superconductors and to reveal the challenges and opportunities in the research on the multiband superconductivity.

Spear-anvil point-contact spectroscopy in pulsed magnetic fields

We describe a new design and experimental technique for point-contact spectroscopy in non-destructive pulsed magnetic fields up to 70 T. Point-contact spectroscopy uses a quasi-dc four-point measurement of the current and voltage across a spear-anvil point-contact. The contact resistance could be adjusted over three orders of magnitude by a built-in fine pitch threaded screw. The first measurements using this set-up were performed on both single-crystalline and exfoliated graphite samples in a 150 ms, pulse length 70 T coil at 4.2 K and reproduced the well known point-contact spectrum of graphite and showed evidence for a developing high field excitation above 35 T, the onset field of the charge-density wave instability in graphite.

Superconductivity with extremely large upper critical fields in Nb2Pd0.81S5

Here, we report the discovery of superconductivity in a new transition metal-chalcogenide compound, i.e. Nb2Pd0.81S5, with a transition temperature Tc is approximately equal to 6.6 K. Despite its relatively low Tc, it displays remarkably high and anisotropic superconducting upper critical fields, e.g. μ0Hc2 (T → 0 K) > 37 T for fields applied along the crystallographic b-axis. For a field applied perpendicularly to the b-axis, μ0Hc2 shows a linear dependence in temperature which coupled to a temperature-dependent anisotropy of the upper critical fields, suggests that Nb2Pd0.81S5 is a multi-band superconductor. This is consistent with band structure calculations which reveal nearly cylindrical and quasi-one-dimensional Fermi surface sheets having hole and electron character, respectively. The static spin susceptibility as calculated through the random phase approximation, reveals strong peaks suggesting proximity to a magnetic state and therefore the possibility of unconventional superconductivity.

Effect of two length scales on the properties of MgB(2) for arbitrary applied magnetic field

Experiments carried out on the intermetallic superconducting material MgB(2) have shown anomalous magnetic field dependence of upper critical field, small angle neutron scattering form factor, specific heat, critical current etc. Similarly, scanning tunnelling microscopy (STM) experiments on vortex structures have shown unusually large vortex core size and two different magnetic and spatial field scales. Also, whereas the specific heat measurements and isotope shift experiments have shown Bardeen-Cooper-Schrieffer-like (BCS-like) behaviour, the temperature dependences of the penetration depth experiments have shown non-BCS-like behaviour. These anomalous behaviours have been attributed to the multiband superconductivity of this material and the nature of the local spatial behaviour of the magnetic induction and the order parameter components having two length scales. We report an analytical investigation of the effect of two length scales on the temperature and the applied magnetic field dependence of several properties of MgB(2), such as, the penetration depth, single vortex and vortex lattice structure, vortex core radius, reversible magnetization, critical current, small angle neutron scattering form factor and the shear modulus of the vortex lattice within the framework of two-order parameter Ginzburg-Landau theory. We solve the corresponding nonlinear Ginzburg-Landau equations numerically exactly using an iterative method for arbitrary applied field H(c1) < H < H(c2), the Ginzburg-Landau parameter and vortex lattice symmetry. This enables us to compute the local spatial behaviour of the magnetic induction and the order parameters accurately for arbitrary applied field and a wide range of temperature. Comparison of the analytical results with experiments on MgB(2) gives very good agreement.

Interplay between magnetism and superconductivity and the appearance of a second superconducting transition in α-FeSe at high pressure

We synthesized tetragonal α-FeSe by melting a powder mixture of iron and selenium at high pressure. Subsequent annealing at normal pressure results in removing traces of hexagonal β-FeSe, formation of a rather sharp transition to a superconducting state at T(c)∼7 K, and the appearance of a magnetic transition near T(M) = 120 K. Resistivity and ac-susceptibility were measured on the annealed sample at hydrostatic pressure up to 4.5 GPa. A magnetic transition visible in ac-susceptibility shifts down under pressure and a resistive anomaly typical for a spin density wave (SDW) antiferromagnetic transition develops near the susceptibility anomaly. T(c), determined by the appearance of a diamagnetic response in susceptibility, increases linearly under pressure at a rate dT(c)/dP = 3.5 K GPa(-1). Below 1.5 GPa, the resistive superconducting transition is sharp, the width of transition does not change with pressure and, T(c), determined by a peak in dρ/dT, increases at a rate ∼3.5 K GPa(-1). At higher pressure, a giant broadening of the resistive transition develops. This effect cannot be explained by possible pressure gradients in the sample and is inherent to α-FeSe. The dependences dρ(T)/dT show a signature for a second peak above 3 GPa which is indicative of the appearance of another superconducting state in α-FeSe at high pressure. We argue that this second superconducting phase coexists with SDW antiferromagnetism in a partial volume fraction and originates from pairing of charge carriers from other sheets of the Fermi surface.

Type-1.5 superconductivity

We demonstrate the existence of a novel superconducting state in high quality two-component MgB2 single crystalline superconductors where a unique combination of both type-1 (lambda{1}/xi{1}<1/sqrt[2]) and type-2 (lambda{2}/xi{2}>1/sqrt[2]) superconductor conditions is realized for the two components of the order parameter. This condition leads to a vortex-vortex interaction attractive at long distances and repulsive at short distances, which stabilizes unconventional stripe- and gossamerlike vortex patterns that we have visualized in this type-1.5 superconductor using Bitter decoration and also reproduced in numerical simulations.

Superconducting density of states and vortex cores of 2H-NbS2

Scanning tunneling microscopy and spectroscopy measurements in the superconducting dichalcogenide 2H-NbS2 show a peculiar superconducting density of states with two well-defined features at 0.97 and 0.53 meV, located, respectively, above and below the value for the superconducting gap expected from the single band s-wave BCS model (Delta=1.76k_(B)T_(c)=0.9 meV). Both features have a continuous temperature evolution and disappear at T_(c)=5.7 K. Moreover, we observe the hexagonal vortex lattice with radially symmetric vortices and a well-developed localized state at the vortex cores. The sixfold star shape characteristic of the vortex lattice of the compound 2H-NbSe2 is, together with the charge density wave order, absent in 2H-NbS2.

Observation of Leggett's collective mode in a multiband MgB2 superconductor

We report observation of Leggett's collective mode in a multiband MgB2 superconductor with Tc=39 K arising from the fluctuations in the relative phase between two superconducting condensates. The novel mode is observed by Raman spectroscopy at 9.4 meV in the fully symmetric scattering channel. The observed mode frequency is consistent with theoretical considerations based on first-principles computations.

Analysis of H(c2)(θ,T) for Mg(B(1-x)C(x))(2) single crystals by using the dirty two-gap model

To understand the effect of carbon doping on the superconductivity in MgB(2), we obtained the angle- and temperature-dependent upper critical fields [H(c2)(θ) and H(c2)(T)] for Mg(B(1-x)C(x))(2) single crystals (x = 0.06 and 0.1) from resistivity measurements while varying the temperature, the field, and the direction of the field. The detailed values of the diffusivity for two different directions for each σ-band and π-band were obtained to explain both the temperature- and the angle-dependent H(c2) by using the dirty-limit two-gap model. The induced impurity scattering of the σ-band and the π-band for both the ab-plane and the c-direction is studied.

Anisotropy of the Sommerfeld coefficient in magnesium diboride single crystals

The anisotropic field dependence of the Sommerfeld coefficient gamma has been measured down to B-->0 by combining specific heat and Hall probe magnetization measurements in MgB2 single crystals. We find that gamma(B,theta) is the sum of two contributions arising from the sigma and pi band, respectively. We show that gammasigma(B,theta)=B/Bc2(theta) where Bc2(theta)=Bc2ab/sqrt[sin2theta+Gamma2cos2theta] with Gamma approximately 5.4 (theta being the angle between the applied field and the c axis) and gammapi(B,theta)=gammapi(B)=B/Bpi(B). The "critical field" of the pi band Bpi is fully isotropic but field dependent increasing from approximately 0.25 T for B< or =0.1 T up to 3 T approximately Bc2c for B-->3 T. Because of the coupling of the two bands, superconductivity survives in the pi band up to 3 T but is totally destroyed above for any orientation of the field.

Observation of the crossover from two-gap to single-gap superconductivity through specific heat measurements in neutron-irradiated MgB2

We report specific heat measurements on neutron-irradiated MgB2 samples, for which the critical temperature is lowered to 8.7 K, but the superconducting transition remains extremely sharp, indicative of a defect structure extremely homogeneous. Our results evidence the presence of two superconducting gaps in the temperature range above 21 K, while single-gap superconductivity is well established as a bulk property, not associated with local disorder fluctuations, when Tc decreases to 11 K.

Spectroscopic evidence for multiple order parameter components in the heavy fermion superconductor CeCoIn5

Point-contact spectroscopy was performed on single crystals of the heavy-fermion superconductor CeCoIn(5) between 150 mK and 2.5 K. A pulsed measurement technique ensured minimal Joule heating over a wide voltage range. The spectra show Andreev-reflection characteristics with multiple structures which depend on junction impedance. Spectral analysis using the generalized Blonder-Tinkham-Klapwijk formalism for d-wave pairing revealed two coexisting order parameter components with amplitudes Delta(1) = 0.95 +/- 0.15 meV and Delta(2) = 2.4 +/- 0.3 meV, which evolve differently with temperature. Our observations indicate a highly unconventional pairing mechanism, possibly involving multiple bands.

Superconducting properties of MgB2 from first principles

Solid MgB(2) has rather interesting and technologically important properties, such as a very high superconducting transition temperature. Focusing on this compound, we report the first nontrivial application of a novel density-functional-type theory for superconductors, recently proposed by the authors. Without invoking any adjustable parameters, we obtain the transition temperature, the gaps, and the specific heat of MgB(2) in very good agreement with experiment. Moreover, our calculations show how the Coulomb interaction acts differently on sigma and pi states, thereby stabilizing the observed superconducting phase.

Anisotropies of the lower and upper critical fields in MgB2 single crystals

The temperature dependence of the upper (H(c2)) and lower (H(c1)) critical fields has been deduced from Hall probe magnetization measurements of high quality MgB2 single crystals along the two main crystallographic directions. We show that Gamma(H(c2))=H(c2 axially ab)/H(c2 axially c) and Gamma(H(c1))=H(c1 axially c)/H(c1 axially ab) differ significantly at low temperature (being approximately 5 and approximately 1, respectively) and have opposite temperature dependencies. We suggest that MgB2 can be described by a single field dependent anisotropy parameter gamma(H) (=lambda(c)/lambda(ab)=xi(ab)/xi(c)) that increases from Gamma(H(c1)) at low field to Gamma(H(c2)) at high field.

Time-resolved photoexcitation of the superconducting two-gap state in MgB2 thin films

Femtosecond pump-probe studies show that carrier dynamics in MgB2 films is governed by the sub-ps electron-phonon (e-ph) relaxation present at all temperatures, the few-ps e-ph process well pronounced below 70 K, and the sub-ns superconducting relaxation below T(c). The amplitude of the superconducting component versus temperature follows the superposition of the isotropic dirty gap and the three-dimensional pi gap dependences, closing at two different T(c) values. The time constant of the few-ps relaxation exhibits a double divergence at temperatures corresponding to the T(c)'s of the two gaps.

Fermi surface topology and the upper critical field in two-band superconductors: application to MgB2

Recent measurements of the anisotropy of the upper critical field B(c2) on MgB2 single crystals have shown a puzzling strong temperature dependence. Here, we present a calculation of the upper critical field based on a detailed modeling of band structure calculations that takes into account both the unusual Fermi surface topology and the two gap nature of the superconducting order parameter. Our results show that the strong temperature dependence of the B(c2) anisotropy can be understood as an interplay of the dominating gap on the sigma band, which possesses a small c-axis component of the Fermi velocity, with the induced superconductivity on the pi-band possessing a large c-axis component of the Fermi velocity. We provide analytic formulas for the anisotropy ratio at T=0 and T=T(c) and quantitatively predict the distortion of the vortex lattice based on our calculations.

Search for E(2g) phonon modes in MgB2 single crystals by point-contact spectroscopy

The electron-phonon interaction in magnesium diboride MgB2 single crystals is investigated by point-contact (PC) spectroscopy. For the first time the electron coupling with E(2g) phonon modes is resolved in the PC spectra. The correlation between intensity of the extremely broad E(2g) modes in the PC spectra and value of the superconducting gap is established. Our observations favor current theoretical models for electron-phonon mediated superconductivity in MgB2, and they better match the harmonic phonon model.

Mixed state of a dirty two-band superconductor: application to MgB2

We investigate the vortex state in a two-band superconductor with strong intraband and weak interband electronic scattering rates. Coupled Usadel equations are solved numerically, and the distributions of the pair potentials and local densities of states are calculated for two bands at different values of magnetic fields. The existence of two distinct length scales corresponding to different bands is demonstrated. The results provide qualitative interpretation of recent scanning tunneling microscopy experiments on vortex structure imaging in MgB2.

The origin of multiple superconducting gaps in MgB2

Magnesium diboride, MgB2, has the highest transition temperature (T(c) = 39 K) of the known metallic superconductors. Whether the anomalously high T(c) can be described within the conventional BCS (Bardeen-Cooper-Schrieffer) framework has been debated. The key to understanding superconductivity lies with the 'superconducting energy gap' associated with the formation of the superconducting pairs. Recently, the existence of two kinds of superconducting gaps in MgB2 has been suggested by several experiments; this is in contrast to both conventional and high-T(c) superconductors. A clear demonstration of two gaps has not yet been made because the previous experiments lacked the ability to resolve the momentum of the superconducting electrons. Here we report direct experimental evidence for the two-band superconductivity in MgB2, by separately observing the superconducting gaps of the sigma and pi bands (as well as a surface band). The gaps have distinctly different sizes, which unambiguously establishes MgB2 as a two-gap superconductor.

Specific heat of single crystal MgB2: a two-band superconductor with two different anisotropies

Heat-capacity measurements of a 39 microg MgB2 single crystal in fields up to 14 T and below 3 K allow the determination of the low-temperature linear term of the specific heat, its field dependence, and its anisotropy. Our results are compatible with two-band superconductivity, the band carrying the smaller gap being isotropic, that carrying the larger gap having an anisotropy of approximately 5. Three different upper critical fields are thus needed to describe the superconducting state of MgB2.

Direct evidence for two-band superconductivity in MgB2 single crystals from directional point-contact spectroscopy in magnetic fields

We present the results of the first directional point-contact spectroscopy experiments in high-quality MgB2 single crystals. Because of the directionality of the current injection into the samples, the application of a magnetic field allowed us to separate the contributions of the sigma and pi bands to the total conductance of our point contacts. By using this technique, we were able to obtain the temperature dependency of each gap independent of the other. The consequent, strong reduction of the error on the value of the gap amplitude as a function of temperature allows a stricter test of the predictions of the two-band model for MgB2.

Two-band superconductivity in MgB2

The study of the anisotropic superconductor MgB2 using a combination of scanning tunneling microscopy and spectroscopy reveals two distinct energy gaps at Delta(1)=2.3 meV and Delta(2)=7.1 meV at 4.2 K. Different spectral weights of the partial superconducting density of states are a reflection of different tunneling directions in this multiband system. Temperature evolution of the tunneling spectra follows the BCS scenario [Phys. Rev. Lett. 3, 552 (1959)]] with both gaps vanishing at the bulk T(c). The data confirm the importance of Fermi-surface sheet dependent superconductivity in MgB2 proposed in the multigap model by Liu et al. [Phys. Rev. Lett. 87, 087005 (2001)]].

Vortex imaging in the pi band of magnesium diboride

We report scanning tunneling spectroscopy imaging of the vortex lattice in single crystalline MgB2. By tunneling parallel to the c axis, a single superconducting gap (Delta=2.2 meV) associated with the pi band is observed. The vortices in the pi band have a large core size compared to estimates based on H(c2) and show an absence of localized states in the core. Furthermore, superconductivity between the vortices is rapidly suppressed by an applied field. These results suggest that superconductivity in the pi band is, at least partially, induced by the intrinsically superconducting sigma band.

Magneto-optical study of the superconducting gap of MgB(2) single crystals

We present magneto-optical reflectivity results in the basal plane of the hexagonal MgB(2). The data were collected on a mosaic of MgB(2) single crystals with T(c)=38 K from the ultraviolet down to the far infrared as a function of temperature and magnetic field oriented along the c axis. In the far infrared, there is a clear signature of the superconducting gap with a gap ratio 2 Delta/k(B)T(c) approximately 1.2, well below the weak-coupling value. The gap is suppressed in an external magnetic field, which is a function of temperature. We extract the upper critical field H(c2) along the c axis. The temperature dependence of H(c2) is compatible with the Helfand-Werthamer behavior.

The origin of the anomalous superconducting properties of MgB(2)

Magnesium diboride differs from ordinary metallic superconductors in several important ways, including the failure of conventional models to predict accurately its unusually high transition temperature, the effects of isotope substitution on the critical transition temperature, and its anomalous specific heat. A detailed examination of the energy associated with the formation of charge-carrying pairs, referred to as the 'superconducting energy gap', should clarify why MgB(2) is different. Some early experimental studies have indicated that MgB(2) has multiple gaps, but past theoretical studies have not explained from first principles the origin of these gaps and their effects. Here we report an ab initio calculation of the superconducting gaps in MgB(2) and their effects on measurable quantities. An important feature is that the electronic states dominated by orbitals in the boron plane couple strongly to specific phonon modes, making pair formation favourable. This explains the high transition temperature, the anomalous structure in the specific heat, and the existence of multiple gaps in this material. Our analysis suggests comparable or higher transition temperatures may result in layered materials based on B, C and N with partially filled planar orbitals.

Vortices with fractional flux in two-gap superconductors and in extended faddeev model

We discuss linear topological defects allowed in two-gap superconductors and equivalent extended Faddeev model. We show that, in these systems, there exist vortices which carry an arbitrary fraction of magnetic flux quantum. Besides that, we discuss topological defects which do not carry magnetic flux and describe features of ordinary one-magnetic-flux-quantum vortices in the two-gap system. The results could be relevant for the newly discovered two-band superconductor MgB2.

de Haas-van Alphen effect in single crystal MgB2

We report observations of quantum oscillations in single crystals of the high temperature superconductor MgB2. Three de Haas-van Alphen frequencies are clearly resolved. Comparison with band structure calculations strongly suggests that two of these come from a single warped Fermi surface tube along the c direction, and that the third arises from cylindrical sections of an in-plane honeycomb network. The measured values of the effective mass range from (0.44-0.68)m(e). By comparing these to calculated band masses, we find that the electron-phonon coupling strength lambda is a factor of approximately 3 larger for the c-axis tube orbits than for the in-plane network orbit, in accord with recent microscopic calculations.