Nonlinear Landauer formula for thermal transport of the electrons

¹ National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University Nanjing 210093, China
² Collaborative Innovation Center of Advanced Microstructures, Nanjing University - Nanjing 210093, China

Received: 6 December 2023
Accepted: 15 February 2024

Abstract

The Landauer formula, originally formulated in the context of linear transport, has been a powerful tool for studying quantum devices. However, recent research has shown that extending its application to nonlinear and nonreciprocal transport is crucial for a more comprehensive understanding. In this work, we develop a nonlinear Landauer formula for thermal transport of the electrons and apply it to investigate thermal transport in graphene. Our study reveals intriguing phenomena especially in the presence of large temperature gradients and at low system temperatures. At these conditions, higher-order nonlinear currents emerge, indicating the significance of nonlinear effects in thermal transport. Unlike thermoelectric conductivity, thermal conductivity can be decomposed into intrinsic and extrinsic terms. This decomposition is based on whether the contributions rely on the derivative of the transmission coefficient with respect to energy. This nonlinear Landauer formula presented here serves as a valuable tool for future investigations into the intricate interplay between temperature gradients, system temperatures, and thermal transport in quantum devices.