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Register a new userStable Sarma State in Two-band Fermi Systems
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We investigate fermionic superconductivity with mismatched Fermi surfaces in a general two-band system. The exchange interaction between the two bands changes significantly the stability structure of the pairing states. The Sarma state with two gapless Fermi surfaces which is always unstable in single-band systems, can be the stable ground state in two-band systems. To realize a visible mismatch window for the stable Sarma state, two conditions should be satisfied: a nonzero inter-band exchange interaction and a large asymmetry between the two bands.
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We discuss the stability of the antiferromagnetic ground state in two spatial dimensions. We start with a general analysis, based on Gribovs current-conservation techniques, of the bosonic modes in systems with magnetic order. We argue that the Goldstone $phi$ and Higgs $h$ modes mix in antiferromagnetic systems, and this leads to an effective $hhphi$ three-point interaction. We then analyze the instability of the antiferromagnetic system in two spatial dimensions by studying the non-perturbative behaviour of the Higgs boson self-energy using the Dyson--Schwinger equations. The ground state turns out to be unstable for all values of the three-point coupling. We interpret this as being due to the formation of a (high-$T_C$) superconducting condensate. The carrier doping dependence of the energy gap has a general behaviour that is consistent with high-$T_C$ superconductivity. Superconductivity co-exists with antiferromagnetic order for large magnetization, or small doping.
We investigate the stability of the Sarma phase in two-component fermion systems in three spatial dimensions. For this purpose we compare strongly-correlated systems with either relativistic or non-relativistic dispersion relation: relativistic quarks and mesons at finite isospin density and spin-imbalanced ultracold Fermi gases. Using a Functional Renormalization Group approach, we resolve fluctuation effects onto the corresponding phase diagrams beyond the mean-field approximation. We find that fluctuations induce a second order phase transition at zero temperature, and thus a Sarma phase, in the relativistic setup for large isospin chemical potential. This motivates the investigation of the cold atoms setup with comparable mean-field phase structure, where the Sarma phase could then be realized in experiment. However, for the non-relativistic system we find the stability region of the Sarma phase to be smaller than the one predicted from mean-field theory. It is limited to the BEC side of the phase diagram, and the unitary Fermi gas does not support a Sarma phase at zero temperature. Finally, we propose an ultracold quantum gas with four fermion species that has a good chance to realize a zero-temperature Sarma phase.
In the usual Ginzburg-Landau theory the critical value of the ratio of two fundamental length scales in the thery $kappa_c=1/sqrt{2}$ separates regimes of type-I and type-II superconductivity. The latter regime possess thermodynamically stable vortex excitations which interact with each other repulsively and tend to form vortex lattices. It was shown in [5] that this dichotomy in broken in U(1)xU(1) Ginzburg-Landau models which possess three fundamental length scales which results in the existence of a distinct phase with vortex excitations which interact attractively at large length scales and repulsively at shorter distances. Here we briefly review these results in particular discussing the role of interband Josephson coupling and the case where only one band is superconducting while superconductivity in another band is induced by interband proximity effect. The report is partially based on E. Babaev, J. Carlstrom, J. M. Speight arXiv:0910.1607.
While multiband systems are usually considered for flat-band physics, here we study one-band models that have flat portions in the dispersion to explore correlation effects in the 2D repulsive Hubbard model in an intermediate coupling regime. The FLEX+DMFT~(the dynamical mean-field theory combined with the fluctuation exchange approximation) is used to show that we have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied, which triggers a crossover from triplet to singlet pairings with a peculiar filling dependence that is dominated by the size of the flat region in the dispersion. A curious manifestation of the flat part appears as larger numbers of nodal lines associated with pairs extended in real space. We further detect non-Fermi liquid behavior in the momentum distribution function, frequency dependence of the self-energy and spectral function. These indicate correlation physics peculiar to flat-band systems.
By numerically solving the Bogoliubov-de Gennes equations for the single vortex state in a two-band superconductor, we demonstrate that the disparity between the healing lengths of two contributing condensates is strongly affected by the band Fermi velocities, even in the presence of the magnetic field and far beyond the regime of nearly zero Josephson-like coupling between bands. Changing the ratio of the band Fermi velocities alters the temperature dependence of the condensate lengths and significantly shifts parameters of the ``length-scales locking regime at which the two characteristic lengths approach one another.
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