Finite-temperature stability and dimensional crossover of exotic superfluidity in lattices

We investigate exotic paired states of spin-imbalanced Fermi gases in anisotropic lattices, tuning the dimension between one and three. We calculate the finite temperature phase diagram of the system using real-space dynamical mean-field theory in combination with the quantum Monte Carlo method. We find that regardless of the intermediate dimensions examined, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state survives to reach about one third of the BCS critical temperature of the spin-density balanced case. We show how the gapless nature of the state found is reflected in the local spectral function. While the FFLO state is found at a wide range of polarizations at low temperatures across the dimensional crossover, with increasing temperature we find out strongly dimensionality-dependent melting characteristics of shell structures related to harmonic confinement. Moreover, we show that intermediate dimension can help to stabilize an extremely uniform finite temperature FFLO state despite the presence of harmonic confinement.

Figure 1

The phase diagram of the spin-polarized Fermi gas for different dimensionalities with two representative density and order parameter profiles along the trapped axis for each value of $t_{\perp }$. In the phase diagrams the notation Normal stands for normal state and pSF for polarized superfluid (including a balanced SF as a special case), while cN refers to a shell structure where the system is in the normal state in the middle of the trap with polarized superfluid or the FFLO state on the edges. Similarly, cFFLO refers to the FFLO state in the middle of the trap and polarized superfluid on the edges. Each error bar is determined by the closest well-converged simulation on each side of the phase boundary while the boundary itself is given by the mean of these two points. (a) The phase diagram for quasi-1D lattice with $t_{\perp }=0.2$ ($U=-2.97$) with (b) the FFLO state and (c) the cFFLO state. (d) The phase diagram for an intermediate interchain hopping $t_{\perp }=0.4$ ($U=-4.44$) with (e) the FFLO state melting to (f) polarized superfluid phase at constant polarization. (g) The phase diagram for a quasi-3D geometry with $t_{\perp }=0.8$ ($U=-6.83$). Panels (h) and (i) demonstrate how the FFLO state is affected by the increasing temperature. The inset of panel (a) is a schematic of the system geometry. All energies and temperatures are in units of $t_{\parallel }=1$.

Figure 2

At the crossing point between quasi-1D and 3D-like behavior, at $t_{\perp }=0.3$ ($U=-3.75$), we find that the FFLO state (here with $P=0.17$ and $T=0.04$) exhibits an exceptionally uniform oscillation amplitude across the whole system in spite of a density profile varying with the trap potential.

Figure 3

(a) The FFLO state near the trap center with $t_{\perp }=0.8$, $T=0.067$, and $P=0.30$. The local spectral functions of the FFLO state on the lattice sites b and c of panel (a) for $\sigma =\uparrow ,\downarrow$ are plotted in panels (b) and (c), respectively. The oscillation of the density profile is revealed to affect the most particles at energies close to the Fermi surface. The gapless nature of the FFLO state is clearly visible in the majority $(\uparrow )$ component on site c, i.e., at the node of the order parameter.