Photo-assisted heat current and Peltier coefficient in a metal/dot/metal junction

TL;DR

This paper investigates the behavior of photo-assisted heat current and Peltier coefficient in a metal/dot/metal junction under time-dependent modulation, revealing complex harmonic structures and non-conservation effects due to energy dissipation.

Contribution

It introduces a detailed analysis of the harmonic content of heat current in a modulated quantum dot system using the Keldysh formalism, highlighting non-trivial step profiles.

Findings

Zero-order harmonic expressed as sum of shifted dc heat currents

Devil staircase profile observed in heat current harmonic

Non-horizontal steps due to energy dissipation in barriers

Abstract

The photo-assisted heat current through a metal/dot/metal junction and its associated Peltier coefficient are computed in the framework of the time-dependent out-of-equilibrium Keldysh formalism in the presence of a dot energy modulation. When the frequency of the modulation is much larger than the amplitude of the modulation, the heat current follows the sinusoidal time evolution of the dot energy. This is no longer the case when the modulation frequency becomes of the order or smaller than the amplitude of the modulation. To characterize this non sinusoidal behavior, we have calculated the harmonics of the photo-assisted heat current. The zero-order harmonic can be expressed as an infinite sum of dc heat currents associated to a dot with shifted energies. It exhibits a devil staircase profile with non horizontal steps whereas it is established that the steps are horizontal for the zero-order harmonic of the photo-assisted electric current. This particularity is related to the fact that the dot heat is not a conserved quantity due to energy dissipation within the tunnel barriers.