Fractional topological insulator precursors in spin-orbit fermion ladders

TL;DR

This paper investigates fractional topological insulator precursors in spin-orbit coupled fermionic ladders, revealing conditions for their stability, competing phases, and a quantized charge pumping signature in a quasi-one-dimensional system.

Contribution

It introduces a microscopic bosonization framework to identify and analyze FTI precursor states and their stability in interacting fermionic ladders with spin-orbit coupling.

Findings

FTI precursors can form in spin-orbit ladders with moderate repulsive interactions.

Competing phases include density wave orders and orbital antiferromagnetic states.

A quantized charge pumping protocol signals the presence of FTI precursors.

Abstract

We study precursor states of fractional topological insulators (FTIs) in interacting fermionic ladders with spin-orbit coupling. Within a microscopically motivated bosonization approach, we investigate different competing phases depending on same-spin and interspin interactions at fractional effective filling $\nu=1/3$ per spin. In the spin-decoupled limit, we find that strong repulsive interactions of already moderate range may lead to a partially gapped state with two time-reversed copies of a quasi-one dimensional Laughlin phase. This FTI precursor competes with an interleg partially gapped phase displaying quasi long-range density wave order, however it may be stabilized if interactions have suitable anisotropy, or are sufficiently near SU($2$) symmetry, in leg space. When the FTI phase is present, it is moderately robust to small interspin interactions; these introduce competing partially gapped phases of orbital antiferromagnetic and bond density wave character. Performing a strong coupling analysis of the FTI precursor regime, we find that the main effect of interspin interactions is to induce correlated quasiparticle backscattering between the precursor FTI edge modes. Although this process competes with the topological phase, we show, by considering an array of ladders, that its influence may disappear upon approaching the two dimensional case. Considering time-reversal symmetry breaking perturbations, we also describe a protocol that adiabatically pumps $1/6$ charge per half-cycle, thus providing a quantized FTI signature arising already in the single ladder regime.