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

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. It is worth noticing that in addition to the numerous papers dealing with two quantum dots tunnel-coupled to the leads and between themselves, also Coulomb-coupled quantum dots [24,25] have attracted increasing interest in the recent years [for a general perspective see [26]. This has been motivated by the advances in the fabrication of nano-devices, energy harvesting [22] with quantum dots, and the experimental possibility to taylor TE properties exploiting Coulomb interaction and the charge carriers correlation [27]. Moreover, in recent years parallel coupled quantum dots made of semiconductors with high spin-orbit interaction have proven promising systems to realize two-spin qubit in quantum information processing [28,29].Enhancing thermoelectric performance in linear regimes, requires maximization of the dimensionlesswhere σ is the electrical conductance, S the thermopower (Seebeck) coefficient, T is the temperature and κ=κ e +κ p is the thermal conductance (which includes electronic and lattice contributions). In the search of optimal thermoelectric response of the device, most important quantities are its maximum efficiency as thermoelectric generator, and the efficiency at the maximum of the output power.A crucial aspect both in the implementation of experimental methods [30], and in the evaluation of the thermoelectric response of bulk and nanostructured materials, is the wide parameters range to be explored simultaneously to determine its optimal functioning. In this context, the possibility of using analytic expressions for all the involved thermoelectric functions greatly simplifies the task. In the literature, the analytic treatment of the c-2QD is confined at sufficiently small temperatures by means of the Sommerfeld expansion, extended when necessary to fourth order in k B T in the evaluation of kinetic parameters [9]. In the case of Lorentzian shape of the transmission function, ...

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