Coherence lengths in attractively interacting Fermi gases with spin-orbit coupling

Abstract

Extensive research has been lavished on the effects of spin-orbit couplings (SOCs) in attractively interacting Fermi systems in both neutral cold-atom systems and condensed-matter systems. Recently, it was suggested that a SOC drives a class of BCS to Bose-Einstein condensate (BEC) crossover that is different from the conventional one without a SOC. Here, we explore what are the most relevant physical quantities to describe such a BCS to BEC crossover and their experimental detections. We extend the concepts of the coherence length and "Cooper-pair size" in the absence of SOC to Fermi systems with SOC. We investigate the dependence of chemical potential, coherence length, and Cooper-pair size on the SOC strength and the scattering length at three dimensions (3D) (the bound-state energy at 2D) for three attractively interacting Fermi gases with 3D Rashba, 3D Weyl, and 2D Rashba SOC, respectively. We show that only the coherence length can be used to characterize this BCS to BEC crossover. Furthermore, it is the only length which can be directly measured by radio-frequency dissociation spectra type of experiments. We stress crucial differences among the coherence length, Cooper-pair size, and the two-body bound-state size. Our results provide the fundamental and global picture of the BCS to BEC crossover and its experimental detections in various cold-atom and condensed-matter systems.

Itinerant magnetic phases and quantum Lifshitz transitions in a three-dimensional repulsively interacting Fermi gas with spin-orbit coupling

“…ωmin denotes the lower edge of inter-band particle-hold continuum, which is taken as the unit in Fig.8(d never a ground state in the former system, but it maybe a ground state in the latter. As shown in the Sec.II, the [SU (2) spin × SO (3) orbit ] D symmetry [13,17] dictates that the dynamical 4 × 4 density-spin susceptibility Eqn.14 can be split into two 2 × 2 subspaces: i) n − L subspace formed by the density and the longitudinal spin mode ii) T 1 − T 2 subspace formed by the two transverse modes. This exact decomposition simplifies the following analytical and numerical calculations considerably.…”

“…So the 3d isotropic (Weyl) SOC is expected to be implemented in very near future experiments. So far, there were extensive theoretical investigations on various effects of SOC on the pairing physics of attractively interacting Fermi gases [12,13]. However, there are still relatively few works in the repulsive side.…”

The effects of hybridization on Cooper-pair binding energy in an intra-band model of superconductivity

“…Spectra for ω 1 (0) and ω 2 (0) in the BEC limit (1/k F a s = +4.0) varying the hybridization V /E F for α = 0.5. In the inset the behavior of ω 2 (0) is shown for (15) where ω 2 (0) also depends of and μ…”

“…The Superconducting-Insulator transition (SIT) observed in these disordered systems as the indium oxide (InO) compound [14] are related to the Cooper-pair localization. Recently Yi-Xiang et al [15] have studied the effects of spin-orbit couplings (SOC) in attractively interacting Fermi systems such as the cold atom systems and usual condensed matter systems. The authors have investigated the effects of SOC on the BCS-BEC crossover.…”

Induced interactions in the BCS-BEC crossover of two-dimensional Fermi gases with Rashba spin-orbit coupling

“…In the presence of the SOC, it has been suggested that a BEC can be realized even at a fixed weak interaction where very strong SOC can lead to the formation of the bosonic bound state called rashbon [30][31][32]. The BCS-BEC crossover in spin-orbit-coupled Fermi gases has been studied with various settings of SOC, interaction, and dimensionality in the mean-field theory [33][34][35][36][37][38][39][40][41][42][43], also in the beyond-mean-field approaches for three [44][45][46][47][48] and two * dongheekim@gist.ac.kr dimensions [49][50][51][52], and very recently by using the quantum Monte Carlo (QMC) method for the ground state in two dimensions [53].…”