Interband Pairing Interaction Research Articles

Coupled ferroelectricity and superconductivity in bilayer Td-MoTe2.

Achieving electrostatic control of quantum phases is at the frontier of condensed matter research. Recent investigations have revealed superconductivity tunable by electrostatic doping in twisted graphene heterostructures and in two-dimensional semimetals such as WTe2 (refs. 1-5). Some of these systems have a polar crystal structure that gives rise to ferroelectricity, in which the interlayer polarization exhibits bistability driven by external electric fields6-8. Here we show that bilayer Td-MoTe2 simultaneously exhibits ferroelectric switching and superconductivity. Notably, a field-driven, first-order superconductor-to-normal transition is observed at its ferroelectric transition. Bilayer Td-MoTe2 also has a maximum in its superconducting transition temperature (Tc) as a function of carrier density and temperature, allowing independent control of the superconducting state as a function of both doping and polarization. We find that the maximum Tc is concomitant with compensated electron and hole carrier densities and vanishes when one of the Fermi pockets disappears with doping. We argue that this unusual polarization-sensitive two-dimensional superconductor is driven by an interband pairing interaction associated with nearly nested electron and hole Fermi pockets.

Quantitative assessment of the role of spin fluctuations in 2D Ising superconductor NbSe2

Accurate determination of the full momentum-dependent spin susceptibility χ(q) is very important for the description of magnetism and superconductivity. While in principle the formalism for calculating χ(q) in the linear response density functional theory (DFT) is well established, hardly any publicly available code includes this capability. Here, we describe an alternative way to calculate the static χ(q), which can be applied to most common DFT codes without additional programming. The method combines standard fixed-spin-moment calculations of χ(0) with direct calculations of the energy of spin spirals stabilized by an artificial Hubbard interaction. From these calculations, χDFT(q) can be extracted by inverting the RPA formula. We apply this recipe to the recently discovered Ising superconductivity in NbSe2 monolayer, one of the most exciting findings in superconductivity in recent years. It was proposed that spin fluctuations may strongly affect the parity of the order parameter. Previous estimates suggested proximity to ferromagnetism, i.e., χ(q) peaked at q=0. We find that the structure of spin fluctuations is more complicated, with the fluctuation spectrum sharply peaked at q≈(0.2,0). Such a spectrum would change the interband pairing interaction and considerably affect the superconducting state.

Superfluid properties of an ultracold Fermi gas with an orbital Feshbach resonance in the BCS-BEC crossover region

We theoretically investigate superfluid properties of a two-band gas of $^{173}$Yb Fermi atoms with an orbital Feshbach resonance (OFR). To describe the BCS-BEC crossover region, we include superfluid fluctuations caused by inter-band and intra-band pairing interactions associated with OFR, by extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink to the two-band case below the superfluid phase transition temperature; however, effects of an experimentally inaccessible deep bound state are removed, to model a real $^{173}$Yb Fermi gas near OFR. We show that the condensate fraction in the upper closed channel gradually becomes smaller than that in the lower open channel, as one moves from the strong- to the weak-coupling regime, because the OFR-pairing mechanism tunes the interaction strengths by adjusting the energy difference between the two bands. However, even when the closed-channel band is much higher in energy than the open-channel band in the weak-coupling regime, the magnitude of the superfluid order parameter in the closed channel is found to be still comparable to that in the open channel. As the reason for this, we point out a pair-tunneling effect by the OFR-induced inter-band interaction. Besides these superfluid quantities, we also examine collective modes, such as the Goldstone mode, Schmid (Higgs) mode, as well as Leggett mode, to clarify how they appear in the spectral weights of pair-correlation functions in each band. Since the realization of a multi-band superfluid Fermi gas is a crucial issue in cold Fermi gas physics, our results would contribute to the basic understanding of this type of Fermi superfluid in the BCS-BEC crossover region.

Singular ground state of multiband inhomogeneous superconductors

The interplay between interband and intraband pairing interactions in multiband systems can result in superconducting order parameter with the broken time-reversal symmetry (BTRS). Here we consider a slightly inhomogeneous superconductor with the BTRS order parameter in the framework of Ginzburg-Landau functional. We show that the Giznburg-Landau functional possesses a minimum with zero spontaneous internal magnetic fields in the absence of the external magnetic fields. This extension of the functional space is important for understanding of experimental situation in multiband superconductors.

Impact of disorder on the superconducting transition temperature near a Lifshitz transition

Multi-band superconductivity is realized in a plethora of systems, from high-temperature superconductors to very diluted superconductors. While several properties of multi-band superconductors can be understood as straightforward generalizations of their single-band counterparts, recent works have unveiled rather unusual behaviors unique to the former case. In this regard, a regime that has received significant attention is that near a Lifshitz transition, in which one of the bands crosses the Fermi level. In this work, we investigate how impurity scattering $\tau^{-1}$ affects the superconducting transition temperature $T_{c}$ across a Lifshitz transition, in the regime where intra-band pairing is dominant and inter-band pairing is subleading. This is accomplished by deriving analytic asymptotic expressions for $T_{c}$ and $\partial T_{c}/\partial\tau^{-1}$ in a two-dimensional two-band system. When the inter-band pairing interaction is repulsive, we find that, despite the incipient nature of the band crossing the Fermi level, inter-band impurity scattering is extremely effective in breaking Cooper pairs, making $\partial T_{c}/\partial\tau^{-1}$ quickly approach the limiting Abrikosov-Gor'kov value of the high-density regime. In contrast, when the inter-band pairing interaction is attractive, pair-breaking is much less efficient, affecting $T_{c}$ only mildly at the vicinity of the Lifshitz transition. The consequence of this general result is that the behavior of $T_{c}$ across a Lifshitz transition can be qualitatively changed in the presence of strong enough disorder: instead of displaying a sharp increase across the Lifshitz transition, as in the clean case, $T_{c}$ can actually display a maximum and be suppressed at the Lifshitz transition. These results shed new light on the non-trivial role of impurity scattering in multi-band superconductors.

Unconventional Multiband Superconductivity in Bulk SrTiO_{3} and LaAlO_{3}/SrTiO_{3} Interfaces.

Although discovered many decades ago, superconductivity in doped SrTiO_{3} remains a topic of intense research. Recent experiments revealed that, upon increasing the carrier concentration, multiple bands cross the Fermi level, signaling the onset of Lifshitz transitions. Interestingly, T_{c} was observed to be suppressed across the Lifshitz transition of oxygen-deficient SrTiO_{3}; a similar behavior was also observed in gated LaAlO_{3}/SrTiO_{3} interfaces. Such a behavior is difficult to explain in the clean theory of two-band superconductivity, as the additional electronic states provided by the second band should enhance T_{c}. Here, we show that this unexpected behavior can be explained by the strong pair-breaking effect promoted by disorder, which takes place if the interband pairing interaction is subleading and repulsive. A consequence of this scenario is that, upon moving away from the Lifshitz transition, the two-band superconducting state changes from opposite-sign gaps to same-sign gaps.

Gap Symmetry of the Heavy Fermion Superconductor CeCu_{2}Si_{2} at Ambient Pressure.

Recent observations of two nodeless gaps in superconducting CeCu_{2}Si_{2} have raised intensive debates on its exact gap symmetry, while a satisfactory theoretical basis is still lacking. Here we propose a phenomenological approach to calculate the superconducting gap functions, taking into consideration both the realistic Fermi surface topology and the intra- and interband quantum critical scatterings. Our calculations yield a nodeless s^{±}-wave solution in the presence of strong interband pairing interaction, in good agreement with experiments. This provides a possible basis for understanding the superconducting gap symmetry of CeCu_{2}Si_{2} at ambient pressure and indicates the potential importance of multiple Fermi surfaces and interband pairing interaction in understanding heavy fermion superconductivity.

Strong Landau-quantization effects in high-magnetic-field superconductivity of a two-dimensional multiple-band metal near the Lifshitz transition

We investigate the onset of superconductivity in magnetic field for a clean two-dimensional multiple-band superconductor in the vicinity of the Lifshitz transition when one of the bands is very shallow. Due to small number of carriers in this band, the quasiclassical Werthamer-Helfand approximation breaks down and Landau quantization has to be taken into account. We found that the transition temperature TC2(H) has giant oscillations and is resonantly enhanced at the magnetic fields corresponding to full occupancy of the Landau levels in the shallow band. This enhancement is especially pronounced for the lowest Landau level. As a consequence, the reentrant superconducting regions in the temperature-field phase diagram emerge at low temperatures near the magnetic fields at which the chemical potential matches the Landau levels. The specific behavior depends on the relative strength of the intraband and interband pairing interactions and the reentrance is most pronounced in the purely interband coupling scenario. The reentrant behavior is suppressed by the Zeeman spin splitting in the shallow band, the separated regions disappear already for very small spin-splitting factors. On the other hand, the reentrance is restored in the resonance cases when the spin-splitting energy exactly matches the separation between the Landau levels. The predicted behavior may realize in the gate-tuned FeSe monolayer.

Two-Fluid Description of Two-Band Superconductors

We present a systematic study of the response properties of two-band (multi-gap) superconductors with spin-singlet (s-wave) pairing correlations, which are assumed to be caused by both intraband (\lambda_{ii}, i=1,2) and interband (\lambda_{12}) pairing interactions. In this first of three planned publications we concentrate on the properties of such superconducting systems in global and local thermodynamic equilibrium, the latter including weak perturbations in the stationary long-wavelength limit. The discussion of global thermodynamic equilibrium must include the solution (analytical in the Ginzburg-Landau and the low temperature limit) of the coupled self-consistency equations for the two energy gaps \Delta_i(T), i=1,2. These solutions allow to study non-universal behavior of the two relevant BCS-M\"uhlschlegel parameters, namely the specific heat discontinuity \Delta C/C_N and the zero temperature gaps \Delta_i(0)/\pi k_B T_c, i=1,2. The discussion of a local equilibrium situation includes the calculation of the supercurrent density as a property of the condensate, and the calculation of both the specific heat capacity and the spin susceptibility as properties of the gas of thermal excitations in the spirit of a microscopic two-fluid description. Non-monotonic behavior in the temperature dependences of the gaps and all these local response functions is predicted to occur particularly for very small values of the interband pair-coupling constant \lambda_{12}.

Superconductivity in multiband disordered systems: A vector recursion approach

We present a vector recursion based approach to study the effect of disorder on superconductivity in a system modeled by the two-band attractive Hubbard model. We use the augmented space formalism for the disorder averaging. In the presence of only intraband pairing in a two-band disordered system with disorder in either or both bands, our calculations reveal that the gap survives in the quasiparticle spectrum; similar to single band systems. However, for interband pairing the gap in the quasiparticle spectrum ceases to exist beyond a critical value of the disorder strength. In the presence of both interband and intraband pairing interaction, depending on the relative magnitude of the pairing strength, only a particular kind of pairing is possible for a half filled two-band system.

Two-band BCS mechanism of superconductivity in a Ba(Fe0.9Co0.1)2As2 high-temperature superconductor

Terahertz and infrared spectra of the conductivity, σ(ν), and dielectric constant, ɛ(ν), of a Ba(Fe0.9Co0.1)2As2 film (Tc = 20 K) have been analyzed together with previous specific-heat and angular resolved photoelectron spectroscopy data. It has been shown that the spectra σ(ν) and ɛ(ν) of Ba(Fe0.9Co0.1)2As2 in the superconducting phase at T = 5 K, as well as the magnetic field penetration depth, can be described well using the standard Bardeen-Cooper-Schrieffer (BCS) model with an additive contribution of electron and hole bands. It has been found that the measured temperature dependence of the magnetic field penetration depth in a wide temperature range 5 K < T < Tc can be described only with the introduction of interband pairing interaction. The coupling constant of electron and hole bands, λ1, 2 = 0.1, as well as the temperature dependences of superconducting gaps in the electron and hole subsystems, has been determined using the model of two-band superconductivity developed earlier for MgB2.

Two-band Bardeen-Cooper-Schrieffer superconducting state of the iron pnictide compound Ba(Fe0.9Co0.1)2As2

The conductivity and permittivity optical spectra of iron-pnictide Ba(Fe0.9Co0.1)2As2 film (Tc=20 K) are analyzed. In the superconducting state, at all temperatures up to Tc the temperature dependences of the magnetic field penetration depth and of the superconducting condensate density are well described within the generalized two-band BCS model with intraband and interband pairing interactions considered. It is shown that the smaller superconducting energy gap 2{\Delta} = 3.7 meV develops in the electronic subsystem while the larger gap 2{\Delta} >= 7 meV opens in the hole subsystem. The normal state parameters (plasma frequencies and scattering rates) of electron and hole conduction bands are determined. At all temperatures the obtained data are consistent with the results of electronic photoemission experiments on Ba(Fe1-x Cox)2As2.

Interband superconductivity in spin-polarized subbands

Singlet superconductivity in spin-polarized subbands, induced by interband pairing interaction, is investigated. A Suhl-type mean-field Hamiltonian is used. The necessary attractive coupling can induce pairing correlations also for the vanishing subbands mismatch shift. The behaviour of superconducting characteristics over the system parameters space is calculated and illustrated. Varying of the pairing strength displays also global phases with inclined metastable superconducting or normal states. First order phase transitions can be expected.

Multiple bands – A key to high-temperature superconductivity in iron arsenides?

In the framework of four-band model of superconductivity in iron arsenides proposed by Barzykin and Gor’kov we analyze the gap ratios on hole-like and electron-like Fermi surface cylinders. It is shown that experimentally observed (ARPES) gap ratios can be obtained only within rather strict limits on the values of intraband and interband pairing coupling constants. The difference of Tc values in 1111 and 122 FeAs systems is reasonably explained by the relative values of partial densities of states, obtained from LDA calculations. The main conclusion following from our analysis is the simple fact that the value of Tc in multiple bands systems is determined by the relations between partial densities of states on different sheets of the Fermi surface, and not only by the total density of states at the Fermi level as in the standard BCS model. The multiple bands electronic structure of iron arsenides leads to a significant enhancement of effective pairing coupling constant determining Tc, so that high enough Tc values can be achieved even for the case of rather small intraband and interband pairing interactions.

Multiple bands: A key to high-temperature superconductivity in iron arsenides?

In the framework of four-band model of superconductivity in iron arsenides proposed by Barzykin and Gor’kov we analyze the gap ratios on hole—like and electron—like Fermi—surface cylinders. It is shown that experimentally observed (ARPES) gap ratios can be obtained only within rather strict limits on the values of pairing coupling constants. The difference of Tc values in 1111 and 122 systems is reasonably explained by the relative values of partial densities of states. The multiple bands electronic structure of these systems leads to a significant enhancement of effective pairing coupling constant determining Tc, so that high enough Tc values can be achieved even for the case of rather small intraband and interband pairing interactions.

Possible pairing states of the Fe-based superconductors

We consider the minimal two-band model for the Fe-based superconductors with a phenomenological pairing interaction which mimics short-range antiferromagnetic fluctuations. Two superconducting (SC) gap solutions are found to exist with the model: sign-changing $s$-wave gap ($\ifmmode\pm\else\textpm\fi{}s$ wave) and double $d$-wave gap states. Both solutions hold the approximate relation ${\ensuremath{\Delta}}_{h}^{\text{max}}{N}_{h}\ensuremath{\approx}{\ensuremath{\Delta}}_{e}^{\text{max}}{N}_{e}$, a generic feature of two-band model with a dominant interband pairing interaction. We carried out the calculations of the SC properties of the both SC states such as the density of states, temperature dependencies of spin-lattice relaxation rate $1/{T}_{1}$, Knight shift, and penetration depth, particularly taking into account of the interband coherence factors. The results are discussed in comparison with the currently available experimental data.

Observation of Interband Pairing Interaction in a Two-Band Superconductor:MgB2

The recently discovered anisotropic superconductor MgB2 is the first of its kind showing the intriguing properties of two-band superconductivity. By tunneling experiments using thin film tunnel junctions, electron-coupled phonon spectra were determined showing that superconductivity in MgB2 is phonon mediated. In a further analysis, which involves first principles calculations, the strongest feature in these spectra could be traced back to the key quantity of two-band superconductivity, the interband pairing interaction. For the phonons, this interaction turns out quite selective. It involves mainly low-energy optical phonon modes, where the boron atoms move perpendicular to the boron planes.

Fermi surface topology and vortex state in MgB 2

Based on a detailed modeling of the Fermi surface topology of MgB 2 we calculated the anisotropy of the upper critical field B c2 within the two gap model. The σ-band is modeled as a distorted cylinder and the π-band as a half-torus, with parameters determined from bandstructure calculations. Our results show that the unusual strong temperature dependence of the B c2 anisotropy, that has been observed recently, can be understood due to the small c-axis dispersion of the cylindrical Fermi surface sheets and the small interband pairing interaction as obtained from bandstructure calculations. We calculate the magnetic field dependence of the density of states within the vortex state for field in c-axis direction and compare with recent measurements of the specific heat on MgB 2 single crystals.

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.

Definitive experimental evidence for two-band superconductivity in MgB2.

The superconducting-gap of MgB2 has been studied by high-resolution angle-resolved photoemission spectroscopy. The results show that superconducting gaps with values of 5.5 and 2.2 meV open on the sigma band and the pi band, respectively, but both the gaps close at the bulk transition temperature, providing a definitive experimental evidence for the two-band superconductivity with strong interband pairing interaction in MgB2. The experiments validate the role of k-dependent electron-phonon coupling as the origin of multiple-gap superconductivity as well as the high transition temperature of MgB2.