# Optimal thermoelectricity with quantum spin-Hall edge states

## TL;DR

This paper investigates how coupling quantum spin Hall edge states to a nanomagnet can optimize thermoelectric performance, achieving near-optimal power generation and high efficiency through engineered transmission properties.

## Contribution

It demonstrates that magnetic coupling to quantum spin Hall edge states can produce transmission functions suitable for optimal thermoelectricity, including high figures of merit.

## Key findings

- Single magnetic domain yields near-optimal power generation.
- Two magnetic domains create resonances leading to high thermoelectric efficiency.
- Estimates suggest feasible fabrication with HgTe quantum wells.

## Abstract

We study the thermoelectric properties of a Kramers pair of helical edge states of the quantum spin Hall effect coupled to a nanomagnet with a component of the magnetization perpendicular to the direction of the spin-orbit interaction of the host. We show that the transmission function of this structure has the desired qualities for optimal thermoelectric performance in the quantum coherent regime. For a single magnetic domain there is a power generation close to the optimal bound. In a configuration with two magnetic domains with different orientations, pronounced peaks in the transmission functions and resonances lead to a high figure of merit. We provide estimates for the fabrication of this device with HgTe quantum-well topological insulators.