Distributed Current Injection into a One-Dimensional Ballistic Edge Channel

TL;DR

This paper extends Landauer's theory to include distributed charge injection along a 1D ballistic channel, relevant for topological insulators, providing criteria to distinguish ballistic from resistive edge channels in experiments.

Contribution

It introduces a generalized model for ballistic transport with distributed injection, applicable to 2D topological insulators and multi-terminal setups.

Findings

Derived criteria to identify ballistic edge channels

Extended Landauer's theory to distributed injection scenarios

Applicable to quantum Hall and topological insulator systems

Abstract

We generalize Landauer's theory of ballistic transport in a one-dimensional (1D) conductor to situations where charge carrier injection and extraction are not any more confined to electrodes at either end of the channel, but may occur along its whole length. This type of distributed injection is expected to occur from the two-dimensional (2D) bulk of, e.g., a quantum spin (or anomalous) Hall insulator to its topologically protected edge states. We apply our conceptual solution to the case of two metal electrodes contacting the 2D bulk, enabling us to derive criteria that discriminate ballistic from resistive edge channels in multi-terminal transport experiments.