The interplay between dimensionality, coherence and interaction in superfluid Fermi gases is analyzed by the phase correlation function of the field of fermionic pairs. We calculate this phase correlation function for a two-dimensional superfluid Fer
mi gas with $s$-wave interactions within the Gaussian pair fluctuation formalism. The spatial behavior of the correlation function is shown to exhibit a rapid (exponential) decay at short distances and a characteristic algebraic decay at large distances, with an exponent matching that expected from Berezinskii-Kosterlitz-Thouless theory of 2D Bose superfluids. We conclude that the Gaussian pair fluctuation approximation is able to capture the physics of quasi long-range order in two-dimensional Fermi gases.
We use a finite temperature effective field theory recently developed for superfluid Fermi gases to investigate the properties of dark solitons in these superfluids. Our approach provides an analytic solution for the dip in the order parameter and th
e phase profile accross the soliton, which can be compared with results obtained in the framework of the Bogoliubov - de Gennes equations. We present results in the whole range of the BCS-BEC crossover, for arbitrary temperatures, and taking into account Gaussian fluctuations about the saddle point. The obtained analytic solutions yield an exact energy-momentum relation for a dark soliton showing that the soliton in a Fermi gas behaves like a classical particle even at nonzero temperatures. The spatial profile of the pair field and for the parameters of state for the soliton are analytically studied. In the strong-coupling regime and/or for sufficiently high temperatures, the obtained analytic solutions match well the numeric results obtained using the Bogoliubov - de Gennes equations.
The interface superconductivity in LaAlO$_{3}$-SrTiO$_{3}$ heterostructures reveals a non-monotonic behavior of the critical temperature as a function of the two-dimensional density of charge carriers. We develop a theoretical description of interfac
e superconductivity in strongly polar heterostructures, based on the dielectric function formalism. The density dependence of the critical temperature is calculated accounting for all phonon branches including different types of optical (interface and half-space) and acoustic phonons. The LO- and acoustic-phonon-mediated electron-electron interaction is shown to be the dominating mechanism governing the superconducting phase transition in the heterostructure.
The polaron optical conductivity is derived within the strong-coupling expansion, which is asymptotically exact in the strong-coupling limit. The polaron optical conductivity band is provided by the multiphonon optical transitions. The polaron optica
l conductivity spectra calculated within our analytic strong-coupling approach and the numerically accurate Diagrammatic Quantum Monte Carlo (DQMC) data are in a good agreement with each other at large $alpha gtrapprox 9$.
The physics of the pseudogap state is intimately linked with the pairing mechanism that gives rise to superfluidity in quantum gases and to superconductivity in high-Tc cuprates, and therefore, both in quantum gases and superconductors, the pseudogap
state and preformed pairs have been under intensive experimental scrutiny. Here, we develop a path integral treatment that provides a divergence-free description of the paired state in two-dimensional Fermi gases. Within this formalism, we derive the pseudogap temperature and the pair fluctuation spectral function, and compare these results with the recent experimental measument of the pairing in the two-dimensional Fermi gas. The removal of the infrared divergence in the number equations is shown both numerically and analytically, through a study of the long-wavelength and low-energy limit of the pair fluctuation density. Besides the pseudogap temperature, also the pair formation temperature and the critical temperature for superfluidity are derived. The latter corresponds to the Berezinski-Kosterlitz-Thouless (BKT) temperature. The pseudogap temperature, which coincides with the pair formation temperature in mean field, is found to be suppressed with respect to the pair formation temperature by fluctuations. This suppression is strongest for large binding energies of the pairs. Finally, we investigate how the pair formation temperature, the pseudogap temperature and the BKT temperature behave as a function of both binding energy and imbalance between the pairing partners in the Fermi gas. This allows to set up phase diagrams for the two-dimensional Fermi gas, in which the superfluid phase, the phase-fluctuating quasicondensate, and the normal state can be identified.
The spectra of low-lying pair excitations for an imbalanced two-component superfluid Fermi gas are analytically derived within the path-integral formalism taking into account Gaussian fluctuations about the saddle point. The spectra are obtained for
nonzero temperatures, both with and without imbalance, and for arbitrary interaction strength. On the basis of the pair excitation spectrum, we have calculated the thermodynamic parameters of state of cold fermions and the first and second sound velocities. The parameters of pair excitations show a remarkable agreement with the Monte Carlo data and with experiment.
