Two-gap Superconductivity Research Articles

Experimental investigation on the crystal structure and superconductivity of germanium-intercalated 2H–NbSe2 system

We report the structural and superconducting properties of Ge-intercalated 2H–NbSe2 polycrystals. GexNbSe2 samples with nominal 0 ≤ x ≤ 0.1 crystallize in the space group P63/mmc with Ge disorderedly occupying the interlayer Se6 octahedral interstices. Superconducting critical temperature Tc monotonically decreases from 7.2 K in NbSe2 to 4.9 K in Ge0.1NbSe2. Studies on resistivity, magnetization and specific heat derive the superconducting- and normal-state parameters, indicating that the suppression of the two-gap superconductivity is mostly caused by the lowered electron-phonon coupling parameter λe-p and density of states at the Fermi level N(EF). Surprisingly, the upper critical field Hc2 and irreversible field Hirr of the low Ge-level samples are enhanced compared with those of the undoped one, which may ascribe to the electron scattering and vortex pinning by nonmagnetic Ge. This study suggests the feasibility for improving high-field performance by slight impurity doping and advances the understanding of superconductivity in transition-metal dichalcogenides.

Two-Gap Superconductivity and the Decisive Role of Rare-Earth d Electrons in Infinite-Layer Nickelates.

We present a theoretical prediction of a phonon-mediated two-gap superconductivity in infinite-layer nickelates Nd_{1-x}Sr_{x}NiO_{2} by performing abinitio GW and GW perturbation theory calculations. Electron GW self-energy effects significantly alter the characters of the two-band Fermi surface and enhance the electron-phonon coupling, compared with results based on density functional theory. Solutions of the fully k-dependent anisotropic Eliashberg equations yield two dominant s-wave superconducting gaps-a large gap on a band of rare-earth Nd d and interstitial orbital characters and a small gap on a band of transition-metal Ni d character. Increasing hole doping induces a non-rigid-band response in the electronic structure, leading to a rapid drop of the superconducting T_{c} in the overdoped regime in agreement with experiments.

Nonequilibrium Effects in Ballistic Point Contacts Ta–Cu and 2H–NbSe2–Cu: Two-Gap Superconductivity in 2H–NbSe2

Nonequilibrium Effects in Ballistic Point Contacts Ta–Cu and 2H–NbSe2–Cu: Two-Gap Superconductivity in 2H–NbSe2

Superconductivity at 215 K in H3SM (M=Ne, Ar, Kr, Xe, Rn) ternary hydrides

The recent discovery of H3S attracts great attention due to the confirmed superconducting critical temperature (Tc) of 203 K. Following the previous structure prediction of H3SXe superconductors, the anisotropic Migdal-Eliashberg (ME) theory is carried out to study the superconducting properties of H3SM (M=Ne, Ar, Kr, Xe, Rn) under pressure. We identify a new H3SRn ternary hydride, with Tc of about 215 K under 240 GPa, belonging to two-gap superconductors with multi-band. H3SNe exhibits remarkable superconductivity with an anomalously low stabilization pressure (Ps) of about 60 GPa. With the motivation of discovering superconductors at the lowest possible pressure, the chemical pressure is quantified based on the same volume-strain effect of physical pressure and chemical pressure. In H3SM, the larger the chemical pressure of the central atom, the larger the physical pressure required for its stabilization. Away from the phase transition, decreasing pressure is beneficial to the superconductivity of the H3SM system. These findings open new avenues for designing and optimizing new high-Tc superconductors with low-Ps.

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 the Centre of Low Temperature Physics Košice (Review article)

Point-contact spectroscopy offers a unique straightforward possibility to study the electronic properties of metals. Soon after the invention of this technique by Igor Yanson in the B. Verkin Institute for Low Temperature Physics and Engineering of the NAS of Ukraine [Sov. Phys. JETP39, 506 (1974)], multiple laboratories adopted this technique and applied it to various topical problems in modern solid-state physics. Here, we offer a brief review of how point-contact spectroscopy has been developed and used in the Centre of Low Temperature Physics Košice. By this technique, we were able to obtain for example the spectrum of the electron-phonon interaction in an unprecedented large energy scale up to 160 meV in LaB6. The Zeeman splitting of the Pr3+ ion levels in the crystal-electric field has been detected for the first time in PrNi5. “Inverse” point-contact spectra of the electron-phonon interaction found in semimetallic arsenic were explained by the weak localization in the point-contact area. The point-contact Andreev reflection spectroscopy enabled to detect not only the superconducting energy gap in YB6, but also the Einstein-like phonon mode responsible for superconductivity. The first spectroscopic evidence of the two-gap superconductivity in MgB2 has been provided in our experiments. High spin polarization in Co2FeSn Heusler nanowires for spintronics has been obtained.

Low temperature singularities of electron density in a two-gap superconductor ZrB12

Fine details of crystal structure of ZrB12 two-gap superconductor are studied at low temperatures by precise x-ray diffraction technique. Small static Jahn-Teller distortions of a face centered cubic lattice are observed in the range 30–70 K, leading to emergence of two types singularities of electron density (ED). These are: (i) dynamic charge stripes along selected directions <110> and <112> in the crystal and (ii) triangular lattice of the ED antinodes located in the interstices of the boron lattice in the {111} planes. The second anomaly was detected for the first time, and it is very pronounced for ZrB12, being intensified at low temperatures. The anisotropy of the two-gap superconductivity in ZrB12 is confirmed by measurements of the low temperature heat capacity in a magnetic field directed along three principal axes in the crystal, H || [100], H || [110] and H || [111]. We conclude in favor of the magnetic field-induced anisotropy arising from the interaction of vortex lattice in this superconductor with fluctuating ED (charge stripes) of a two-type filamentary structure.

Superconducting ground state study of the valence-skipped compound AgSnSe2

Valence-skipped superconductors are natural candidates for unconventional superconductivity because they can exhibit a negative effective, attractive interaction for electron pairing. This work reports comprehensive x-ray diffraction, magnetization, specific heat, and muon spin rotation and relaxation measurements ($\ensuremath{\mu}\mathrm{SR}$) on the valence-skipped compound ${\mathrm{AgSnSe}}_{2}$. The temperature dependences of the electronic specific heat $[{C}_{\mathrm{el}}(T)]$ and the upper critical field $[{H}_{c2}(T)]$ provide evidence of two-gap superconductivity, which is also confirmed by our transverse-field $\ensuremath{\mu}\mathrm{SR}$ measurements. Zero-field $\ensuremath{\mu}\mathrm{SR}$ measurements reveal at most a slight increase $[\ensuremath{\sim}0.002(1)\phantom{\rule{3.33333pt}{0ex}}\ensuremath{\mu}{\text{s}}^{\ensuremath{-}1}]$ in relaxation in the superconducting state, much less than reported in a range of superconductors with broken time-reversal symmetry. Further measurements with greatly improved statistics will be required to make a definitive determination of the possible presence of broken time-reversal symmetry.

Multi-band analysis on physical properties of superconducting FeSe films

The origins of superconductivity and pairing symmetry of order parameters are still controversial problems for FeSe thin films up to date. Under the Neumann boundary conditions, the electromagnetic properties of this system are investigated using the two-band Ginzburg–Landau theory. We calculate the temperature dependence of upper critical field in arbitrary direction and critical supercurrent density through the FeSe film. It is revealed that the normalized upper critical field is independent of the film thickness and all of our theoretical results are in accordance with the experimental data. These thus strongly indicate the existence of two-gap s-wave superconductivity in this material.

Multi-Band Analysis on Physical Properties of the Quasi-Two-Dimensional Superconductor NbSe2

The discovery of quasi-two-dimensional superconductors bears consequences for both basic research and practical applications. However, the mechanism of superconductivity and the form of order parameters are still controversial problems for the transition metal dichalcogenide NbSe2 thin film. Under the Neumann boundary condition, the physical properties of this compound are investigated within the two-component Ginzburg–Landau theory. We compute the upper critical field in an arbitrary direction and the temperature dependence of critical supercurrent density through this layered system. All of our theoretical calculations fit the experimental measurements well; thus, this study strongly provides evidence of two-gap s-wave superconductivity in the NbSe2 thin film.

Ginzburg–Landau Analysis on the Physical Properties of the Kagome Superconductor CsV3Sb5

The kagome lattice consisting of corner-sharing triangles has been studied in the context of quantum physics for more than seventy years. For the novel discovered kagome superconductor CsV3Sb5, identifying the pairing symmetry of order parameter remained an elusive problem until now. Based on the two-band Ginzburg–Landau theory, we study the temperature dependence of upper critical field and magnetic penetration depth for this compound. All theoretical results are consistent with the experimental data, which strongly indicates the existence of two-gap s-wave superconductivity in this system. In addition, it is worth noting that the anisotropy of effective masses in the band with large (or small) gap is about 70 (or 2.4). With the calculation of the Kadowaki–Woods ratio as 0.58×10−5μΩ cm mol2 K2 mJ−2, the semi-heavy-fermion feature is suggested in the compound CsV3Sb5.

Boundary Effect and Critical Temperature of Two-Band Superconducting FeSe Films

Based on two-band Bogoliubov–de Gennes theory, we study the boundary effect of an interface between a two-gap superconductor FeSe and insulator (or vacuum). New boundary terms are introduced into two-band Ginzburg–Landau formalism, which modifies the boundary conditions for the corresponding order parameters of superconductor. The theory allows for a mean-field calculation of the critical temperature suppression with the decrease in FeSe film thickness. Our numerical results are in good agreement with the experimental data observed in this material.

Spin–orbit coupling controlling the superconducting dome of artificial superlattices of quantum wells

While it is known that a resonant amplification of Tc in two-gap superconductors can be driven by using the Fano–Feshbach resonance tuning the chemical potential near a Lifshitz transition, little is known on tuning the Tc resonance by cooperative interplay of the Rashba spin–orbit coupling (RSOC) joint with phonon mediated (e-ph) pairing at selected k-space spots. Here, we present first-principles quantum calculation of superconductivity in an artificial heterostructure of metallic quantum wells with 3 nm period where quantum size effects give two-gap superconductivity with RSOC controlled by the internal electric field at the interface between the nanoscale metallic layers intercalated by insulating spacer layers. The key results of this work show that fundamental quantum mechanics effects including RSCO at the nanoscale [Mazziotti et al., Phys. Rev. B, 103, 024523 (2021)] provide key tools in applied physics for quantitative material design of unconventional high temperature superconductors at ambient pressure. We discuss the superconducting domes where Tc is a function of either the Lifshitz parameter (η) measuring the distance from the topological Lifshitz transition for the appearing of a new small Fermi surface due to quantum size effects with finite spin–orbit coupling and the variable e-ph coupling g in the appearing second Fermi surface linked with the energy softening of the cut off ω0.

Strong-coupling superconductivity in the kagome metal CsV3Sb5 revealed by soft point-contact spectroscopy

The nature of the superconducting state in kagome metals $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ is a key issue in need of experimental clarification. Here, we report on a study of the superconducting order parameter in the kagome superconductor ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ through simultaneous ``soft'' point-contact spectroscopy and resistivity measurements under both ambient and a hydrostatic pressure. Signatures of two-gap superconductivity are resolved in the soft point-contact spectra, accompanied by an asymmetric excess conductance above ${T}_{c}$. Quantitative analysis based on the two-dimensional Blonder-Tinkham-Klapwijk model reveals an ($s+s$)-wave superconducting gap with $2{\mathrm{\ensuremath{\Delta}}}_{0}/{k}_{B}{T}_{c}\ensuremath{\simeq}7.2$, placing ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ in the strong-coupling regime. The strong-coupling two-gap feature indicates a high electronic density of states (DOS) and possible existence of flat-band-driven multiple van Hove singularities (VHSs) at the Fermi level. The presence of asymmetric excess spectral conductance above ${T}_{c}$ hints at a modest electronic correlation in ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$. Under a hydrostatic pressure of 2.1 kbar, the nodeless multigap nature of the superconducting state remains, whereas both the larger gap and the excess spectral conductance are greatly suppressed, accompanied by an enhanced ${T}_{c}$. An estimate of the spectral-weighted gap ratio reveals a weakened coupling strength, indicative of a reduced total superconducting DOS upon pressure. Our results point to key roles of both flat-band-associated VHSs and electronic correlation in the onset of kagome superconductivity and shed some light on the interplay between charge-density-wave order and superconductivity in vanadium-based kagome superconductors.

Superconductivity and topological aspects of two-dimensional transition-metal monohalides

Two-dimensional (2D) superconducting states have attracted much recent interest, especially when they coexist with nontrivial band topology which affords a promising approach towards Majorana fermions. Using first-principles calculations, we predict van der Waals monolayered transition-metal monohalides MX (M = Zr, Mo; X = F, Cl) as a class of 2D superconductors with remarkable transition temperature (5.9–12.4 K). Anisotropic Migdal-Eliashberg theory reveals that ZrCl have a single superconducting gap ∆ ~ 2.14 meV, while MoCl is a two-gap superconductor with ∆ ~ 1.96 and 1.37 meV. The Z2 band topology of 2D MX is further demonstrated that MoF and MoCl are candidates for realizing topological superconductivity. Moreover, the Dirac phonons of ZrCl and MoCl contribute w-shape phononic edge states, which are potential for an edge-enhanced electron-phonon coupling. These findings demonstrate that 2D MX offers an attractive platform for exploring the interplay between superconductivity, nontrivial electronic and phononic topology.

Biaxial strain engineering on the superconducting properties of MgB2 monolayer

The effect of biaxial strain on the superconducting properties of MgB2 monolayer was studied by first-principles calculations. The stability analyses by phonon dispersions show that a biaxial strain of as much as 7% can be applied onto MgB2 without inducing any imaginary frequency. The superconducting property calculations based on the frame of Migdal-Eliashberg theory successfully reproduce the two-gap superconductivity of MgB2. The results show that the tensile biaxial strain can increase the critical temperature of MgB2 by as much as ∼20% while the compressive biaxial strain would decrease the critical temperature by ∼29%. The detailed microscopic mechanism of the biaxial strain effect on the superconducting properties was studied by calculations of electronic structures and phonon dispersions. The increased Tc is a combining result of the increased electron density at the Fermi level and the in-plane boron phonon softening. By means of high-throughput screening of proper substrates, it is found that most of the substrates would result in tensile strain in MgB2 film, some of which can result in tensile strain of higher than 10%, consistent with many experimental works that the MgB2 thin film has increased Tc. The results in this work provide a detailed understanding of the biaxial strain engineering mechanism and demonstrate that biaxial strain engineering can be an effective way of tuning the superconducting properties of MgB2 and other similar materials.

Two-gap superconductivity in a Janus MoSH monolayer

Hydrides under ultrahigh pressure, such as ${\mathrm{H}}_{3}\mathrm{S}$ and ${\mathrm{LaH}}_{10}$, can achieve coveted superconducting critical temperatures via the conventional electron-phonon coupling mechanism. In this work, we report first-principles investigation of high-temperature phonon-mediated superconductivity in a two-dimensional metal hydride, namely, the Janus MoSH monolayer. The MoSH sheet is a recently synthesized intermediate in realizing Janus transition metal dichalcogenides by involving stripping the top-layer S of ${\mathrm{MoS}}_{2}$ with H atoms [X. Wan et al., ACS Nano 15, 20319 (2021); A. Y. Lu et al., Nat. Nanotechnol. 12, 744 (2017)]. We find coupling of electrons from $\mathrm{Mo}\text{\ensuremath{-}}d$ orbitals around the Fermi level to ultrahigh frequency H- and S-derived phonons, analogous to superconducting hydrides of ${\mathrm{H}}_{3}\mathrm{S}$ and ${\mathrm{LaH}}_{10}$. This leads to strong coupling two-gap superconductivity with the calculated critical temperature ${T}_{c}$ being about 28.58 K at atmosphere pressure. The presence of soft phonon bands from the Mo in-plane vibrations, in cooperation with the electron susceptibility, accounts for the strong electron-phonon coupling of the MoSH monolayer. By further aligning the Fermi level via doping, the ${T}_{c}$ can be boosted to 37.31 K, close to the McMillan limit (39 K). Thus, our work points out a real metal hydride for the realization of two-dimensional high-temperature superconductivity at atmosphere pressure and facilitates further studies on new families of Janus transition-metal sulfhydrates.

Spectroscopic evidence of multigap superconductivity in noncentrosymmetric AuBe

AuBe is a chiral, non-centrosymmetric superconductor with transition temperature $T_C$ $\simeq$ 3.25 K. The broken inversion symmetry in its crystal structure makes AuBe a possible candidate to host a mixed singlet-triplet pairing symmetry in its superconducting order parameter ($\Delta$). This possibility was investigated by transport, thermodynamic, and muon-spin rotation/relaxation experiments in AuBe. However, this issue was not addressed using direct spectroscopic probes so far. In addition, certain ambiguities exist in the description of superconductivity in AuBe based on $\mu$SR experiments reported earlier. Here we report scanning tunneling spectroscopy (STS) on AuBe down to 300 mK. We found a signature of two superconducting gaps (with 2$\Delta_1/k_{B}T_{C}$ = 4.37 and 2$\Delta_2/k_{B}T_{C}$ = 2.46 respectively) and a clean BCS-like temperature dependence of both the gaps. We have also performed band structure calculations to identify the different bands that might give rise to the observed two-gap superconductivity in AuBe.

Checkerboard patterns of charge stripes in the two-gap superconductor ZrB12

Inhomogeneous superconductivity in the high quality single crystals of ZrB12 (Tc = 6 K) has been studied using the heat capacity and x-ray diffraction (XRD) data. Evidence of two-band superconductivity with two branches of upper critical field Hc2(Tc) is obtained in a magnetic field applied along the [110] axis of the crystal. On the contrary, at H //[100], the only dependence Hc2(Tc) is observed. This finding is supplemented with the checkerboard-type patterns of the charge stripes in ZrB12 deduced from the detailed analysis of XRD data. These patterns are compared to the structure of the charge stripes in the weakly bound superconductor LuB12, whose Tc is 15 times lower than that of ZrB12. Probable nature of the two-gap superconductivity in ZrB12 with strongly enhanced characteristics is discussed.

Real-space anisotropy of the superconducting gap in the charge-density wave material 2H-NbSe2

We present a scanning tunneling microscopy (STM) and ab-initio study of the anisotropic superconductivity of 2H-NbSe2 in the charge-density-wave (CDW) phase. Differential-conductance spectra show a clear double-peak structure, which is well reproduced by density functional theory simulations enabling full k- and real-space resolution of the superconducting gap. The hollow-centered (HC) and chalcogen-centered (CC) CDW patterns observed in the experiment are mapped onto separate van der Waals layers with different electronic properties. We identify the CC layer as the high-gap region responsible for the main STM peak. Remarkably, this region belongs to the same Fermi surface sheet that is broken by the CDW gap opening. Simulations reveal a highly anisotropic distribution of the superconducting gap within single Fermi sheets, setting aside the proposed scenario of a two-gap superconductivity. Our results point to a spatially localized competition between superconductivity and CDW involving the HC regions of the crystal.