Quantum Heat Transport across Capacitively Coupled Quantum Dots

Recently, thermal transport in the quantum-coherent regime has attracted significant attention, particularly in studies of quantum heat engines. The roles of coherence and measurement in heat transport have also been actively investigated. While most heat carriers are bosonic particles―such as photons, phonons, and magnons―electronic heat currents, often accompanied by charge currents, are of interest for thermoelectric applications. However, purely electronic heat currents in the absence of charge flow remain relatively unexplored. Theoretical studies have examined capacitively coupled quantum dots (QDs), each tunnel-coupled to a reservoir in local thermal equilibrium, in both weak and strong coupling regimes. Most results can be explained without invoking quantum coherence.

In this work, we extend the model to investigate quantum effects on heat transport in a capacitively coupled QD system. The setup consists of three QDs: two parallel QDs each tunnel-coupled to a left reservoir, and a third QD tunnel-coupled to a right reservoir. The left and right QDs are capacitively coupled without direct tunneling. Key parameters include the temperature difference, the energy-level offset δ between the two left QDs, and the line-width energy ℏΓ representing the reservoir–QD coupling strength. The heat current is calculated using both a quantum master equation under the weak-coupling (ℏΓ) assumption and the Keldysh non-equilibrium Green’s function formalism. When the two left QDs are closely spaced and δ < ℏΓ, indirect quantum coherence mediated by the left reservoir can arise. We quantitatively analyze the effects of correlation and coherence on heat transport and also examine the transient behavior of the heat current.