Interplay between intrinsic and emergent topological protection on interacting helical modes

Abstract

The interplay between topology and interactions on the edge of a two dimensional topological insulator with time reversal symmetry is studied. We consider a simple non-interacting system of three helical channels with an inherent Z2 topological protection, and hence a zero-temperature conductance of G = e 2 /h. We show that when interactions are added to the model, the ground state exhibits two different phases as function of the interaction parameters. One of these phases is a trivial insulator at zero temperature, as the symmetry protecting the non-interacting topological phase is spontaneously broken. In this phase there is zero conductance (G = 0) at zerotemperature. The other phase displays enhanced topological properties, with a topologically protected zero-temperature conductance of G = 3e 2 /h and an emergent Z3 symmetry not present in the lattice model. The neutral sector in this phase is described by a massive version of Z3 parafermions. This state is an example of a dynamically enhanced symmetry protected topological state.

Helical liquids in semiconductors

“…In this review, we focus on an isolated helical channel and its transport properties. For a nanoribbon or stripe-like geometry in which the interchannel coupling becomes nonnegligible, the stability of multiple parallel helical liquids has been investigated (Xu and Moore 2006, Santos et al 2019. In addition, there is a first-principle study on interedge scattering due to a single nonmagnetic bulk impurity, a relevant backscattering source for narrow ribbons (Vannucci et al 2020), as well as works on Coulomb drag in two parallel interacting helical edge modes (Zyuzin and Fiete 2010, Chou et al 2015, Kainaris et al 2017, Chou 2019, Du et al 2021.…”

Strong zero modes from geometric chirality in quasi-one-dimensional Mott insulators

“…One of the most intriguing paradigms where zero modes appear are quantum clock models with Z n≥3 symmetry [1][2][3][4]. The zero modes include Z n -parafermions, signifying a (nonlocal) relation to electronic systems proposed for beyond-Majorana schemes of topological quantum computation [1][2][3][4][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. To support strong zero modes, the clock models require a chiral (i.e., reflectionsymmetry breaking) deformation of their couplings [1][2][3][4][34][35][36].…”