Critical behavior in one dimension: Unconventional pairing, phase separation, BEC-BCS crossover, and magnetic Lifshitz transition

Abstract

We study the superconducting properties of population-imbalanced ultracold Fermi mixtures in one-dimensional (1D) optical lattices that can be effectively described by the spin-imbalanced attractive Hubbard model (AHM) in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain the ground state phase diagrams including some unconventional superconducting phases such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, and the η phase (an extremal case of the FFLO phase), both for the case of a fixed chemical potential and for a fixed number of particles. It allows to determine optimal regimes for the FFLO phase as well as η-pairing stability. We also investigate the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, at T = 0. Finally, the obtained results show that despite of the occurrence of the Lifshitz transition induced by an external magnetic field, the superconducting state can still exist in the system, at higher magnetic field values.

Superfluidity of fermionic pairs in a harmonic trap. Comparative studies: Local Density Approximation and Bogoliubov-de Gennes solutions

“…In this case, the oscillating character of n i at relatively low polarization has not been reproduced within the LDA method. Moreover, the LDA calculations underestimate critical parameters of the system, with respect to the results obtained within the DMRG [57] or the BdG approach [22]. The situation can be even more complicated in the two dimensional systems.…”

“…Hence, the corresponding SOP Δ can be found by minimization of W D ( )at fixed μ i [19][20][21]. In fact, this way is equivalent to the one in which equation (9) should be solved [22]. The huge advantage of this method is based on the fact that it is relatively simple to implement and quite quickly solvable even for a trapped system, due to an efficient procedure of finding the solution for a homogeneous system.…”

“…In the weak coupling limit, at a large spin imbalacne (i.e. polarization) [22,38], the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase [52,53] can occur. In this case, the SOP is characterized by oscillations in real space and at non-zero local polarization [13,54].…”

“…In this case, the SOP is characterized by oscillations in real space and at non-zero local polarization [13,54]. If the polarization is equal to zero or low, the connection between the phase diagrams of the system without a trapping potential and in the presence of the harmonic trap [55] exists, in the LDA method [22]. Unfortunately, the LDA approach cannot account for the oscillating character of the SOP as well as the oscillations of the average number of particles in the FFLO phase [13,56].…”

Phase separations induced by a trapping potential in one-dimensional fermionic systems as a source of core-shell structures

“…Equally important is the better comprehension of unconventional phases that can appear in fermionic superfluids with population imbalance, the latter being the effect of a magnetic (Zeeman) field or the result of preparing a mixture with the desired composition. In the weak coupling limit, states with nontrivial Cooper pairs can exist at large population imbalance [20][21][22][23][24] .…”