Interplay of Rashba and Dresselhaus Spin-Orbit Couplings on the Stability of Topological FFLO Phases in 1D Fermi Gases

TL;DR

The paper addresses how Rashba and Dresselhaus spin-orbit couplings influence the stability of topological FFLO phases in a 1D spin-imbalanced Fermi gas under a Zeeman field. Using a Fermi-Hubbard model solved by density matrix renormalization group, the authors map phase diagrams and analyze real-space and momentum-space pairing via the pair momentum distribution and the entanglement spectrum. They find that DSOC uniquely promotes intraband FFLO by enhancing spin polarization within a single helicity band and suppressing interband coherence, while RSOC supports zero-momentum BCS pairing; their interplay produces MP, mixed-FFLO, intra-FFLO, and topo-intra-FFLO phases, with entanglement degeneracy signaling topology. The results offer actionable guidance for realizing tunable topological superfluids and Majorana modes in ultracold atoms and related spin-orbit coupled platforms, with potential impact on topological quantum computation.

Abstract

We investigate the stabilization of topological Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases, with a specific emphasis on the intraband FFLO phase, in a one-dimensional (1D) Fermi gas subjected to an external magnetic field. This research highlights the crucial role of the interplay between Rashba spin-orbit coupling (RSOC) and Dresselhaus spin-orbit coupling (DSOC). Employing a Fermi-Hubbard model alongside the density matrix renormalization group (DMRG) method, we examine the combined effects of RSOC and DSOC on these exotic superfluid phases, taking into account attractive fermionic interactions. Our principal finding reveals that while RSOC primarily stabilizes conventional zero-momentum pairing, DSOC performs a distinct and crucial role in selectively stabilizing the intraband FFLO phase. This stabilization is achieved by enhancing spin polarization within a single helicity band and suppressing interband coherence, thereby facilitating the formation of finite-momentum FFLO pairs within the same band and resulting in the emergence of a topologically nontrivial superfluid. This targeted control of intraband FFLO pairing paves the way for new strategies in the manipulation of superfluid phases in spin-orbit coupled systems and offers essential insights for experimental realizations in ultracold atomic gases, with implications for topological quantum computing and Majorana fermions.

Figures (10)

• Figure 1: (Color online) Single-particle band structures illustrating unconventional pairings in a 1D Fermi gas of ultracold atoms. The panels depict band structures corresponding to various parameter sets. Arrows represent the spin polarization vectors (or spin orientation) specifically evaluated at the Fermi points.
• Figure 2: (Color online) (a) (a) Phase diagram of a 1D Fermi gas system in the $h-\mu$ plane, for $U = -2$ and zero SOCs. Panels (b)-(e) illustrate the properties of a chain with $L = 40$ sites as a function of the chemical potential $\mu$: (b) fermion population $n$, (c) compressibility $\chi_{\mu}$, (d) spin densities ($n_{\uparrow},n_{\downarrow}$), and (e) spin polarization $p$ for various magnetic field strengths: $h = 0.0$ (squares), $h = 1.0$ (circles), and $h = 2.0$ (triangles). In panel (d), $n_{\uparrow}$ is represented by open symbols, while $n_{\downarrow}$ is represented by filled symbols.
• Figure 3: (Color online) (a,b) Pair momentum distribution, $n_{k}^{\rm pair}$: The PMD in momentum space is presented for (a) the BCS state $(h=0, \mu=1)$ and (b) the inter-FFLO phase $(h=2, \mu=1)$, corresponding to specific points in the main phase diagram illustrated in [Fig. \ref{['fig:pt1']}(a)]. (c-f) Real-space correlations ($P_{ll'}^{\rm pair}$) and spin densities ($n_{\uparrow},n_{\downarrow}$) for an $L=40$ site chain: These panels depict the real-space properties for selected points from the BCS and inter-FFLO phase regions of the main phase diagram shown in [Fig. \ref{['fig:pt1']}(a)]. Specifically, panels (c) and (e) illustrate the real-space pairing correlations, while panels (d) and (f) present the corresponding spin densities. Panels (c) and (d) characterize the BCS phase, whereas panels (e) and (f) represent the inter-FFLO phase.
• Figure 4: (Color online) (a,c) Pair momentum distribution, $n_{k}^{\text{pair}}$: Evaluation of the PMD in momentum space for specific regions of the main phase diagram [Fig. \ref{['fig:pt1']}(a)] while varying the RSOC strengths: $\alpha= 0$ (dotted line), $\alpha=0.4$ (dashed line), and $\alpha= 0.8$ (solid line). Panel (a) pertains to the NG region ($h=2.0$, $\mu=2.0$), whereas (c) illustrates the inter-FFLO region ($h=2.0$, $\mu=1.0$). (b,d) Entanglement spectrum, $-2\log(\lambda)$: The entanglement spectrum as a function of the RSOC strength ($\alpha$), corresponding to the same phase diagram points as panels (a) and (c). Panel (b) represents the NG region ($h=2.0$ and $\mu=2.0$), while panel (d) depicts the inter-FFLO region ($h=2.0$ and $\mu=1.0$). The dots in panels (b,d) denote the eigenvalues of the entanglement Hamilatonian, $H_{\rm E}=-\ln \rho_{\rm L}$. In topological phases, the entanglement spectrum is expected to exhibit a twofold degeneracy. Insets: Each panel is accompanied by an inset that illustrates the spin densities $(n_{\uparrow},n_{\downarrow})$ as a function of the RSOC strength.
• Figure 5: (Color online) Phase diagrams of a 1D Fermi gas system in the $h-\mu$ plane. These diagrams are constructed for fixed parameters $U = -2$ and $\beta=0$, while varying the strengths of RSOC: (a) $\alpha=0.05$, (b) $\alpha=0.2$, and (c) $\alpha=0.6$.