Transmission through a potential barrier in Luttinger liquids with a topological spin gap

Abstract

We study theoretically the transport of the one-dimensional single-channel interacting electron gas through a strong potential barrier in the parameter regime where the spin sector of the low-energy Luttinger liquid theory is gapped by interaction. This phase is of particular interest since it exhibits non-trivial interaction-induced topological properties. Using bosonization and an expansion in the tunneling strength, we calculate the conductance through the barrier as a function of the temperature as well as the local density of states (LDOS) at the barrier. Our main result concerns the mechanism of bound-state mediated tunneling. The characteristic feature of the topological phase is the emergence of protected zero-energy bound states with fractional spin located at the impurity position. By flipping the fractional spin the edge states can absorb or emit spinons and thus enable single electron tunneling across the impurity even though the bulk spectrum for these excitations is gapped. This results in a finite LDOS below the bulk gap and in a non-monotonic behavior of the conductance. The system represents an important physical example of an interacting symmetry-protected topological phase-which combines features of a topological spin insulator and a topological charge metal-in which the topology can be probed by measuring transport properties. arXiv:1709.08965v1 [cond-mat.str-el]

Symmetry-protected spin gaps in quantum wires

“…We therefore find that the spin sector is gapped for both g = 0 and g = 0 and the ground state develops a nonvanishing expectation value cos √ 2φ σ . While this gap may occur generally in models with appropriately tuned values of the couplings, in our situation the gap is protected by the symmetry of the wavefunctions (7) which involves both spin and orbital degrees of freedom. The gap ultimately arises from the negative sign of the matrix element (12) which provides an effective attraction despite the underlying Coulomb interaction being repulsive.…”

“…Whereas Luttinger liquid properties are extremely challenging to identify in experiment, the predicted experimental signatures of the Luther-Emery phase are striking. The spin gap manifests as a vanishing of the single particle density of states at low energies 5 , a flux periodicity of 2e indicative of fermionic pairing 6 , and vanishing backscattering from impurities at the Fermi level 7 . These characteristics, which bear remarkable similarities with the superconducting state appear nevertheless in the absence of superconducting order.…”

Interplay between intrinsic and emergent topological protection on interacting helical modes

“…Although it will renormalise to zero at T = 0, there may be an intermediate energy scale below the scale set by the neutral gap ∆ n where the impurity is still strong and in this intermediate regime one can see the parafermionic edge states (c.f. the equivalent case for two edges discussed in [48]).…”

One-dimensional repulsive Hubbard model with mass imbalance: Orders and filling anomaly

“…πSG phase with additional spinful time-reversal symmetry has been considered to be topological, with characterizations of edge mode [30,31] and string order [32]. For the mass imbalanced Hubbard model, spinful timereversal symmetry is absent while inversion symmetry survives.…”