Fractional topological insulator precursors in spin-orbit fermion ladders

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 ν = 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.

From quantum wires to the Chern-Simons description of the fractional quantum Hall effect

“…Thenceforth, the quantum wires approach has been a subject of great interest and used in several recent investigations. We mention in particular the generalization for other (Abelian and non-Abelian) quantum Hall phases [5][6][7][8], the description of topological insulators [9][10][11][12][13][14] and superconductors [15,16], constructions of topologically ordered spin liquids [17][18][19][20][21], and also the generalization for higher dimensional topological phases [22][23][24]. Furthermore, it has been proved a fruitful approach in the study of the recently discovered dualities in three-dimensional field theories -the web of dualities [25,26], where the quantum wires can be thought as a discretized version of a 2+1 dimensional fermionic theory.…”

Adiabatic almost-topological pumping of fractional charges in noninteracting quantum dots

“…It reduces to Eq. (19) for λ = 0, since arctan(x) + arctan(1/x) = sgn[x]π/2. We take X max → ∞ to get the pumping for a contour that corresponds to one enclosing the peak of Eq.…”

“…great interest in exotic systems which exhibit topological pumping of fractional charges, meaning that any two driving contours with the same topology will drive the same fractional charge. Such fractional charge pumping has been found in models of Coulomb-blockaded quantum dots 15,16 , topological insulators [17][18][19][20] , systems with fractional quantum Hall physics, 19,21 fermionic gases with short range interactions, 22 fractional levitons, 23 and the Bose-Hubbard model. 24 These models have either strong interaction effects or non-trivial topological properties (non-zero Chern numbers, or similar).…”

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

“…In later studies, the CL model has been realized in photonic [ 67 , 68 ] and cold atom [ 69 , 70 ] systems, and utilized in the investigations of Aharonov–Bohm cages [ 71 , 72 ], topological pumping [ 73 ], localization [ 74 , 75 ], and many-body topological matter [ 76 , 77 , 78 , 79 , 80 ]. Recently, spin- extensions of the CL model have also been explored in several studies [ 81 , 82 , 83 ], leading to the discoveries of richer topological features. Furthermore, when time-periodic drivings are applied to the spin- CL, a series of Hermitian Floquet topological phases in the CII symmetry class were found [ 84 ].…”