Interband Pairing Research Articles

Spontaneous Appearance of the Spin-Triplet Fulde-Ferrell-Larkin-Ovchinnikov Phase in a Two-Band Model: Possible Application to LaFeAsO 1−x F x

The possibility of a spontaneous spin-triplet paired phase of the Fulde-Ferrell-Larkin-Ovchinnikov type is studied. As it is shown in a system with the dominant interband pairing and two distinct Fermi surface sheets, the Fermi wave-vector mismatch can be compensated by a nonzero center-of-mass momentum of the Cooper pairs. This idea is examined with the use of a model which describes the two hole-like bands in the iron-based superconductor. It is shown that for the proper range of model parameters, the minima of the free energy appear which correspond to a nonzero Cooper pair momentum. Different superconducting gap symmetries are analyzed, and the corresponding phase diagrams are shown.

Intra-inter band pairing, order parameter symmetry in Fe-based superconductors: A model study

In the quest of why there should be a single transition temperature in a multi-gapped system like Fe-based materials we use two band model for simplicity. The model comprises of spin density wave (SDW), orbital density wave (ODW) arising due to nested pieces of the electron and hole like Fermi surfaces; together with superconductivity of different pairing symmetries around electron and hole like Fermi surfaces. We show that either only intra or only inter band pairing is insufficient to describe some of the experimental results like large to small gap ratio, thermal behaviour of electronic specific heat jump etc. It is shown that the inter-band pairing is essential in Fe-based materials having multiple gaps to produce a single global Tc. Some of our results in this scenario, matches with the earlier published work (Dolgov et al., 2009), and also have differences. The origin of difference between the two is also discussed. Combined intra–inter band pairing mechanism produces the specific heat jump to superconducting transition temperature ratio proportional to square of the transition temperature, both in the electron and hole doped regime, for sign changing s± wave symmetry which takes the d+s pairing symmetry form. Our work thus demonstrates the importance of combined intra-inter band pairing irrespective of the pairing mechanism.

Complex state induced by impurities in multiband superconductors

We study the role of impurities in a two-band superconductor, and elucidate the nature of the recently predicted transition from the ${s}_{\ifmmode\pm\else\textpm\fi{}}$ state to the ${s}_{++}$ 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 ${s}_{\ifmmode\pm\else\textpm\fi{}}$ and ${s}_{++}$ states by continuous phase transitions. Based on our results, we suggest a phase diagram for systems with weak repulsive interband pairing, and discuss its relevance to iron-based superconductors.

Spin fluctuations, Fermi surface hotspots and nesting in PuCoGa5

ABSTRACTSurprisingly little is known about the mechanism and symmetry of superconducting pairing in PuCoGa5. A common thread with other unconventional superconductors is the presence of spin fluctuations in the normal state, which in this particular case is controlled by strong spin–orbit coupling split bands. The many and anisotropic Fermi surfaces make the guessing of the potential spin-fluctuation nesting vector and resulting symmetry of the pairing function a nontrivial task. To provide much needed guidance for the identification of the pairing symmetry in this multiband superconductor, we perform first-principles based magnetic spin susceptibility calculations to identify the dominant nesting vectors that potentially give rise to interband pairing with nodal d- or s±-wave gap functions.

Leggett modes in iron-based superconductors as a probe of time-reversal symmetry breaking

Since their discovery, it has been suggested that pairing in pnictides can be mediated by spin fluctuations between hole and electron bands. In this view, multiband superconductivity would substantially differ from other systems like MgB2, where pairing is predominantly intraband. Indeed, interband-dominated pairing leads to the coexistence of bonding and antibonding superconducting channels. Here we show that this has profound consequences on the nature of the low-energy superconducting collective modes. In particular, the so-called Leggett mode for phase fluctuations is absent in the usual two-band description of pnictides. On the other hand, when also the repulsion between the hole bands is taken into account, a more general three-band description should be used, and a Leggett mode is then allowed. Such a model, that has been proposed for strongly hole-doped 122 compounds, can also admit a low-temperature s+is phase which breaks the time reversal symmetry. We show that the (quantum and thermal) transition from the ordinary superconductor to the s+is state is accompanied by the vanishing of the mass of Leggett-like phase fluctuations, regardless the specific values of the interaction parameters. This general result can be obtained by means of a generalized construction of the effective action for the collective degrees of freedom that allows us also to deal with the non-trivial case of dominant interband pairing.

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 with Rashba spin–orbit coupling and magnetic field

Two-dimensional electron systems at oxide interfaces are often influenced by a Rashba type spin–orbit coupling, which is tunable by a transverse electric field. Ferromagnetism near the interface can simultaneously induce strong local magnetic fields. This combination of spin–orbit coupling and magnetism leads to asymmetric two-sheeted Fermi surfaces, on which either intra- or inter-band pairing is favored. The superconducting order parameters are derived within a microscopic pairing model realizing both the Bardeen–Cooper–Schrieffer superconductor with inter-band pairing and a mixed parity state with finite-momentum intra-band pairing. We present a phase diagram for the superconducting groundstates and analyze the density of states, the spectra, and the momentum distribution functions of the different phases. The results are discussed in the context of superconductivity and ferromagnetism at LaAlO3–SrTiO3 interfaces and superconductors with broken inversion symmetry.

Topological Transitions of Gapless Paired States in Mixed-Geometry Lattices

We propose a mixed-geometry system of fermionic species selectively confined in lattices of different geometry. We investigate how such asymmetry can lead to exotic multiband fermion pairing in an example system of honeycomb and triangular lattices. A rich phase diagram of interband pairing with gapped and gapless excitations is found at zero temperature. We find that the two-band contribution of the honeycomb lattices to the paired state helps to stabilize the gapless phase with one or two Fermi surfaces. We also show that the Fermi surface topology further divides the gapless phase into subclasses between which the system undergoes density-driven Lifshitz transitions.

Two-band superconductivity in doped SrTiO3films and interfaces

We investigate the possibility of multi-band superconductivity in SrTiO$_{3}$ films and interfaces using a two-dimensional two-band model. In the undoped compound, one of the bands is occupied whereas the other is empty. As the chemical potential shifts due to doping by negative charge carriers or application of an electric field, the second band becomes occupied, giving rise to a strong enhancement of the transition temperature and a sharp feature in the gap functions, which is manifested in the local density of states spectrum. By comparing our results with tunneling experiments in Nb-doped SrTiO$_{3}$, we find that intra-band pairing dominates over inter-band pairing, unlike other known multi-band superconductors. Given the similarities with the value of the transition temperature and with the band structure of LaAlO$_{3}$/SrTiO$_{3}$ heterostructures, we speculate that the superconductivity observed in SrTiO$_{3}$ interfaces may be similar in nature to that of bulk SrTiO$_{3}$, involving multiple bands with distinct electronic occupations.

Theory of nonequilibrium dynamics of multiband superconductors

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 V12 which is much larger than the intraband pairing terms. The second model, relevant for MgB2, deals with the opposite limit where the intraband interactions are dominant and the interband pair scattering V12 is weak but attractive. For ultrashort pump pulses, both of these models exhibit a nonadiabatic behavior which is characterized by oscillations of the superconducting order parameters. We find that for nonvanishing V12, the superconducting gap on each band exhibits two oscillatory frequencies which are determined by the long-time asymptotic values of the gaps. The relative strength of these two frequency components depends sensitively on the magnitude of the interband interaction V12.

Quantum normal-to-inhomogeneous superconductor phase transition in nearly two-dimensional metals

In multi-band systems, electrons from different orbitals coexist at the Fermi surface. An attractive interaction among these quasi-particles gives rise to inter-band or hybrid pairs which eventually condense in a superconducting state. These quasi-particles have a natural mismatch of their Fermi wave-vectors, $\delta k_F$, which depends on the strength of the hybridization between their orbitals. The existence of this natural scale suggests the possibility of inhomogeneous superconducting ground states in these systems, even in the absence of an applied magnetic field. Furthermore, since hybridization $V$ depends on pressure, this provides an external parameter to control the wave-vectors mismatch at the Fermi surface. In this work, we study the phase diagram of a two-dimensional, two-band metal with inter-band pairing. We show that as the mismatch between the Fermi wave-vectors of the two hybrid bands is reduced, the system presents a normal-to-inhomogeneous superconductor quantum phase transition at a critical value of the hybridization $V_c=\Delta_0$. The superconducting ground state for $V<V_c$ is characterized by a wave-vector with magnitude $|\mathbf{q}_c|=q_c=2 \Delta_0/\bar{v}_f$. Here $\Delta_0$ is the superconducting gap in the homogeneous state and $\bar{v}_f$ the average Fermi velocity. We discuss the nature of the quantum critical point (QCP) at $V_c$ and obtain the associated quantum critical exponents.

THE PSEUDOGAP IN MULTIBAND SUPERCONDUCTIVITY

The pseudogap (PG) excitation is analyzed as a natural event in multiband superconductivity. It corresponds to minimal quasiparticle excitation energy of an electron band not touched by the chemical potential. The critical points of the phase diagram are determined by vanishing conditions for normal state pseudogaps (NPG). For two bands (gapped or overlapping) these are positioned on edges of the superconducting dome. Theoretical background for a three-band system with two interband pairing channels is developed. There are three independent superconducting gaps (SCG). The PG is associated with the band component possessing a bare gap which can be quenched by doping. At low doping the PG and the SCG of another band component coexist. The critical point is not fixed in respect of the transition temperature (Tc) dome background. The depletion of the PG associated states is restored here. This effect can also be indirect by the participation of these states in determining the chemical potential position. At the critical point the PG looses its normal state contribution and continues as the SCG of the same band. Illustrative examples on the doping scale have been calculated.

Whether There is the Intrinsic Hall Effect in a Multi-Band Superconductor?

The interplay of the microscopic models and the symmetry considerations in application to the superconducting state of putative chiral superconductor Sr2RuO4 are presented. There is demonstrated that chiral two-band superconducting ordering recently proposed as candidate for the superconducting state in this material and having the long-expected property such as the intrinsic Hall effect does not exist as energetically disadvantageous in comparison with the states not supporting the Hall effect. Other chiral multi-band superconducting states with intraband pairing do not support an intrinsic Hall properties as well. The superconducting states with direct interband pairing could serve as the probable candidates for the Hall effect existence.

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.

Designing heterostructures with higher-temperature superconductivity

We propose to increase the superconducting transition temperature ${T}_{c}$ of strongly correlated materials by designing heterostructures which exhibit a high pairing energy as a result of magnetic fluctuations. More precisely, applying an effective theory of the doped Mott insulator, we envisage a bilayer Hubbard system where both layers exhibit intrinsic intralayer (intraband) $d$-wave superconducting correlations. Introducing a finite asymmetry between the hole densities of the two layers such that one layer becomes slightly more underdoped and the other more overdoped, we show a visible enhancement of ${T}_{c}$ compared to the optimally doped isolated layer. Using the bonding and antibonding band basis, we show that the mechanism behind this enhancement of ${T}_{c}$ is the interband pairing correlation mediated by the hole asymmetry which strives to decrease the paramagnetic nodal contribution to the superfluid stiffness. For two identical layers, ${T}_{c}$ remains comparable to that of the isolated layer until moderate values of the interlayer single-particle tunneling term. These heterostructures shed new light on fundamental questions related to superconductivity.

On the interband pairing in doped graphane

An estimation shows that the interband pairing channel between the valence band components of doped graphane can support a superconducting transition temperature (or a contribution into this expected event) of the order of 100 K at the coupling strength near 1 eV.

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.

Electron transport across the interface of a normal metal and a two-band superconductor with interband pairing

A consistent scheme taking into account both intra- and interband pairings has been proposed for diagonalizing the Hamiltonian of a superconductor. The temperature dependence of the order parameter of the superconductor with interband pairing has been calculated. The electron transport across the interface of a normal metal and the two-band superconductor with interband pairing has been analyzed.

Pair density wave instability and Cooper pair insulators in gapped fermion systems

By analyzing simple models of fermions in lattice potentials we argue that the zero-temperature pairing instability of any ideal band-insulator occurs at a finite momentum. The resulting supersolid state is known as "pair density wave". The pairing momentum at the onset of instability is generally incommensurate as a result of phase-space restrictions and relative strengths of interband and intraband pairing. However, commensurate pairing occurs in the strong-coupling limit and becomes a Cooper-channel analogue of the Halperin-Rice exciton condensation instability in indirect bandgap semiconductors. The exceptional sensitivity of incommensurate pairing to quantum fluctuations can lead to a strongly-correlated insulating regime and a non-BCS transition, even in the case of weak coupling as shown by an exact renormalization group analysis.