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

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.

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.

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.

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'.

Ultrafast Hot Phonon Dynamics in MgB_{2} Driven by Anisotropic Electron-Phonon Coupling

The zone-center E_{2g} modes play a crucial role in MgB_{2}, controlling the scattering mechanisms in the normal state as well the superconducting pairing. Here, we demonstrate via first-principles quantum-field theory calculations that, due to the anisotropic electron-phonon interaction, a hot-phonon regime where the E_{2g} phonons can achieve significantly larger effective populations than other modes, is triggered in MgB_{2} by the interaction with an ultrashort laser pulse. Spectral signatures of this scenario in ultrafast pump-probe Raman spectroscopy are discussed in detail, revealing also a fundamental role of nonadiabatic processes in the optical features of the E_{2g} mode.

Relation between Crystal Structure and Transition Temperature of Superconducting Metals and Alloys

Using the Roeser–Huber equation, which was originally developed for high temperature superconductors (HTSc) (H. Roeser et al., Acta Astronautica 62 (2008) 733), we present a calculation of the superconducting transition temperatures, T c , of some elements with fcc unit cells (Pb, Al), some elements with bcc unit cells (Nb, V), Sn with a tetragonal unit cell and several simple metallic alloys (NbN, NbTi, the A15 compounds and MgB 2 ). All calculations used only the crystallographic information and available data of the electronic configuration of the constituents. The model itself is based on viewing superconductivity as a resonance effect, and the superconducting charge carriers moving through the crystal interact with a typical crystal distance, x. It is found that all calculated T c -data fall within a narrow error margin on a straight line when plotting ( 2 x ) 2 vs. 1 / T c like in the case for HTSc. Furthermore, we discuss the problems when obtaining data for T c from the literature or from experiments, which are needed for comparison with the calculated data. The T c -data presented here agree reasonably well with the literature data.

Point contact Andreev reflection studies of a non-centro symmetric superconductor Re6Zr

Re₆Zr, a non-centrosymmetric superconductor is an interesting system as recent experimental evidence suggests that the superconducting state breaks time reversal symmetry. This implies a mixing of spin singlet-triplet states leading to a complex order parameter in this system. Here, we report point contact Andreev Reflection (PCAR) measurements on a single crystal of Re₆Zr (superconducting transition temperature (T_c) = 6.78 K). We observe multiple gap features in the PCAR spectra which depends on the type of tip and contact. Spectral features appear at voltages 1.0 ± 0.1 mV, 0.75 ± 0.05 mV and 0.45 ± 0.1 mV suggesting that there are at least more than one band contributing to superconductivity. However, strong surface inter-band scattering is possibly responsible for the uncertainty in observing them together distinctly in a single contact in the PCAR measurements. Interestingly, the bulk gap (Δ  = 1.95k_BT_c = 1.1 meV) is occasionally observed in PCAR spectra, mostly with ferromagnetic tips. The gap features associated with the other two smaller gaps disappear at the bulk T_c. In addition, no anisotropy in the upper critical field was observed. Our results suggest an unconventional superconducting order in this compound: Multiband singlet states dominated by inter-band pairing which break the time reversal symmetry or singlet mixed with triplet states.

Interband Electron Pairing for Superconductivity from the Breakdown of the Born-Oppenheimer Approximation

The origin of interband electron pairing, responsible for enhancing superconductivity, and the factors controlling its strength were examined. We show that interband electron pairing is a natural consequence of breaking down the Born-Oppenheimer approximation during electron-phonon interactions. Its strength is determined by the pair-state excitations around the Fermi surfaces that take place to form a superconducting state. Fermi surfaces favorable for the pairing were found, and the implications of this observation are discussed.

Critical analysis of soft point contact Andreev reflection spectra between superconducting films and pressed In

We present a critical analysis of an alternative technique of point contact Andreev reflection (PCAR) spectroscopy used to extract energy resolved information of superconductors which is based on making 'soft-contacts' between superconductors and indium. This technique is not sensitive to mechanical vibrations and hence can be used in a cryogen free platform increasing its accessibility to users having no access to cryogenic liquids. Through our experiments on large number of superconducting films we show that the PCAR spectra below the T _c of In show sub-harmonic gap structures consistent with the theory of multiple Andreev reflection (MAR) and a zero bias conductance (ZBC) anomaly associated with the Josephson supercurrent. Furthermore, we demonstrate that large contact resistance with low transparency ballistic contacts in the PCAR regime are required to obtain reliable spectroscopic data. One limitation of the technique arises for low contact resistance junctions where the superconducting proximity effect (SPE) reduces the value of the superconducting energy gap.

First-Principles Calculation of the Real-Space Order Parameter and Condensation Energy Density in Phonon-Mediated Superconductors

We show that the superconducting order parameter and condensation energy density of phonon-mediated superconductors can be calculated in real space from first principles density functional theory for superconductors. This method highlights the connection between the chemical bonding structure and the superconducting condensation and reveals new and interesting properties of superconducting materials. Understanding this connection is essential to describe nanostructured superconducting systems where the usual reciprocal space analysis hides the basic physical mechanism. In a first application we present results for MgB2, CaC6 and hole-doped graphane.

Possible s±-wave pairing evidenced by midgap surface bound states in Fe-pnictide superconductors

A phenomenological theory of tunneling spectroscopy for Fe-pnictide superconductors is developed by taking into consideration asymmetric interface scattering between particle and holes. It is shown that, consistent with anti-phase s(±)-wave pairing, appreciable zero-energy surface bound states exist on the [100] surface of Fe-pnictide superconductors. However, in contrast to the [110] bound states in d-wave cuprate superconductors, these bound states arise as a result of non-conservation of momentum perpendicular to the interface for tunneling electrons and the s(±) pairing, and hence they can only exist in a small window (~ ± 6°) in the orientation of edges near the [100] direction. Our results explain why a zero-bias conductance peak is often observed in tunneling spectroscopy and why, when it disappears, two coherent peaks show up. These results provide unambiguous signals to test for possible s(±)-wave pairing in Fe-pnictide superconductors.

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.

Andreev spectra and subgap bound states in multiband superconductors

A theory of Andreev conductance is formulated for junctions involving normal metals (N) and multiband superconductors (S) and applied to the case of superconductors with nodeless extended s(+/-)-wave order parameter symmetry, as possibly realized in the recently discovered ferropnictides. We find qualitative differences from tunneling into s-wave or d-wave superconductors that may help to identify such a state. First, interband interference leads to a suppression of Andreev reflection in the case of a highly transparent N/S interface and to a current deficit in the tunneling regime. Second, surface bound states may appear, both at zero and at nonzero energies.

Fully band-resolved scattering rate in MgB2 revealed by the nonlinear hall effect and magnetoresistance measurements

We have measured the normal state temperature dependence of the Hall effect and magnetoresistance in epitaxial MgB2 thin films with variable disorders characterized by the residual resistance ratio RRR ranging from 4.0 to 33.3. A strong nonlinearity of the Hall effect and magnetoresistance have been found in clean samples, and they decrease gradually with the increase of disorders or temperature. By fitting the data to the theoretical model based on the Boltzmann equation and ab initio calculations for a four-band system, for the first time, we derived the scattering rates of these four bands at different temperatures and magnitude of disorders. Our method provides a unique way to derive these important parameters in multiband systems.

Evidence for gap anisotropy in CaC6 from directional point-contact spectroscopy

We present the first results of directional point-contact spectroscopy in high-quality CaC6 samples both along the ab plane and in the c-axis direction. The superconducting order parameter Delta(0), obtained by fitting the Andreev-reflection (AR) conductance curves at temperatures down to 400 mK with the single-band 3D Blonder-Tinkham-Klapwijk model, presents two different distributions in the two directions of the main current injection, peaked at 1.35 and 1.71 meV, respectively. By ab initio calculations of the AR conductance spectra, we show that the experimental results are in good agreement with the recent predictions of gap anisotropy in CaC6.

Physical properties of the noncentrosymmetric superconductor Mg10Ir19B16

Specific heat, electrical resistivity, and magnetic susceptibility measurements on a high quality sample of Mg10Ir19B16 provide a self-consistent determination of its superconducting properties. They indicate that Mg10Ir19B16 is a type-II superconductor [T{C}=4.45 K, kappa(0) approximately 20], with an electron-phonon coupling constant lambda{ep}=0.66. An analysis of the T-dependent specific heat shows that superconducting properties are dominated by an s-wave gap (Delta=0.7 meV). Point contact tunneling data provide evidence for multiple superconducting gaps, as expected from strong asymmetric spin-orbit coupling.

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.

Experimental evidence for two gaps in the high-temperature La1.83Sr0.17CuO4 superconductor

The in-plane magnetic field penetration depth (lambda(ab)) in single-crystal La1.83Sr0.17CuO4 was investigated by muon-spin rotation (muSR). The temperature dependence of lambda(ab)(-2) has an inflection point around 10-15 K, suggesting the presence of two superconducting gaps: a large gap (Delta(1)(d)) with d-wave and a small gap (Delta(2)(s)) with s-wave symmetry. The zero-temperature values of the gaps at mu(0)H=0.02 T were found to be Delta(1)(d)(0)=8.2(1) meV and Delta(2)(s)(0)=1.57(8) meV.

Effect of magnetic impurities in a two-band superconductor: a point-contact study of mn-substituted single crystals

We present the first results of directional point-contact measurements in Mg1-xMnxB2 single crystals, with x up to 0.015 and bulk Tc down to 13.3 K. The order parameters Deltasigma and Deltapi were obtained by fitting the conductance curves with the two-band Blonder-Tinkham-Klapwijk model. BothDeltapi and Deltasigma decrease with the critical temperature of the junctions TAC, but remain clearly distinct up to the highest Mn content. Once analyzed within the Eliashberg theory, the results indicate that spin-flip scattering is dominant in the sigma band, as also confirmed by first-principles band-structure calculations.

Field dependence of the vortex core size in a multiband superconductor

The magnetic field dependence of the vortex core size in the multiband superconductor NbSe2 has been determined from muon spin rotation measurements. The spatially extended nature of the quasiparticle core states associated with the smaller gap leads to a rapid field-induced shrinkage of the core size at low fields, while the more tightly bound nature of the states associated with the larger gap leads to a field-independent core size for fields greater than 4 kOe. A simple model is proposed for the density of delocalized core states that establishes a direct relationship between the field-induced reduction of the vortex core size and the corresponding enhancement of the electronic thermal conductivity. We show that this model accurately describes both NbSe2 and the single-band superconductor V3Si.

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.

Effect of two gaps on the flux-lattice internal field distribution: evidence of two length scales in Mg(1-x)AlxB2 from muSR

We have measured the transverse field muon spin precession in the flux-lattice (FL) state of the two-gap superconductor MgB2 and of the electron doped compounds Mg(1-x)AlxB2 in magnetic fields up to 2.8 T. We show the effect of the two gaps on the internal field distribution in the FL, from which we determine two coherence length parameters and the doping dependence of the London penetration depth. This is an independent determination of the complex vortex structure already suggested by the STM observation of large vortices in a MgB2 single crystal. Our data agree quantitatively with STM and we thus validate a new phenomenological model for the internal fields.

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.

Anomalous coherence peak in the microwave conductivity of c-axis oriented MgB2 thin films

The temperature dependence of the real part of the microwave complex conductivity at 17.9 GHz obtained from surface impedance measurements of two c-axis oriented MgB2 thin films reveals a pronounced maximum at a temperature around 0.6 times the critical temperature. Calculations in the frame of a two-band model based on Bardeen-Cooper-Schrieffer (BCS) theory suggest that this maximum corresponds to an anomalous coherence peak resembling the two-gap nature of MgB2. Our model assumes there is no interband impurity scattering and a weak interband pairing interaction, as suggested by band structure calculations. In addition, the observation of a coherence peak indicates that the pi band is in the dirty limit and dominates the total conductivity of our films.

Effects of two-band superconductivity on the flux-line lattice in magnesium diboride

We present neutron scattering from the flux line lattice (FLL) in MgB2. Between 0.5 and 0.9 T the FLL undergoes a 30 degrees reorientation, and simultaneously the scattered intensity falls sharply consistent with the weaker superconducting pi band being suppressed with increasing field. We speculate that the pi and sigma bands favor different FLL orientations, and that the reorientation is driven by the suppression of the pi band. When the c axis of the crystal is rotated 45 degrees to the applied field the penetration depth anisotropy could be measured, and rises both as a function of applied field and temperature.

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.