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 are $\mathrm{SU}\left(2\right)$ symmetric, or have suitable anisotropy, 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.

• Received 10 July 2018
• Revised 17 September 2019

DOI:https://doi.org/10.1103/PhysRevB.100.235122