Anomalous Seebeck effect and counter-propagating ballistic currents in graphene

TL;DR

This paper investigates the breakdown of Kelvin's relation for the Seebeck effect in graphene caused by non-local ballistic transport, revealing counter-propagating currents and their magnetic field separation.

Contribution

It introduces a formalism to explain non-local Seebeck effects in graphene, highlighting the role of counter-propagating ballistic currents and magnetic field effects.

Findings

Kelvin's relation may fail in graphene due to non-local effects.

Counter-propagating ballistic currents coexist in graphene.

Magnetic fields can separate hot and cold electron currents.

Abstract

The Seebeck effect consists in the induction of a voltage drop due to the temperature difference in a conductor. In the middle of XIXth century, Lord Kelvin has proposed a relation between the Seebeck coefficient and the derivative of the chemical potential over temperature in the broken circuit regime. This relation appears to be nearly universal as it equally well applies to metals, semimetals and semiconductors. We show that it may fail, however, in graphene, due to the non-locality effects in the ballistic electronic transport regime. The correction to the Kelvin's formula emerges due to the coexistence of counter-propagating non-dissipative currents of cold and hot electrons. The external magnetic field normal to the graphene sample allows separating hot and cold currents in real space. The developed formalism may help interpreting the recent experimental data on ballistic edge currents in graphene bi-layers in the quantum Hall regime [1].