Quantum coherent three-terminal thermoelectrics: maximum efficiency at given power output

TL;DR

This paper derives a quantum-origin upper bound on efficiency at given power for three-terminal thermoelectric devices, applicable to systems with or without magnetic fields, extending previous two-terminal results.

Contribution

It establishes a universal quantum bound on efficiency for three-terminal thermoelectrics, generalizing prior two-terminal findings and including systems with broken time-reversal symmetry.

Findings

The efficiency bound is of quantum origin and stricter than Carnot's bound.

The same efficiency bound applies to three-terminal systems with or without magnetic fields.

Achievability of the bound is demonstrated for various system types.

Abstract

We consider the nonlinear scattering theory for three-terminal thermoelectric devices, used for power generation or refrigeration. Such systems are quantum phase-coherent versions of a thermocouple, and the theory applies to systems in which interactions can be treated at a mean-field level. We consider an arbitrary three-terminal system in any external magnetic field, including systems with broken time-reversal symmetry, such as chiral thermoelectrics, as well as systems in which the magnetic field plays no role. We show that the upper bound on efficiency at given power output is of quantum origin and is stricter than Carnot's bound. The bound is exactly the same as previously found for two-terminal devices, and can be achieved by three-terminal systems with or without broken time-reversal symmetry, i.e. chiral and non-chiral thermoelectrics.