Charge fluctuations in nonlinear heat transport

Abstract

We show that charge fluctuation processes are crucial for the nonlinear heat conductance through an interacting nanostructure, even far from a resonance. We illustrate this for an Anderson quantum dot accounting for the first two leading orders of the tunneling in a master equation. The often made assumption that off-resonant transport proceeds entirely by virtual occupation of charge states, underlying exchange-scattering models, can fail dramatically for heat transport. The identified energy-transport resonances in the Coulomb blockade regime provide qualitative information about relaxation processes, for instance, by a strong negative differential heat conductance relative to the heat current. These can go unnoticed in the charge current, making nonlinear heat-transport spectroscopy with energy-level control a promising experimental tool. [6]. Here, by analyzing the generic effects of Coulomb interactions on the nonlinear heat transport in nanoscale systems, we will show that this is very promising.Interaction effects have long been probed using gate controlled charge-current spectroscopy, a well-developed experimental tool to access the discrete quantum levels of nanostructures. Two prominent features in the charge current driven by a source-drain voltage underpin this successful method. The first is resonant or single-electron tunneling (SET), which depends on the level position relative to the electrochemical potential, μ R in Fig. 1(a): An electron jumps into or out of an orbital level, directly leading to a real change of its occupancy. The current shows sharp steps as new resonant transport processes are switched on with increasing bias. These processes are routinely identified in a three-terminal setup by plotting the charge conductance as function of the applied bias V and the gate voltage, as exemplified in Fig. 2(a). Two-terminal measurements, e.g., using a scanning probe, correspond to line traces through such a plot. The second type of resonance is independent of the level position and appears as a horizontal line at V = since it originates in the inelastic excitation by an energy at fixed local electron number on the nanostructure. This off-resonant feature requires a second-order tunneling process in which an electron "scatters through," other charge states being only visited virtually [see Fig. 1(b)]. This is known as inelastic electron tunneling (IETS) [7,8] or inelastic cotunneling (ICOT) [9][10][11][12].This inelastic tunneling resonance develops into a nonequilibrium Kondo resonance for low and low temperatures [13][14][15], which is much sharper [11,12] Thermoelectric transport has also been investigated within the two above-mentioned physical transport pictures. Theory mostly focused on the thermopower in the linear-response regime. This includes the study of resonant tunneling [26], inelastic tunneling [27][28][29], and Kondo processes [30][31][32][33]. Works addressing the nonlinear regime have either applied effective single-particle descriptions [34][35][36][37][38] or focused on th...

Thermoelectrics in Coulomb-coupled quantum dots: Cotunneling and energy-dependent lead couplings

“…Whereas the calculation of charge currents involves the electron-tunneling rates that enter the ME (3), and therefore does not require any additional steps once the ME has been set up and solved, the heat currents must be calculated via the heat tunneling rates in a postprocessing step, similar to the procedure in full density-matrix treatments [20].…”

“…Furthermore, when operated under strong nonequilibrium conditions in which linear-response theory breaks down, a theoretical treatment taking into account the * nicwall@nanotech.dtu.dk † kkaa@nanotech.dtu.dk full nonlinear properties is needed [16][17][18][19]. Only recently have these issues been discussed in strongly interacting QD systems [9,[20][21][22].…”

Thermoelectric response of a correlated impurity in the nonequilibrium Kondo regime

“…3,4,9-13), allows to resolve electronic level splittings (e.g., in semiconductor nanostructures 14 , carbon nanotubes 15,16 , dopant atoms 17 ), vibrational frequencies 18 , spin splittings due to a magnetic field 19 , exchange interactions 11,12,20 , magnetic anisotropies (e.g., in molecules 21,22 or adatoms 23 ), and spin-orbit coupling 24 . While these have long been probed by gate controlled electrical transport spectroscopy, recent advancements in the experimental investigation of thermoelectric properties on the nanoscale [25][26][27][28][29][30][31] provide a promising route for the detection of additional information on the relaxation processes not accessible in the electrical transport 32 . Theoretically, the development of powerful techniques led to significant progress in the understanding of correlated quantum dots out of equilibrium 6,7, .…”

“…While the electronic transport has been studied extensively, the thermoelectric transport theory mostly focused on the linear response regime 13,25,[71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89] . The nonlinear regime has been addressed mainly in the weak coupling limit 32,78,[90][91][92][93][94][95][96][97] , a systematic analysis including renormalization effects 66,67,98,99 beyond the perturbative regime is still missing. Recent findings 90,99 indicate a Seebeck coefficient which is enhanced with respect to the equilibrium result.…”

Nonlinear Heat Conduction in Coulomb-blockaded Quantum Dots

“…Larger temperature biases may give rise to rectification effects, a subject that has lately attracted much attention [19][20][21][22][23]. In the following, we will consider Coulomb blockade effects also for temperature-driven heat currents.…”