Topological Fulde-Ferrell and Larkin-Ovchinnikov states in spin-orbit coupled lattice system

TL;DR

This paper demonstrates the stabilization of topological Fulde-Ferrell and Larkin-Ovchinnikov states with distinct Chern numbers in spin-orbit coupled lattice systems under Zeeman fields, revealing rich phase diagrams and edge state properties.

Contribution

It introduces the realization of topological FF and LO states with specific Chern numbers in lattice systems, highlighting their unique topological and spatial features compared to prior continuum models.

Findings

Topological FF state with Chern number -1 (tFF₁) stabilized in lattice systems.

Topological LO state with Chern number 2 (tLO₂) stabilized in lattice systems.

Distinct edge states and local density of states spectra for these topological inhomogeneous states.

Abstract

The spin-orbit coupled lattice system under Zeeman fields provides an ideal platform to realize exotic pairing states. Notable examples range from the topological superfluid/superconducting (tSC) state, which is gapped in the bulk but metallic at the edge, to the Fulde-Ferrell (FF) state (having a phase-modulated order parameter with a uniform amplitude) and the Larkin-Ovchinnikov (LO) state (having a spatially varying order parameter amplitude). Here, we show that the topological FF state with Chern number ($\mathcal{C}=-1$) (tFF$_{1}$) and topological LO state with $\mathcal{C}=2$ (tLO$_{2}$) can be stabilized in Rashba spin-orbit coupled lattice systems in the presence of both in-plane and out-of-plane Zeeman fields. Besides the inhomogeneous tSC states, in the presence of a weak in-plane Zeeman field, two topological BCS phases may emerge with $\mathcal{C}=-1$ (tBCS$_{1}$) far from half filling and $\mathcal{C}=2$(tBCS$_{2}$) near half filling. We show intriguing effects such as different spatial profiles of order parameters for FF and LO states, the topological evolution among inhomogeneous tSC states, and different non-trivial Chern numbers for the tFF$_{1}$ and tLO$_{1,2}$ states, which are peculiar to the lattice system. Global phase diagrams for various topological phases are presented for both half-filling and doped cases. The edge states as well as local density of states spectra are calculated for tSC states in a 2D strip.