Resistance of helical edges formed in a semiconductor heterostructure

TL;DR

This paper develops a detailed theoretical model of how quantum dots and charge puddles affect the resistance of helical edges in topological insulators, explaining experimental observations and predicting future outcomes.

Contribution

It introduces a comprehensive theory of puddle-induced resistance in helical edges, including effects of the Kondo phenomenon and statistical charge puddle distributions.

Findings

Quantum dots with odd electron numbers significantly increase resistance.

Temperature dependence of resistance is weak due to Kondo effects.

Charge puddles can explain high resistance and edge conduction coexistence.

Abstract

Time-reversal symmetry prohibits elastic backscattering of electrons propagating within a helical edge of a two-dimensional topological insulator. However, small band gaps in these systems make them sensitive to doping disorder, which may lead to the formation of electron and hole puddles. Such a puddle -- a quantum dot -- tunnel-coupled to the edge may significantly enhance the inelastic backscattering rate, due to the long dwelling time of an electron in the dot. The added resistance is especially strong for dots carrying an odd number of electrons, due to the Kondo effect. For the same reason, the temperature dependence of the added resistance becomes rather weak. We present a detailed theory of the quantum dot effect on the helical edge resistance. It allows us to make specific predictions for possible future experiments with artificially prepared dots in topological insulators. It also provides a qualitative explanation of the resistance fluctuations observed in short HgTe quantum wells. In addition to the single-dot theory, we develop a statistical description of the helical edge resistivity introduced by random charge puddles in a long heterostructure carrying helical edge states. The presence of charge puddles in long samples may explain the observed coexistence of a high sample resistance with the propagation of electrons along the sample edges.