Steady-state density functional theory for thermoelectric effects

Abstract

The recently proposed density functional theory for steady-state transport (i-DFT) is extended to include temperature gradients between the leads. Within this framework, a general and exact expression is derived for the linear Seebeck coefficient which can be written as the sum of the Kohn-Sham coefficient and an exchange-correlation contribution. The formalism is applied to the singleimpurity Anderson model for which approximate exchange-correlation functionals are suggested for temperatures both above and below the Kondo temperature. A certain structural property of the exchange-correlation potentials in the Coulomb blockade regime allows to recover an earlier result expressing the Seebeck coefficient in terms of quantities of equilibrium density functional theory. The numerical i-DFT results are compared to calculations with the numerical renormalization group over a wide range of temperatures finding a reasonable agreement while i-DFT comes at a much lower computational cost.

Thermoelectric transport within density functional theory

“…The SSM may be viewed as the limiting case of a SIAM weakly coupled to leads and the Eqs. (31) become more accurate as the ratio T /γ increases 29 . Insertion of Eqs.…”

“…To this end, we extend the recently proposed DFT framework for steady-state transport 18 , also called i-DFT, which in principle captures the steady state density n(r) in the central region C, as well as the steady current I through it. By construction, in the linear-response regime, i-DFT gives access to the (many-body) electrical conductance and can also describe the Seebeck coefficient 29 . On the other hand, the energy or heat currents are not guaranteed to be reproduced in i-DFT and therefore also the thermal conductance is not captured.…”

“…In earlier work 29 , we have extended the original i-DFT formalism to not only give the many-body electrical conductance but also the many-body Seebeck coefficient, while for the thermal conductance one still has κ = κ s . In iq-DFT, this corresponds to the approximation…”

“…By construction, i-DFT does not give access to the heat current (although the Seebeck coefficient can be extracted 29 ). In the present work, we will close this gap and generalize i-DFT to iq-DFT, a new formalism which allows to compute not only the (steady-state) density and electrical current but also the heat current.…”

Differential thermopower images as a probe of many-body effects in quantum point contacts

“…In order to clarify this connection, we extend density functional theory (DFT) previously developed to describe the microscopic state of QPCs at equilibrium, to incorporate non-equilibrium effects on the potential due to finite bias and different source/drain temperatures. Although exact steady-state DFT has, in principle, been formulated for non-equilibrium conditions [23,24], a Landauer+DFT approach [25,26] is used here (see the SI) due to the lack of a corresponding exchange-correlation functional.…”