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arXiv:0705.1201 · Journal of Physics Condensed Matter

Asymmetric superconductivity in metallic systems

M. A. Contínentino, Igor Tavares Padilha

Published Feb 14, 2008• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0953-8984/20/9/095216

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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.
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.
The study of multi-band superconductivity is relevant for a variety of systems, from ultra cold atoms with population imbalance to particle physics, and condensed matter. As a consequence, this problem has been widely investigated bringing to light many new and interesting phenomena. In this work we point out and explore a correspondence between a two-band metal with a kkk-dependent hybridization and a uniformly polarized fermionic system in the presence of spin-orbit coupling (SOC). We study the ground state phase diagram of the metal in the presence of an attractive interaction. We find a remarkable behavior of its superconducting properties whenever hybridization mixes orbitals of different parities in neighboring sites. We show this enhances superconductivity and drives the crossover from weak to strong coupling in analogy with SOC in cold atoms. We obtain the quantum phase transitions between the normal and superfluid states, as the intensity of different parameters characterizing the metal are varied, including Lifshitz transitions, with no symmetry breaking, associated with the appearance of soft modes in the Fermi surface.
The study of multi-band superconductivity is relevant for a variety of systems, from ultra cold atoms with population imbalance to particle physics, and condensed matter. As a consequence, this problem has been widely investigated bringing to light many new and interesting phenomena. In this work we point out and explore a correspondence between a two-band metal with a kkk-dependent hybridization and a uniformly polarized fermionic system in the presence of spin-orbit coupling (SOC). We study the ground state phase diagram of the metal in the presence of an attractive interaction. We find remarkable superconducting properties whenever hybridization mixes orbitals of different parities in neighboring sites. We show that this mechanism enhances superconductivity and drives the crossover from weak to strong coupling in analogy with SOC in cold atoms. We obtain the quantum phase transitions between the normal and superfluid states, as the intensity of different parameters characterizing the metal are varied, including Lifshitz transitions, with no symmetry breaking, associated with the appearance of soft modes in the Fermi surface.
The study of superconductivity in correlated systems is an exciting area of condensed matter physics. In this paper we consider superconducting ground states in systems described by two-band models with different effective masses. These two bands are coupled through an effective hybridization that can be directly tuned by pressure. We consider the cases of s-wave superconductivity associated with the electrons in a narrow band and also with inter-band pairing. To study the system in the strong coupling regime we introduce the s-wave scattering length a(s), and obtain the superconducting order parameters and the chemical potential as functions of the interaction strength 1/k(F)a(s) along the BCS-BEC crossover at T = 0. Finally, we discuss the phase diagram of this model as a function of external pressure and how our results can be applied for two-band systems as Fe pnictides or heavy fermions. The main result of this study is the occurrence of a superconducting quantum critical point (SQCP) in this two-band model.
Candidate homogeneous, isotropic superfluid or superconducting states of paired fermion species with different chemical potentials, can lead to quasiparticle excitation energies that vanish at either 0, 1, or 2 spheres in momentum space. With no zeros, we have a conventional BCS superconductor. The other two cases, ``gapless'' superconductors, appear in mean- field theory for sufficiently large mismatches and/or sufficiently large coupling strengths. Here we examine several stability criteria for those candidate phases. Positivity of number susceptibility appears to provide the most powerful constraint, and renders all the two-zero states that we have examined mechanically unstable. Our results should apply directly to ultracold fermionic atom systems.
In this paper, the sixth in series, we continue our analysis of the interplay between non-Fermi liquid and pairing in the effective low-energy model of fermions with singular dynamical interaction $V({\mathrm{\ensuremath{\Omega}}}_{m})={\overline{g}}^{\ensuremath{\gamma}}/{|{\mathrm{\ensuremath{\Omega}}}_{m}|}^{\ensuremath{\gamma}}$ (the $\ensuremath{\gamma}$ model). The model describes low-energy physics of various quantum-critical metallic systems at the verge of an instability towards density or spin order, pairing of fermions at the half-filled Landau level, color superconductivity, and pairing in SYK-type models. In previous papers I--V, we analyzed the $\ensuremath{\gamma}$ model for $\ensuremath{\gamma}\ensuremath{\le}2$ and argued that the ground state is an ordinary superconductor, but there is an infinite number of local minima of the condensation energy. We further argued that the condensation energy spectrum becomes continuous and gapless, and superconducting Tc{T}_{c}Tc​ vanishes due to critical longitudinal gap fluctuations. In this paper, we consider larger $2<\ensuremath{\gamma}<3$. We show that the system moves away from criticality in that the condensation energy spectrum again becomes discrete and gapless, and Tc{T}_{c}Tc​ becomes finite. Yet, we show that the gap functions for $\ensuremath{\gamma}>2$ and $\ensuremath{\gamma}<2$ are topologically different as they live on different sheets of the Riemann surface. This makes $\ensuremath{\gamma}=2$ a topological quantum-critical point. We further show that the fermionic excitation spectrum for $\ensuremath{\gamma}>2$ acquires a new feature---a bound state at the edge of a continuum, with a macroscopic degeneracy, which is a fraction of the total number of states in the system. We obtain the phase diagram on the $({\ensuremath{\omega}}_{D},\ensuremath{\gamma})$ plane, where ${\ensuremath{\omega}}_{D}$ is a mass of a pairing boson, and on the $(T,\ensuremath{\gamma})$ plane. The latter consists of two distinct superconducting phases at $\ensuremath{\gamma}<2$ and $\ensuremath{\gamma}>2$ and the intermediate pseudogap state of preformed pairs in between.