ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

TL;DR

This paper models charge and heat transport in a quantum dot chain with self-consistent reservoirs, deriving profiles and currents that follow classical laws, and demonstrating their independence from reservoir distributions.

Contribution

It introduces a self-consistent approach for quantum dot chains, revealing universal transport profiles and currents independent of reservoir statistics.

Findings

Transport profiles are independent of reservoir distributions.

Electric and heat currents follow Ohm and Fourier laws.

Numerical results confirm typical macroscopic behavior.

Abstract

We introduce a model for charge and heat transport based on the Landauer-Buttiker scattering approach. The system consists of a chain of $N$ quantum dots, each of them being coupled to a particle reservoir. Additionally, the left and right ends of the chain are coupled to two particle reservoirs. All these reservoirs are independent and can be described by any of the standard physical distributions: Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. In the linear response regime, and under some assumptions, we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix the boundary values (T_L,\mu_L) and (T_R,mu_R), and adjust the parameters (T_i,mu_i), for i = 1,...,N, so that the net average electric and heat currents into all the intermediate reservoirs vanish. This condition leads to expressions for the temperature and chemical potential profiles along the system, which turn out to be independent of the distribution describing the reservoirs. We also determine the average electric and heat currents flowing through the system and present some numerical results, using random matrix theory, showing that these currents are typically governed by Ohm and Fourier laws.