Analytic treatment of the thermoelectric properties for two coupled quantum dots threaded by magnetic fields

G Menichetti,G Grosso,G Pastori Parravicini

doi:10.1088/2399-6528/aac423

Abstract

Coupled double quantum dots (c-2QD) connected to leads have been widely adopted as prototype model systems to verify interference effects on quantum transport at the nanoscale. We provide here an analytic study of the thermoelectric properties of c-2QD systems pierced by a uniform magnetic field. Fully analytic and easy-to-use expressions are derived for all the kinetic functionals of interest. Within the Green’s function formalism, our results allow a simple inexpensive procedure for the theoretical description of the thermoelectric phenomena for different chemical potentials and temperatures of the reservoirs, different threading magnetic fluxes, dot energies and interdot interactions; moreover they provide an intuitive guide to parametrize the system Hamiltonian for the design of best performing realistic devices. We have found that the thermopower S can be enhanced by more than ten times and the figure of merit ZT by more than hundred times by the presence of a threading magnetic field. Most important, we show that the magnetic flux increases also the performance of the device under maximum power output conditions.

Highlights

Quantum dot systems have attracted enormous interest as workable thermoelectric device candidates for the study of electronic and thermal quantum transport at the nanoscale
We have found that the thermopower S may be enhanced by more than ten times and the figure of merit ZT by more than hundred times due to a threading magnetic field
We have presented in this paper a systematic analytic study of the thermoelectric response functions of a coupled double quantum dot system, pierced by a magnetic field, connected to left and right reservoirs, in the linear regime

Summary

INTRODUCTION

Quantum dot systems have attracted enormous interest as workable thermoelectric device candidates for the study of electronic and thermal quantum transport at the nanoscale. The system composed by two single-level quantum dots coupled to each other (c-2QD) via metallic leads, in two terminal or multiterminal setups[20], and via an interdot tunneling are most appropriate to probe how the Hamiltonian system parameters and external conditions can be varied to optimize the energy conversion efficiency and the output power of the thermoelectric device. The pole structure of the transmission function T (E) is discussed, and the analytic expressions of the kinetic parameters, produced by T (E), are obtained in terms of the Bernoulli numbers and of the trigamma function[23,24] routinely contained in common software libraries We have exploited such expressions to study the variation of Seebeck coefficient, figure of merit, energy conversion efficiency and output power, as function of temperatures and chemical potentials of the reservoirs, and of the magnetic field threading the c-2QD.

SYSTEM DESCRIPTION AND MODEL

Green’s function of the degenerate double dot in magnetic fields

Transmission function of the symmetric double dot in magnetic fields

Magnetic field effects on the transmission function

RESULTS AND DISCUSSION

CONCLUSIONS