Nonlinear phenomena in quantum thermoelectrics and heat

Abstract

We review recent developments in nonlinear quantum transport through nanostructures and mesoscopic systems driven by thermal gradients or in combination with voltage biases. Low-dimensional conductors are excellent platforms to analyze both the thermoelectric and heat dynamics beyond linear response because due to their small size a small temperature difference applied across regions gives rise to large thermal biases. We offer a theoretical discussion based on the scattering approach to highlight the differences between the linear and the nonlinear regimes of transport. We discuss recent experiments on quantum dots and molecular junctions subjected to strong temperature differences. Theoretical predictions concerning the Kondo effect and heat rectification proposals are briefly examined. An important issue is the calculation of thermoelectric efficiencies including nonlinearities. Cross Seebeck effects and nonlinear spin filtering arise in superconductors and topological insulators while mixed noises between charge and heat currents are also considered. Finally, we provide an outlook on the possible future directions of the field.Comment: Review article. Comments are welcome. v2: Added references. Published versio

Reversal of Thermoelectric Current in Tubular Nanowires

“…In these examples the charge carriers are electrons and the sign change of the thermopower means that they travel from the cold side to the hot side, which may appear counterintuitive. Other nonlinear effects can occur if the characteristic relaxation length of electrons and or phonons exceeds the sample size [10], because the energy of electrons and/or phonons is no longer controlled by the temperature of the bath, but by the generated electric bias, including Coulomb interactions [11,12].Observing such negative thermopower at the nanoscale is difficult for at least two reasons: the currents tend to be small and it is hard to maintain a constant temperature difference across such short distances. Here we argue that a generic class of tubular nanowires, to be defined in more detail below, are ideal systems for both realizing and observing negative thermopower.…”

“…In these examples the charge carriers are electrons and the sign change of the thermopower means that they travel from the cold side to the hot side, which may appear counterintuitive. Other nonlinear effects can occur if the characteristic relaxation length of electrons and or phonons exceeds the sample size [10], because the energy of electrons and/or phonons is no longer controlled by the temperature of the bath, but by the generated electric bias, including Coulomb interactions [11,12].…”

Nonlinear electric and thermoelectric Andreev transport through a hybrid quantum dot coupled to ferromagnetic and superconducting leads

“…In contrast, we are here interested in the regime where a normal current is transformed into a supercurrent as in the Andreev reflection. The issue is interesting in view of recent developments in the field of nonlinear quantum thermoelectrics [33] and its connection to spin caloritronics (i.e., the production of spin currents with thermal means) in superconductors [34].…”

Fate of the spin- 12 Kondo effect in the presence of temperature gradients

“…Despite the fact that nonlinear thermoelectrics [20] in Kondo-correlated systems is quite a new topic, there is already a number of interesting results in the last years. Most of them are focused on the study of the Seebeck coefficient S = V th θ employing a large variety of methods: nonperturbative resonant tunneling approximation [21], second-order perturbation theory for the onsite Coulomb interaction [22], slave-boson noncrossing approximation (NCA) [23], generalized Keldyshbased NCA [24], nonequilibrium Green's functions beyond Hartree-Fock [25], quantum [26] and auxiliary [27] master equation approaches and dual fermions renormalized perturbation theory [28].…”