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Quantum Thermoelectrics

Nonlinear energy and heat currents through interacting nanostructures

The often-made assumption that off-resonant transport proceeds entirely by the virtual occupation of charge states can fail dramatically for heat transport in interacting nanostructures. We have established a classification of the nonlinear energy transport signatures based on physical models that allow for charge fluctuations employing a nonequilibrium transport theory that can deal with strong interactions as well as at least the leading plus next-to-leading order of tunnelling processes. Often theoretical descriptions are based on effective models that include only effective exchange- and potential scattering terms, for example in scanning-probe spectroscopy or Coulomb-blockaded quantum dots. These, however, may fail badly for the energy current since they include only inelastic tunnelling -- keeping the charge fixed -- and eliminate the real charge fluctuations that turn out to be crucially important for energy transport.

The nonequilibrium competition between real and virtual processes, together with the sign of the energy currents, leads to an unexpectedly rich energy current spectrum. The energy-transport resonances that we identify in the Coulomb blockade regime provide new qualitative information about relaxation processes, for instance, by a strong negative differential heat conductance relative to the heat current. These can go completely unnoticed in the charge current spectroscopy. Nonlinear heat-transport spectroscopy with energy-level control is thus a promising new experimental tool.

Work done together with D. Schuricht's group at Utrecht University

(M. R. Wegewijs)

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Time-dependent heat-current relaxation in interaction nanostructures

Relaxation to equilibrium of a electronic system coupled to an electron resevoir in the weak coupling limit seems to be a well-understood problem. Surprisingly, a simple Born-Markov master equation calculation of the heat-current relaxation exhibits a poorly-understood dependence on the physical parameters which can be probed in pump-probe heat current measurements. Most strikingly, the decay mode amplitudes for a nanostructure with strong repulsive interactions show strong signatures of electron-electron attraction.

We show that such relations are not specific to simple quantum dot systems in simple regimes but hold generally for flat, wide-band electronic reservoirs, even at low temperatures, with strong tunnel coupling, and for strong interactions. The surprising dependence derives from an exact duality between open-fermion systems with opposite signs of the interactions (and other energies). Their time-evolutions turn out to be related in an amazingly simple way once formulated as a Liouville-space quantum field theory.

Work done together with J. Splettstoesser's group at Chalmers University, Sweden

J. Schulenborg, R. B. Saptsov, F. Haupt, J. Splettstoesser, and M. R. Wegewijs
Phys. Rev. B 93, 081411(R) (2016)

(M. R. Wegewijs)

Duality

Enhanced Thermoelectric Effect by Attractive Interaction

The thermoelectric efficiency of solid state materials is encapsulated in the so-called "figure of merit" ZT. Optimal ZT, in linear response theory, is obtained by enhancing the Seebeck coefficient and the conductance and reducing the thermal conductivities through the device.

The figure shows lower/upper bounds on ZT for several gate voltages for a quantum dot with attractive local Coulomb interaction.  Since quantum dots are tunable, optimal ZT values are obtained at any temperature by suitable choice of a gate voltage. This "negative-U" mechanism for enhancing the thermopower and ZT of quantum dots demonstrates how novel correlation effects may help to improve thermoelectric efficiency at the nanoscale with possible applications to energy efficiency and cooling in quantum devices.

S. Andergassen, T. A. Costi, V. Zlatic, Phys. Rev. B 84, 241107  (2011)

(L.Merker, T.Costi)

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