A non-magnetic mechanism of backscattering in helical edge states

TL;DR

This paper identifies a non-magnetic backscattering mechanism for helical edge states in 2D topological insulators by coupling the edge to a nearby puddle whose zero-mode fluctuations act as an effective fluctuating flux. The authors develop a minimal TP model with a tunable S-matrix, show that non-interacting cases yield no backscattering at zero flux, and demonstrate that weak electron-electron interactions induce backscattering via zero-mode phase fluctuations; energy averaging and static ZM fluctuations lead to a finite, temperature-insensitive rate for $T\gg\Delta$. Dephasing—including dynamics of zero-mode fluctuations—further enhances backscattering and yields a universal, puddle-independent result in the strong-dephasing regime, with a small AB-oscillation imprint. An RG treatment reveals slow flow of the tunneling parameters, predicting a weak, scale-dependent backscattering that can reproduce the observed near-constant edge resistivity in experiments. Overall, the work provides a plausible mechanism for observed backscattering in long TI edges without invoking inelastic processes.

Abstract

We study interaction-induced backscattering mechanism for helical edge states of a two-dimensional topological insulator which is tunnel-coupled to a puddle located near the edge channel. The mechanism does not involve inelastic scattering and is due to the zero-mode fluctuations in a puddle. We discuss in detail a simple model of a puddle - a cavity in the bulk of the topological insulator. Such a cavity also has helical edge states with tunneling coupling to helical states encompassing the topological insulator. We analyze effect of the edge current in the puddle. Although averaged value of this current is equal to zero, its zero-mode fluctuations act, in the presence of electron-electron interaction, similar to magnetic flux thus allowing backscattering processes, which involve tunneling through the puddle. Rectification of these fluctuations leads to a finite probability of backscattering. This effect is further enhanced due to dephasing process which is also dominated by zero-mode fluctuations. Remarkably, for temperature exceeding level spacing in the puddle, the rate of backscattering does not depend on temperature in a good agreement with recent experiments.

Figures (2)

• Figure 1: (a) Topological puddle, formed by a cavity in the bulk of TI, tunnel-coupled to the HES of TI. Contact region is shown by gray color. Dashed lines illustrate two processes corresponding to backscattering $1\to 1^\prime$: (i) jump from $1$ to $3^\prime$ with amplitude $f$, rotation clockwise with arbitrary number of winding and jump back to $1^\prime$ with amplitude $r$; (ii) jump from $1$ to $4^\prime$ with amplitude $r$, rotation counterclockwise with arbitrary number of winding and jump back to $1^\prime$ with the amplitude $-f$; (b) and (c) different geometries of the contact described by the same $\hat{S}$ matrix (see Eq. \ref{['SmatTIdefect']}): (b) curved edge Delplace2012, (c) contact with spin-flip channels Niyazov2023.
• Figure 2: Dependence of backscattering probability on magnetic flux calculated by using second line of Eq. \ref{['RR']} for $T/\Delta = 3$, $g = 0.1,$$\gamma_\varphi$ given by Eq. \ref{['Gammaf']}, and different tunneling couplings: $\gamma=0.003$ (red curve) and $\gamma=0.07$ (blue curve).