Multigap Superconductivity Research Articles

Resonant multi-gap superconductivity at room temperature near a Lifshitz topological transition in sulfur hydrides

The maximum critical temperature for superconductivity in pressurized hydrides appears at the top of superconducting domes in Tc vs pressure curves at a particular pressure, which is not predicted by standard superconductivity theories. The high-order anisotropic Van Hove singularity near the Fermi level observed in band-structure calculations of pressurized sulfur hydride, typical of a supermetal, has been associated with the array of metallic hydrogen wire modules forming a nanoscale heterostructure at an atomic limit called the superstripe phase. Here, we propose that pressurized sulfur hydrides behave as a heterostructure made of a nanoscale superlattice of interacting quantum wires with a multicomponent electronic structure. We present first-principles quantum calculation of a universal superconducting dome where Tc amplification in multi-gap superconductivity is driven by the Fano–Feshbach resonance due to a configuration interaction between open and closed pairing channels, i.e., between multiple gaps in the BCS regime, resonating with a single gap in the BCS–Bose–Einstein condensation crossover regime. In the proposed three dimensional phase diagram, the critical temperature shows a superconducting dome where Tc is a function of two variables: (i) the Lifshitz parameter (η) measuring the separation of the chemical potential from the Lifshitz transition normalized by the inter-wire coupling and (ii) the effective electron–phonon coupling (g) in the appearing new Fermi surface including phonon softening. The results will be of help for material design of room-temperature superconductors at ambient pressure.

Isotropic single-gap superconductivity of elemental Pb

The unconventional multi-gap superconductivity in elemental Pb were reported previously by surface sensitive tunneling experiments, as well as predicted by several theory works. To obtain bulk evidence for such multiple gap behavior, the thermodynamic critical field $B_{\rm c}$ was measured along three different crystallographic directions ([100], [110], and [111]) in a high-quality Pb single crystal by means of muon spin rotation/relaxation. No difference in temperature evolution of $B_{\rm c}$ for all three directions was detected. The average reduced gap $\alpha=\Delta/k_{\rm B}T_{\rm c}=2.312(3)$ ($\Delta$ is the zero-temperature gap value and $T_{\rm c}$ is the transition temperature) was further obtained by employing the phenomenological $\alpha-$model. Our results imply that the elemental Pb is an isotropic superconductor with a single energy gap.

Superconductivity in gallenene

Among the large variety of two-dimensional (2D) materials discovered to date, elemental monolayers that host superconductivity are very rare. Using ab initio calculations we show that recently synthesized gallium monolayers, coined gallenene, are intrinsically superconducting through electron–phonon coupling. We reveal that Ga-100 gallenene, a planar monolayer isostructural with graphene, is the structurally simplest 2D superconductor to date, furthermore hosting topological edge states due to its honeycomb structure. Our anisotropic Eliashberg calculations show distinctly three-gap superconductivity in Ga-100, in contrast to the alternative buckled Ga-010 gallenene which presents a single anisotropic superconducting gap. Strikingly, the critical temperature (T c ) of gallenene is in the range of 7–10 K, exceeding the T c of bulk gallium from which it is exfoliated. Finally we explore chemical functionalization of gallenene with hydrogen, and report induced multigap superconductivity with an enhanced T c in the resulting gallenane compound.

Time-reversal symmetry breaking and multigap superconductivity in the noncentrosymmetric superconductor La7Ni3

The Th$_{7}$Fe$_{3}$ family of superconductors provides a rich playground for unconventional superconductivity. La$_7$Ni$_3$ is the latest member of this family, which we here investigate by means of thermodynamic and muon spin rotation and relaxation measurements. Our specific heat data provides evidence for two distinct and approximately isotropic superconducting gaps. The larger gap has a value slightly higher than that of weak-coupling BCS theory, indicating the presence of significant correlations. These observations are confirmed by transverse-field muon-rotation measurements. Furthermore, zero-field measurements reveal small internal fields in the superconducting state, which occur close to the onset of superconductivity and indicate that the superconducting order parameter breaks time-reversal symmetry. We discuss two possible microscopic scenarios -- an unconventional $E_{2}(1,i)$ state and an $s+i\,s$ superconductor, which is reached by two consecutive transitions -- and illustrate which interactions will favor these phases. Our results establish La$_{7}$Ni$_{3}$ as the first member of the Th$_{7}$Fe$_{3}$ family displaying both time-reversal-symmetry-breaking and multigap superconductivity.

Room temperature superconductivity dome at a Fano resonance in superlattices of wires

Recently room temperature superconductivity with degrees Celsius has been discovered in a pressurized complex ternary hydride, CSH x , which is a carbon- and hydrogen-doped H3S alloy. The nanoscale structure of H3S is a particular realization of the 1993 patent claim of superlattice of quantum wires for room temperature superconductors and the maximum T C occurs at the top of a superconducting dome. Here we focus on the electronic structure of materials showing nanoscale heterostructures at the atomic limit made of a superlattice of quantum wires like hole-doped cuprate perovskites, and organics focusing on A15 intermetallics and pressurized hydrides. We provide a perspective of the theory of room temperature multigap superconductivity in heterogeneous materials tuned at a shape resonance or Fano resonance in the superconducting gaps near a Lifshitz transition focusing on H3S where the maximum T C occurs where the multiband metal is tuned by pressure near a Lifshitz transition. Here the superconductivity dome of T C vs. pressure is driven by both electron-phonon coupling and contact exchange interaction. We show that the T C amplification up to room temperature is driven by the Fano resonance between a superconducting gap in the anti-adiabatic regime and other gaps in the adiabatic regime. In these cases the T C amplification via contact exchange interaction is the missing term in conventional multiband BCS and anisotropic Migdal-Eliashberg theories including only Cooper pairing.

One or two gaps in Mo8Ga41 superconductor? Local Hall-probe magnetometry study

The magnetization properties of the endohedral cluster superconductor Mo8Ga41 are studied by sensitive Hall-probe magnetometry. The temperature dependence of the lower critical magnetic field H c1 is obtained and compared to theoretical models accounting for single-gap and two-gap superconductivity. Data can be described by both models with minor differences. These results are confronted with our previous measurements which evidence that the system is inherently single-gap s-wave superconductor but minor additional phases are present also in seemingly perfect samples. We discuss how presence of such additional phases with varying size of the penetration depth and H c1 field is reflected in magnetization measurements which could lead to misinterpretation of the multigap superconductivity in Mo8Ga41.

Multigap superconductivity at an unconventional Lifshitz transition in a three-dimensional Rashba heterostructure at the atomic limit

It is well known that the critical temperature of multi-gap superconducting 3D heterostructures at atomic limit (HAL) made of a superlattice of atomic layers with an electron spectrum made of several quantum subbands can be amplified by a shape resonance driven by the contact exchange interaction between different gaps. The $T_C$ amplification is achieved tuning the Fermi level near the singular nodal point at a Lifshitz transition for opening a neck. Recently high interest has been addressed to the breaking of inversion symmetry which leads to a linear-in-momentum spin-orbit induced spin splitting, universally referred to as Rashba spin-orbit coupling (RSOC) also in 3D layered metals. However the physics of multi-gap superconductivity near unconventional Lifshitz transitions in 3D HAL with RSOC, being in a non-BCS regime, is not known. The key result of this work getting the superconducting gaps by Bogoliubov theory and the 3D electron wave functions by solution of the Dirac equation is the feasibility of tuning multi-gap superconductivity by suitably matching the spin-orbit length with the 3D superlattice period. It is found that the presence of the RSOC amplifies both the k dependent anisotropic gap function and the critical temperature when the Fermi energy is tuned near the circular nodal line. Our results suggest a method to effectively vary the effect of RSOC on macroscopic superconductor condensates via the tuning of the superlattice modulation parameter in a way potentially relevant for spintronics functionalities in several existing experimental platforms and tunable materials needed for quantum devices for quantum computing.

Multigap superconductivity in the Mo5PB2 boron–phosphorus compound

The tetragonal Mo5PB2 compound was recently reported to show superconductivity with a critical temperature up to 9.2 K. In search of evidence for multiple superconducting gaps in Mo5PB2, comprehensive measurements, including magnetic susceptibility, electrical resistivity, heat capacity, and muon-spin rotation and relaxation measurements were carried out. Data from both low-temperature superfluid density and electronic specific heat suggest a nodeless superconducting ground state in Mo5PB2. Two superconducting energy gaps Δ0 = 1.02 meV (25%) and 1.49 meV (75%) are required to describe the low-T electronic specific-heat data. The multigap features are clearly evidenced by the field dependence of the electronic specific-heat coefficient and the Gaussian relaxation rate in the superconducting state (i.e., superfluid density), as well as by the temperature dependence of the upper critical field. By combining our extensive experimental results with numerical band-structure calculations, we provide compelling evidence of multigap superconductivity in Mo5PB2.

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.

Mo6Ga31 endohedral cluster superconductor

Endohedral cluster compounds are a rich source of new superconductors, where nontrivial properties are expected, including strong coupling regime and multigap superconductivity. Here, we report on the synthesis, crystal and electronic structure, and physical properties of the Mo6Ga31 endohedral cluster superconductor. The compound has two crystallographic modifications, monoclinic and triclinic, which are built by the Mo@Ga10 endohedral clusters. Both structures possess qualitatively the same electronic density of states showing a high peak at the Fermi level. Due to the proximity effect of the triclinic and monoclinic domains, which are in the strong contact with each other, bulk Mo6Ga31 exhibits single superconducting transition at the critical temperature of 8.2 K in zero magnetic field. The upper critical field, which is 7.8 T at zero temperature, shows clear enhancement with respect to the Werthamer-Helfand-Honenberg prediction. Accordingly, heat capacity measurements indicate strong electron-phonon coupling in the superconducting state with the large ratio of 2Δ(0)/(kBTc)=4.5, where 2Δ(0)=3.2 meV is the full superconducting gap at zero temperature.

Superconductivity in Quantum Complex Matter: the Superstripes Landscape

While in XX century the theory of superconductivity has focused on a homogeneous metal with a rigid lattice which can be reduced to a single effective conduction band in the dirty limit. Today in the XXI century, the physics of superconductivity is focusing on complexity of quantum matter where novel quantum functionalities with lattice inhomogeneity at nanoscale (between 1 nm and 100 nm) and at mesoscopic scale (in the range 100-10000 nm), where the electronic structure need to be described by multiple Fermi surfaces and multiple gaps in the superconducting phase in the clean limit. The present issue of Journal of superconductivity and Novel magnetism collects papers presented at the International Conference Superstripes 2019 which was held on June 23-29, 2019, in Ischia Island, Italy. The series of Stripes conference started on Dec 8 1996 and it has contributed to scientific advances in the new physics of superconductivity in quantum complex systems in these last 23 years where polarons, strain, multigap superconductivity, exchange interaction between condensates, granular superconductivity and percolation play a key role. The articles collected in this issue cover hot topics of the new quantum physics of complex matter including the mechanism of high temperature superconductivity, complex magnetic orders and orbital physics in strongly correlated materials which have been growing rapidly in these last two years opening new perspectives also in mesoscopic quantum engineering.

Crossover from multiple- to single-gap superconductivity in Nb5Ir3−xPtxO alloys

By using mostly the muon-spin rotation/relaxation ($\mu$SR) technique, we investigate the superconductivity (SC) of Nb$_5$Ir$_{3-x}$Pt$_x$O ($x = 0$ and 1.6) alloys, with $T_c = 10.5$ K and 9.1 K, respectively. At a macroscopic level, their superconductivity was studied by electrical resistivity, magnetization, and specific-heat measurements. In both compounds, the electronic specific heat and the low-temperature superfluid density data suggest a nodeless SC. The superconducting gap value and the specific heat discontinuity at $T_c$ are larger than that expected from the Bardeen-Cooper-Schrieffer theory in the weak-coupling regime, indicating strong-coupling superconductivity in the Nb$_5$Ir$_{3-x}$Pt$_x$O family. In Nb$_5$Ir$_3$O, multigap SC is evidenced by the field dependence of the electronic specific heat coefficient and the superconducting Gaussian relaxation rate, as well as by the temperature dependence of the upper critical field. Pt substitution suppresses one of the gaps, and Nb$_5$Ir$_{1.4}$Pt$_{1.6}$O becomes a single-gap superconductor. By combining our extensive experimental results, we provide evidence for a multiple- to single-gap SC crossover in the Nb$_5$Ir$_{3-x}$Pt$_x$O family.

MgB4 trilayer film: A four-gap superconductor

Since the discovery of two-gap superconductivity in bulk ${\mathrm{MgB}}_{2}$, many efforts have been devoted to searching for multigap superconductors. Recently, a monolayer of ${\mathrm{MgB}}_{2}$ and a trilayer film of ${\mathrm{AlB}}_{4}$ were predicted to be robust three-gap superconductors. Here we investigate using the fully anisotropic Migdal-Eliashberg theory the superconducting behaviors in a series of boron-based monolayers and trilayer films that are dynamically stable but not synthesized experimentally heretofore. Remarkably, we find that the trilayer film of ${\mathrm{MgB}}_{4}$ has an exciting four-gap superconducting nature with a high transition temperature ${T}_{c}\ensuremath{\sim}52$ K. We demonstrate that this high-${T}_{c}$ four-gap superconductivity is closely related to the Fermi surface exhibiting an unusually strong electron-phonon coupling with evident four-region distribution characteristics. The electron-lattice coupling is dominated by the acoustic modes of a softening kink and the high-energy optical phonons around the Brillouin-zone center, of which the former ones place the system on the verge of a latent charge density wave state. To our knowledge, no material with more than three superconducting gaps has been reported. At the same time, we also show that the ${\mathrm{GaB}}_{4}$ trilayer film has a robust three-gap nature with ${T}_{c}\ensuremath{\sim}51$ K, and the trilayer films of ${\mathrm{BeB}}_{4}$ and ${\mathrm{LiB}}_{4}$ are two-gap superconductors with ${T}_{c}$'s of $\ensuremath{\sim}39$ and 32 K, respectively.

Time-dependent Ginzburg–Landau equations for multi-gap superconductors**Project supported by the National Natural Science Foundation of China (Grant Nos. 11564003 and 11865005) and the Natural Science Foundation of Guangxi Province of China (Grant No. 2018GXNSFAA281024).

We numerically solve the time-dependent Ginzburg–Landau equations for two-gap superconductors using the finiteelement technique. The real-time simulation shows that at low magnetic field, the vortices in small-size samples tend to form clusters or other disorder structures. When the sample size is large, stripes appear in the pattern. These results are in good agreement with the previous experimental observations of the intriguing anomalous vortex pattern, providing a reliable theoretical basis for the future applications of multi-gap superconductors.

Unconventional Multi-gap Superconductivity and Antiferromagnetic Spin Fluctuations in New Iron-arsenide LaFe2As2 in Heavily Electron-doped Regime

We report 75As-NMR/NQR results on new iron-arsenide compounds (La0.5-xNa0.5+x)Fe2As2. The parent compound x=0 exhibits a stripe-type antiferromagnetic (AFM) order below T_N=130 K. The measurement of nuclear spin relaxation rate at hole-doped x=+0.3 and heavily electron-doped x=-0.5 revealed that the normal-state properties are dominated by AFM spin fluctuations (AFMSFs), which are more significant at x=+0.3 than at x=-0.5. Their superconducting (SC) phases are characterized by unconventional multi-gap SC state, where the smaller SC gaps are particularly weaken in common. The experimental results indicate the close relationship between the AFMSFs and the SC from the hole-doped state to heavily electron-doped state, which shed light on a unique SC phase emerged in the heavily electron-doped regime being formally equivalent to non-SC compound Ba(Fe0.5Co0.5)Fe2As2.

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.

Self-Consistent Two-Gap Description of MgB2 Superconductor

A self-consistent two-gap γ -model is used to quantitatively describe several thermodynamic properties of MgB 2 superconductor. The superconducting coupling matrix, ν i j , was obtained from the fitting of the superfluid density in the entire superconducting temperature range. Using this input, temperature-dependent superconducting gaps, specific heat, and upper critical fields were calculated with no adjustable parameters and compared with the experimental data as well as with the first-principles calculations. The observed agreement between fit and data shows that γ -model provides adequate quantitative description of the two-gap superconductivity in MgB 2 and may serve as a relatively simple and versatile self-consistent description of the thermodynamic quantities in multi-gap superconductors.

Multigap Superconductivity in RbCa2Fe4As4F2 Investigated Using μSR Measurements

The superconducting properties of the recently discovered double Fe$_2$As$_2$ layered high-$T_c$ superconductor RbCa$_2$Fe$_4$As$_4$F$_2$ with $T_c\approx$ 30~K have been investigated using magnetization, heat capacity, transverse-field (TF) and zero-field (ZF) muon-spin rotation/relaxation ($\mu$SR) measurements. Our low field magnetization measurements and heat capacity (C$_p$) reveal an onset of bulk superconductivity with $T_{\bf c}\sim$ 30.0(4) K. Furthermore, the heat capacity exhibits a jump at $T_{\bf c}$ of $\Delta$C$_p$/$T_{\bf c}$=94.6 (mJ/mole-K$^2$) and no clear effect of applied magnetic fields was observed on C$_p$(T) up to 9 T between 2 K and 5 K. Our analysis of the TF-$\mu$SR results shows that the temperature dependence of the magnetic penetration depth is better described by a two-gap model, either isotropic $s$+$s$-wave or $s$+$d$-wave than a single gap isotropic $s$-wave or $d$-wave model for the superconducting gap. The presence of two superconducting gaps in RbCa$_2$Fe$_4$As$_4$F$_2$ suggests a multiband nature of the superconductivity, which is consistent with the multigap superconductivity observed in other Fe-based superconductors, including ACa$_2$Fe$_4$As$_4$F$_2$ (A=K and Cs). Furthermore, from our TF-$\mu$SR study we have estimated an in-plane penetration depth $\lambda_{\mathrm{ab}}$$(0)$ =231.5(3) nm, superconducting carrier density $n_s = 7.45 \times 10^{26}~ $m$^{-3}$, and carrier's effective-mass $m^*$ = 2.45\textit{m}$_{e}$. Our ZF $\mu$SR measurements do not reveal a clear sign of time reversal symmetry breaking at $T_{\bf c}$, but the temperature dependent relaxation between 150 K and 1.2 K might indicate the presence of spin-fluctuations. The results of our present study have been compared with those reported for other Fe pnictide superconductors.

Massless and quantized modes of kinks in the phase space of superconducting gaps

We investigated quantized modes of kinks in the phase space of superconducting gaps in a superconductor with multiple gaps. The kink is described by the sine-Gordon model in a two-gap superconductor and by the double sine-Gordon model in a three-gap superconductor. A fractional-flux vortex exists at the edge of the kink, and a fractional-flux vortex will be stable in a three-gap superconductor with time-reversal symmetry breaking. The kink and fractional-flux vortex exhibit massless modes as a sliding motion. We show further that there are one zero-energy mode (massless mode) and quantized excitation modes in kinks, which are characteristic features of multi-gap superconductors. The equation of quantized modes for the double sine-Gordon model is solved numerically. The correction to the ground-state energy is calculated based on the renormalization theory.

Multigap superconductivity in chiral noncentrosymmetric TaRh2B2

We report the first observation of multigap superconductivity in TaRh$_{2}$B$_{2}$. We show TaRh$_{2}$B$_{2}$ is a bulk type-II superconductor with a transition temperature, $T_{\mathrm{c}} = 6.00(5)$ K. We present transverse-field muon spin relaxation data where the superconducting gap can be fit using a two-gap $\left(s+s\right)$-wave model. We also report the zero-field electronic specific heat in the superconducting state that is best described by the same $\left(s+s\right)$ model providing further evidence of multiband behavior in this superconductor. Zero-field muon spin relaxation measurements show time-reversal symmetry is preserved in the superconducting state. We demonstrate that TaRh$_{2}$B$_{2}$ has an upper critical field of $15.2(1)$ T, which is significantly higher than previously reported and exceeds the Pauli limit.