Superconductivity in strongly correlated systems is a remarkable phenomenon that attracts a huge interest. The study of this problem is relevant for materials as the high
Tc oxides, pnictides and heavy fermions. These systems also have in common the existence of electrons of several orbitals that coexist at a common Fermi-surface. In this paper we study the effect of pressure, chemical or applied on multi-band superconductivity. Pressure varies the atomic distances and consequently the overlap of the wave-functions in the crystal. This rearranges the electronic structure that we model including a pressure dependent hybridization between the bands. We consider the case of two-dimensional systems in a square lattice with inverted bands. We study the conditions for obtaining a pressure induced superconductor quantum critical point and show that hybridization, i.e., pressure can induce a BCS-BEC crossover in multi-band systems even for moderate interactions. We briefly discuss the influence of the symmetry of the order parameter in the results.
Superconductivity in iron-based, magnesium diborides, and other novel superconducting materials has a strong multi-band and multi-gap character. Recent experiments support the possibillity for a BCS-BEC crossover induced by strong-coupling and proximity of the chemical potential to the band edge of one of the bands. Here we study the simplest theoretical model which accounts for the BCS-BEC crossover in a two-band superconductor, considering tunable interactions and tunable energy separations between the bands. Mean-field results for condensate fraction, correlation length, and superconducting gap are reported in typical crossover diagrams to locate the boundaries of the BCS, crossover, and BEC regimes. When the superconducting gap is of the order of the local chemical potential, superconductivity is in the crossover regime of the BCS-BEC crossover and the Fermi surface of the small band is smeared by the gap opening. In this situation, small and large Cooper pairs coexist in the total condensate, which is the optimal condition for high-Tc superconductivity. The ratio between the gap and the Fermi energy in a given band results to be the best detection parameter for experiments to locate the system in the BCS-BEC crossover. Using available experimental data, our analysis shows that iron-based superconductors have the partial condensate of the small Fermi surface in the crossover regime of the BCS-BEC crossover, supporting the recent ARPES findings.
In fermionic systems with different types of quasi-particles, attractive interactions can give rise to exotic superconducting states, such as pair density wave (PDW) superconductivity and breached pairing. In recent years the search for these new types of ground states in cold atoms and in metallic systems has been intense. In the case of metals the different quasi-particles may be the up and down spin bands in an external magnetic field or bands arising from distinct atomic orbitals that coexist at a common Fermi surface. These systems present a complex phase diagram as a function of the difference between the Fermi wavevectors of the different bands. This can be controlled by external means, varying the density in the two-component cold atom system or, in a metal, by applying an external magnetic field or pressure. Here we study the zero temperature instability of the normal system as the Fermi wavevector mismatch of the quasi-particles (bands) is reduced and find a second order quantum phase transition to a PDW superconducting state. From the nature of the quantum critical fluctuations close to the superconducting quantum critical point (SQCP), we obtain its dynamic critical exponent. It turns out to be z = 2 and this allows us to fully characterize the SQCP for dimensions d ≥ 2.
We analyze the interplay between superconductivity and the formation of bound pairs of fermions (BCS-BEC crossover) in a 2D model of interacting fermions with small Fermi energy
EF and weak attractive interaction, which extends to energies well above
EF. The 2D case is special because a two-particle bound state forms at arbitrary weak interaction, and already at weak coupling, one has to distinguish between the bound-state formation and superconductivity. We briefly review the situation in the one-band model and then consider two different two-band models: one with one hole band and one electron band and another with two hole or two electron bands. In each case, we obtain the bound-state energy
2E0 for two fermions in a vacuum and solve the set of coupled equations for the pairing gaps and the chemical potentials to obtain the onset temperature of the pairing
Tins and the quasiparticle dispersion at
T=0. We then compute the superfluid stiffness ${\ensuremath{\rho}}_{s}(T=0)$ and obtain the actual
Tc. For definiteness, we set
EF in one band to be near zero and consider different ratios of
E0 and
EF in the other band. We show that at ${E}_{F}\ensuremath{\gg}{E}_{0}$, the behavior of both two-band models is BCS-like in the sense that ${T}_{c}\ensuremath{\approx}{T}_{\mathrm{ins}}\ensuremath{\ll}{E}_{F}$ and $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}{T}_{c}$. At ${E}_{F}\ensuremath{\ll}{E}_{0}$, the two models behave differently: in the model with two hole/two electron bands, ${T}_{\mathrm{ins}}\ensuremath{\sim}{E}_{0}/ln\frac{{E}_{0}}{{E}_{F}}, \mathrm{\ensuremath{\Delta}}\ensuremath{\sim}{({E}_{0}{E}_{F})}^{1/2}$, and ${T}_{c}\ensuremath{\sim}{E}_{F}$, like in the one-band model. In between
Tins and
Tc, the system displays a preformed pair behavior. In the model with one hole and one electron bands,
Tc remains of order
Tins, and both remain finite at
EF=0 and of the order of
E0. The preformed pair behavior still does exist in this model because
Tc is numerically smaller than
Tins. For both models, we reexpress
Tins in terms of the fully renormalized two-particle scattering amplitude by extending to the two-band case (the method pioneered by Gorkov and Melik-Barkhudarov back in 1961). We apply our results for the model with a hole and an electron band to Fe pnictides and Fe chalcogenides in which a superconducting gap has been detected on the bands that do not cross the Fermi level, and to FeSe, in which the superconducting gap is comparable to the Fermi energy. We apply the results for the model with two electron bands to Nb-doped
SrTiO3 and argue that our theory explains the rapid increase of
Tc when both bands start crossing the Fermi level.
Ultranarrow superconductors are in the strong quantum confinement regime with formation of multiple coherent condensates associated with the many subbands of the electronic structure. Here we analyze the multiband BCS-BEC crossover induced by the chemical potential tuned close to a subband bottom, in correspondence of a superconducting shape resonance. The evolution of the condensate fraction and of the pair correlation length in the ground state as functions of the chemical potential demonstrates the tunability of the BCS-BEC crossover for the condensate component of the selected subband. The extension of the crossover regime increases when the pairing strength and/or the characteristic energy of the interaction get larger. Our results indicate the coexistence of large and small Cooper pairs in the crossover regime, leading to the optimal parameter configuration for high transition temperature superconductivity.
Different types of superfluid ground states have been investigated in systems of two species of fermions with Fermi surfaces that do not match. This study is relevant for cold atomic systems, condensed matter physics, and quark matter. In this paper we consider this problem when the fermionic quasi-particles can transmute into one another and only their total number is conserved. We use a Bardeen–Cooper–Schrieffer (BCS) approximation to study superconductivity in two-band metallic systems with inter-and intra-band interactions. Tuning the hybridization between the bands varies the mismatch of the Fermi surfaces and produces different instabilities. For inter-band attractive interactions, we find a first-order normal–superconductor transition and a homogeneous metastable phase with gapless excitations. In the case of intra-band interactions, the transition from the superconductor to the normal state is continuous as hybridization increases and associated with a quantum critical point. The case when both interactions are present is also considered.