In contrast to single-component superconductors, which are described at the level of Ginzburg-Landau theory by a single parameter κand are divided in type-I κ<1/\sqrt{2} and type-II κ>1/\sqrt{2} classes, two-component systems in general possess three fundamental length scales and have been shown to possess a separate "type-1.5" superconducting state. In that state, as a consequence of the extra fundamental length scale, vortices attract one another at long range but repel at shorter ranges, and therefore should form clusters in low magnetic fields. In this work we investigate the appearance of type-1.5 superconductivity and the interpretation of the fundamental length scales in the case of two bands with substantial interband couplings such as intrinsic Josephson coupling, mixed gradient coupling and density-density interactions. We show that in the presence of substantial intercomponent interactions of the above types the system supports type-1.5 superconductivity with fundamental length scales being associated with the mass of the gauge field and two masses of normal modes represented by mixed combinations of the density fields.
Chiral superconductors support chiral edge modes and potentially spontaneous edge currents at their boundaries. Motivated by the putative multiband chiral p-wave superconductor Sr$_2$RuO$_4$, we study the influence of the interference between different bands at the edges, which may appear in the presence of moderate edge disorder or in edge tunneling measurements. We show that interband interference can strongly modify the measurable quantities at the edges when the order parameter exhibits phase difference between the bands. This is illustrated by investigating the edge dispersion and the edg…
Contrary to the usual assumption, the electron Bloch states in crystals with spin-orbit coupling do not always transform under symmetry operations in the same way as the pure spin-1/2 states. This has profound consequences for the symmetry properties and nodal structure of superconductors, especially for the interband gap functions. Focusing on tetragonal superconductors, we show that the interband pairing in the conventional (s-wave) channel can have features which are traditionally associated with unconventional pairing, such as triplet components and odd parity, and can produce line nodes i…
We investigate pairing mechanism in multiband superconductors. To put our feet on firm ground, unbiased renormalization group analysis is carried out for iron-based superconductors. It is quite remarkable that, after integrating out quantum fluctuations, the renormalization-group flows agree exceedingly well with a mean-field Hamiltonian where interband pair hopping plays an essential role. Through interband pair hopping, electrons can overcome the repulsive interaction between them and form resonating Cooper pairs between different bands. Unlike the conventional superconductors, the pairing m…
Isotope effects in a multiband superconductor with a leading interband pairing channel are investigated. A relatively small electron-phonon contribution into the pair-transfer interaction can cause effects of observed magnitude. A multiband model which interpolates the cuprate properties is used for illustrative calculations. Isotope exponents of the transition temperature ($α$), supercarrier density ($α_n$), paired carrier effective mass ($α_m$) and of the penetration depth ($α_λ$) on the doping scale have been obtained. The known opposite trend of $α$ and $T_c$ is reflected. The trends of $α…
We study the nonequilibrium dynamics of multiband BCS superconductors subjected to ultrashort pump pulses. Using density-matrix theory, the time evolution of the Bogoliubov quasiparticle densities and the superconducting order parameters are computed as a function of pump pulse frequency, duration, and intensity. Focusing on two-band superconductors, we consider two different model systems. The first one, relevant for iron-based superconductors, describes two-band superconductors with a repulsive interband interaction $V_{12}$ which is much larger than the intraband pairing terms. The second m…
Motivated by the recent discovery of iron-based superconductors, with high critical temperatures and multiple bands crossing the Fermi level, we address the conditions for the presence of chiral superconducting phases configurations in the in-plane magnetic field vs. temperature phase diagram of a quasi-2D frustrated three-band superconductor. Due to Zeeman splitting, the coupled superconducting gap equations present a complex set of solutions. For weak interband couplings, chiral configurations are only attained in a narrow strip of the in-plane magnetic field vs. temperature phase diagram. T…
We show that weak interband pair-transfer interaction affects weaker-superconductivity component of a two-gap system as an external field associated with the order parameter, similarly to an external magnetic field for ferromagnetics or an external electric field for ferroelectrics.
We analyze in detail the superconductivity that arises in an extended Hubbard model describing a multiband system with repulsive interactions. We show that virtual interband processes induce an effective attractive interaction for small momentum transfers, a situation not found in most models of superconductivity from repulsion. This attraction can be traced back, in real space, to the presence of correlated hopping terms induced by interband polarization. We reveal this physics with both strong-coupling expansion and many-body perturbation theory, supplemented by numerical calculations. Final…
The recently discovered multiband superconductors have created a new class of novel superconductors. In these materials multiple superconducting gaps arise due to the formation of Cooper pairs on different sheets of the Fermi surfaces. An important feature of these superconductors is the interband couplings, which not only change the individual gap properties, but also create new collective modes. Here we investigate the effect of the interband couplings in the Ginzburg-Landau theory. We produce a general $τ^{(2n+1)/2}$ expansion ($τ= 1-T/T_c$) and show that this expansion has unexpected behav…
We investigate the temperature dependence of the upper critical field $H_{c 2} $ as a tool to probe the possible presence of multiband superconductivity at the interface of LAO/STO. The behaviour of $H_{c 2} $ can clearly indicate two-band superconductivity through its nontrivial temperature dependence. For the disorder scattering dominated two-dimensional LAO/STO interface we find a characteristic non-monotonic curvature of the $H_{c 2} (T) $. We also analyse the $H_{c 2} $ for multiband bulk STO and find similar behaviour.
The origin of interband electron pairing responsible for enhancing superconductivity and the factors controlling its strength were examined. We show that the interband electron pairing is a natural consequence of breaking down the Born-Oppenheimer approximation during the 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 its implications were discussed.
We report a self-consistent microscopic theory of characteristic length scales, vortex structure and type-1.5 superconducting state in two-band systems using two-band Eilenberger formalism.
The thermal conductivity of the heavy fermion superconductor PrOs4Sb12 was measured down to Tc/40 throughout the vortex state. At lowest temperatures and for magnetic fields H ~ 0.07Hc2, already 40% of the normal state thermal conductivity is restored. This behaviour (similar to that observed in MgB2) is a clear signature of multiband superconductivity in this compound.
A theoretical overview of the classes of superconductors encompassing (a) high-Tc cuprate, (b) iron-based and (c) aromatic superconductors is given. Emphasis is put on the multiband natures of all the three classes, where the differences in the multiorbits and their manifestations in the electronic structures and pairing are clarified. From these, future directions and prospects are discussed.
We show that a clean multiband superconductor may display one or several phase transitions with increasing temperature from or to frustrated configurations of the relative phases of the superconducting order parameters. These transitions may occur when more than two bands are involved in the formation of the superconducting phase and when the number of repulsive interband interactions is odd. These transitions are signalled by slope changes in the temperature dependence of the superconducting gaps.
We study the superconductivity in the three-dimensional multiband d-p model, in which a Cu$_2$O$_3$-ladder layer and a CuO$_2$-chain layer are alternately stacked, as a model of the superconducting spin-chain ladder cuprate. $p_z$-Wave-like triplet superconductivity is found to be the most stable, and its dependence on interlayer coupling can explain the superconducting transition temperature dependence on pressure in real superconducting spin-chain ladder cuprates. The superconductivity may be enhanced if hole transfer from the chain layer to the ladder layer can be promoted beyond the typica…
The discovery of high-$T_c$ superconductivity in the pnictides, materials with a Fermi surface determined by several bands, highlights the need to understand how superconductivity arises in multiband systems. In this effort, using symmetry considerations and mean-field approximations, we discuss how strong hybridization among orbitals may lead to both intra and interband pairing, and we present calculations of the spectral functions to guide the experimental search for this kind of state.
A short review of the optical and far-infrared measurements on MgB$_{2}$ is given. Multiband and multigap effects are analyzed by comparing optical properties with other experiments and {\em ab initio} calculations. The covered topics are: the plasma frequency, electron-phonon interaction, impurity scattering, the effects of C and Al substitution, interband transitions and the far-infrared signatures of the superconducting gaps.
The newly discovered iron pnictide superconductors apparently present an unusual case of interband-channel pairing superconductivity. Here we show that, in the limit where the pairing occurs within the interband channel, several surprising effects occur quite naturally and generally: different density-of-states on the two bands lead to several unusual properties, including a gap ratio which behaves inversely to the ratio of density-of-states; the weak-coupling limit of the Eliashberg and the BCS theory, commonly taken as equivalent, in fact predict qualitatively different dependence of the $Δ_…
In strontium titanate, the Froehlich electron - LO-phonon interaction dominates the electron response and can also provide superconductivity. Because of high LO-phonon frequencies in SrTiO3, the superconducting system is non-adiabatic. We demonstrate that the dielectric function approach is an adequate theoretical method for superconductivity in SrTiO3 and on the SrTiO3-LaAlO3 interface. The critical temperatures are calculated using realistic material parameters. The obtained critical temperatures are in line with experimental data both for bulk and interface superconductivity. The present me…
The upper critical field Hc2(T) of the multiband superconductor KFe2As2 has been studied via low-temperature thermal expansion and magnetostriction measurements. We present compelling evidence for Pauli-limiting effects dominating Hc2(T) for H || a, as revealed by a crossover from second- to first-order phase transitions to the superconducting state in the magnetostriction measurements down to 50 mK. Corresponding features were absent for H || c. To our knowledge, this crossover constitutes the first confirmation of Pauli limiting of the Hc2(T) of a multiband superconductor. The results are su…
Despite being of fundamental importance and potential interest for topological quantum computing, spin-triplet superconductors remain rare in solid state materials after decades of research. In this work, we present a general mechanism for spin-triplet superconductivity in multi-band systems, where a non-retarded pairing interaction between conduction electrons is produced by their electronic repulsion to a third-electron undergoing a virtual interband transition. Our theory is analytically controlled by an interband hybridization parameter, and explicitly demonstrated in doped band insulators…
We present a method to produce superconducting tips to be used in Scanning Tunneling Microscopy/Spectroscopy experiments. We use these tips to investigate the evolution of the electronic density of states of NbSe2 from 0.3K up to its critical temperature (7.2K). The use of a superconducting tip (Pb) as ounterelectrode provides an enhancement of the different features related to the DOS of NbSe2 in the tunneling conductance curves, along all the studied thermal range. The analysis of the experimental results gives evidence of the presence of multiband superconductivity in NbSe2.
The superconductivity of a kagome superconductor CsV3Sb5 is studied by scanning tunneling microscopy / spectroscopy at an ultralow temperature with high resolution. Two kinds of superconducting gaps with multiple sets of coherent peaks and residual zero-energy density of states are observed on both half-Cs and Sb surfaces, implying multiband superconductivity with gap nodes. Sixfold star-shaped magnetic vortex is observed with conventional Caroli-de Gennes-Matricon bound states inside. Magnetic impurities suppress the superconductivity, while nonmagnetic impurities do not, suggesting the absen…
Ta$_4$Pd$_3$Te$_{16}$ is a recently discovered superconductor that has been suggested to be an unconventional superconductor near magnetism. We report electronic structure calculations showing that in spite of the layered crystal structure the material is an anisotropic three dimensional metal. The Fermi surface contains prominent one and two dimensional features, including nested 1D sheets, a 2D cylindrical section and a 3D sheet. The electronic states that make up the Fermi surface are mostly derived from Te $p$ states, with small Ta $d$ and Pd $d$ contributions. This places the compound far…
We propose a two band model for superconductivity. It turns out that the simplest nontrivial case considers solely interband scattering, and both bands can be modeled as symmetric (around the Fermi level) and flat, thus each band is completely characterized by its half-band width $W_{n}$ (n=1,2). A useful dimensionless parameter is $δ$, proportional to $W_{2}-W_{1}$. The case $δ=0$ retrieves the conventional BCS model. We probe the specific heat, the ratio gap over critical temperature, the thermodynamic critical field and tunneling conductance as functions of $δ$ and temperature (from zero to…
A mean-field treatment is presented of a square lattice two-orbital-model for ${\rm BiS_2}$ taking into account intra- and inter-orbital superconductivity. A rich phase diagram involving both types of superconductivity is presented as a function of the ratio between the couplings of electrons in the same and different orbitals (${\rm η= V_{XX}/V_{XY}}$) and electron doping $x$. With the help of a quantity we call orbital-mixing ratio, denoted as $R(ϕ)$, the phase diagram is analyzed using a simple and intuitive picture based on how $R(ϕ)$ varies as electron doping increases. The predictive pow…
We report point contact Andreev Reflection (PCAR) measurements on a high-quality single crystal of the non-centrosymmetric superconductor Re6Zr. We observe that the PCAR spectra can be fitted by taking two isotropic superconducting gaps with Delta_1 ~ 0.79 meV and Delta_2 ~ 0.22 meV respectively, suggesting that there are at least two bands which contribute to superconductivity. Combined with the observation of time reversal symmetry breaking at the superconducting transition from muon spin relaxation measurements (Phys. Rev. Lett. 112, 107002 (2014)), our results imply an unconventional super…
The pseudogap (PG) excitations in the framework of multiband superconductivity are analysed. Calculations for the doping phase diagram of electron-doped cuprate superconductors have been made. A nonrigid multiband model has been used. The interband pairing acts between the upper Hubbard band (UHB) and midgap states created (and shifted upwards) by doping. The appearance of two PG and two phase diagram critical points (CP) is suggested. The larger antinodal PG reflects the destruction of the long-range antiferromagnetic (AF) order. The second, smaller PG is a near-nodal event with exposed dopin…
Superconductivity in Pb, H under extreme pressure and CaBeSi, in the framework of the density functional theory for superconductors, is discussed. A detailed analysis on how the electron-phonon and electron-electron interactions combine together to determine the superconducting gap and critical temperature of these systems is presented. Pb, H under pressure and CaBeSi are multigap superconductors. We will address the question under which conditions does a system exhibits this phenomenon. The presented results contribute to the understanding of multiband and anisotropic superconductivity, which…
We consider a model for superconductivity in a two-band superconductor, having an anisotropic electronic structure made of two partially overlapping bands with a first hole-like and a second electron-like fermi surface. In this pairing scenario, driven by the interplay between interband $V_{i,j}$ and intraband $V_{i,i}$ pairing terms, we have solved the two gap equations at the critical temperature $T = T_c$ and calculate $T_c$ and the chemical potential $μ$ as a function of the number of carriers $n$ for various values of pairing interactions, $V_{1,1}$, $V_{2,2}$, and $V_{1,2}$. The results …
We study three-dimensional time-reversal-invariant topological superconductivity in noncentrosymmetric materials such as RhSi, CoSi, and AlPt which host coupled multifold nodes energetically split by the spin-orbit coupling at the same time-reversal-invariant momentum (TRIM). The topological superconductivity arises from the $s_{+} \oplus s_{-}$ gap function, which is $\boldsymbol{k}$ independent, but with opposite signs for the two nodes split at the same TRIM. We consider various electron-electron interactions in the tight-binding model for RhSi and find that the topological superconducting …
I solved the Eliashberg equations for multiband non-phononic $s\pm$ wave spin glass superconductor and I calculated the temperature dependence of the gaps and superfluid density that reveals unusual behavior as non monotonic temperature dependence and reentrant superconductivity. For particular values of input parameters the phase diagram is still more complex with two different ranges of temperature where the superconductivity appears.
We report measurements of the London penetration depth $Δλ(T)$ and the electronic specific heat $C_e(T)$ on high-quality single crystals of the filled-skutterudite superconductor PrPt$_4$Ge$_{12}$ ($T_c\simeq$8K). Both quantities show a weak temperature dependence at $T\ll T_c$, following $Δλ\sim T^n$ ($n\simeq 3.2$) and $C_e/T\sim T^{2.8}$. Such temperature dependences deviate from both conventional s-wave type and nodal superconductivity. A detailed analysis indicates that the superfluid density $ρ_s(T)$, derived from the penetration depth, as well as the electronic specific heat can be cons…
Recently, superconductivity with spontaneous time-reversal or parity symmetry breaking is attracting much attention owing to its exotic properties, such as nontrivial topology and nonreciprocal transport. Particularly fascinating phenomena are expected when the time-reversal and parity symmetry are simultaneously broken. This work shows that time-reversal symmetry-breaking mixed-parity superconducting states generally exhibit an unusual asymmetric Bogoliubov spectrum due to nonunitary interband pairing. For generic two-band models, we derive the necessary conditions for the asymmetric Bogoliub…
Point-contact spectroscopy was originally developed for the determination of the electron-phonon spectral function in normal metals. However, in the past 20 years it has become an important tool in the investigation of superconductors. As a matter of fact, point contacts between a normal metal and a superconductor can provide information on the amplitude and symmetry of the energy gap that, in the superconducting state, opens up at the Fermi level. In this paper we review the experimental and theoretical aspects of point-contact spectroscopy in superconductors, and we give an experimental surv…
We carried out the measurements of magnetoresistance, magnetic susceptibility and specific heat on crystals of the low-dimensional transition metal telluride Ta$_4$Pd$_3$Te$_{16}$. Our results indicate that Ta$_4$Pd$_3$Te$_{16}$ is an anisotropic type-II superconductor with the extracted Ginzburg-Landau parameter $κ_{\text{GL}}=$ 84. The upper critical field $H_{c2}$($T$) shows a linear dependence at low temperature and the anisotropy of $H_{c2}$($T$) is strongly $T$-dependent, both of which indicate a multiband scenario. A detailed analysis reveals that the electronic specific heat $C_{\text{…
Recently it has been demonstrated that the pair-exchange coupling of quasi-one-dimensional (Q1D) bands with conventional higher-dimensional bands in one multiband superconducting material can result in the formation of robust aggregate pair condensate. In particular, it has been found that the Q1D thermal pair fluctuations are suppressed in the presence of deep conventional band(s), where the Fermi level is much larger than the characteristic cut-off energy. Here we report that impact of the Q1D fluctuations is significantly weakened even in the presence of nearly shallow higher-dimensional ba…
We report 31P-NMR and specific heat measurements on an iron (Fe)-based superconductor SrFe2(As0.65P0.35)2 with Tc=26 K, which have revealed the development of antiferromagnetic correlations in the normal state and the unconventional superconductivity(SC) with nodal gap dominated by the gapless low-lying quasiparticle excitations. The results are consistently argued with an unconventional multiband SC state with the gap-size ratio of different bands being significantly large; the large full gaps in s\pm-wave state keep Tc high, whereas a small gap with a nodal-structure causes gapless feature u…
We have investigated the specific heat of optimally-doped iron chalcogenide superconductor Fe(Te0.57Se0.43) with a high-quality single crystal sample. The electronic specific heat Ce of this sample has been successfully separated from the phonon contribution using the specific heat of a non-superconducting sample (Fe0.90Cu0.10)(Te0.57Se0.43) as a reference. The normal state Sommerfeld coefficient gamma_n of the superconducting sample is found to be ~ 26.6 mJ/mol K^2, indicating intermediate electronic correlation. The temperature dependence of Ce in the superconducting state can be best fitted…
We study the intrinsic anisotropy of the superconducting state in KFe$_2$As$_2$, using small-angle neutron scattering to image the vortex lattice as the applied magnetic field is rotated towards the FeAs crystalline planes. The anisotropy is found to be strongly field dependent, indicating multiband superconductivity. Furthermore, the high field anisotropy significantly exceeds that of the upper critical field, providing further support for Pauli limiting in KFe$_2$As$_2$ for field applied in the basal plane. The effect of Pauli paramagnetism on the unpaired quasiparticles in the vortex cores …
Emergence of superconductivity in a two-band system coupled with breathing and Jahn-Teller phonons is discussed in a weak-coupling limit. With the use of a standard quantum mechanical procedure, the phonon-mediated attraction is derived. From the analysis of the model including such attraction, a BCS-like formula for a superconducting transition temperature $T_{\rm c}$ is obtained. When only the breathing phonon is considered, $T_{\rm c}$ is the same as that of the one-band model. On the other hand, when Jahn-Teller phonons are active, $T_{\rm c}$ is significantly enhanced by the interband att…
Measurements of the London penetration depth and tunneling conductance in single crystals of the recently discovered stoicheometric, iron - based superconductor, CaKFe$_4$As$_4$ (CaK1144) show nodeless, two effective gap superconductivity with a larger gap of about 6-9 meV and a smaller gap of about 1-4 meV. Having a critical temperature, $T_{c,onset}\approx$35.8 K, this material behaves similar to slightly overdoped Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ (e.g. $x=$0.54, $T_c \approx$ 34 K)---a known multigap $s_{\pm}$ superconductor. We conclude that the superconducting behavior of stoichiometric CaK11…
We examine the impact of interfacial phonons on the superconducting state of FeSe/SrTiO$_3$ developing a material's specific multiband, full bandwidth, and anisotropic Eliashberg theory for this system. Our self-consistent calculations highlight the importance of the interfacial electron-phonon interaction, which is hidden behind the seemingly weak-coupling constant λ$_m$ = 0.4, in mediating the high T$_c$, and explain other puzzling experimental observations, such as the s-wave symmetry and replica bands. We discover that the formation of replica bands has a T$_c$ decreasing effect that is ne…
We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. The Fermi-Dirac statistics of electrons allows a spin-triplet s-wave pairing order as well as a spin-singlet s-wave order parameter due to the two-band degree of freedom. In a spin-singlet superconductor, $T_c$ is insensitive to the impurity concentration when we estimate the self-energy due to the random impurity potential within the Born approximation. On the other hand in …
The phenomenology of LiFeAs superconductor can be explained in the framework of a four-band s$\pm$-wave Eliashberg theory. We have examined the experimental data available in literature and we have found out that it is possible to reproduce the experimental critical temperature, the gap values and the upper critical magnetic field within an effective model in moderate strong-coupling regime that must include both an intraband term $λ_{11}\sim0.9$ and an interband spin-fluctuations ($λ_{tot}^{sf}\sim1.5$) coupling. The presence of a non negligible intraband coupling can be a fictitious effect o…
We study the role of impurities in a two-band superconductor, and elucidate the nature of the recently predicted transition from s_{+-} state to s_{++} state induced by interband impurity scattering. Using a Ginzburg-Landau theory, derived from microscopic equations, we demonstrate that close to T_c this transition is necessarily a direct one, but deeper in the superconducting state an intermediate complex state appears. This state has a distinct order parameter, which breaks the time-reversal symmetry, and is separated from the s_{+-} and s_{++} states by phase transitions. Based on our resul…
Optical conductivity signatures of strong correlations and multiband superconductivity in infinite-layer nickelates
Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）；Department of Applied Physics, Stanford University（斯坦福大学应用物理系）；Department of Material Science Engineering, Pusan National University（釜山国立大学材料科学与工程系）；Department of Physics, Stanford University（斯坦福大学物理系）；Center for Correlated Electron Systems, Institute for Basic Science（基础科学研究院相关电子系统中心）；Department of Physics and Astronomy, Seoul National University（首尔国立大学物理与天文学系）；State Key Laboratory of Surface Physics and Department of Physics, Fudan University（复旦大学表面物理国家重点实验室及物理系）；Department of Physics, Hanyang University（汉阳大学物理系）
