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“Signature of the Transition to a Bound State in Thermoelectric Quantum Transport” by É. Jussiau, M. Hasegawa, and R.S. Whitney
We are studying a quantum dot coupled to two semiconducting reservoirs when the dot level and the electrochemical potential are both close to a band edge in the reservoirs. We have modelled this with an exactly solvable Hamiltonian without interactions (the Fano–Anderson model). The model is known to show an abrupt transition for a broad class of band structures as the dot–reservoir coupling is increased into the strong-coupling regime. This transition involves an infinite-lifetime bound state appearing in the band gap. We determined a signature of this transition in the continuum states of the model, visible as a discontinuous behavior of the dot’s transmission function. This can result in steady-state DC electric and thermoelectric responses having a very strong dependence on coupling close to critical coupling. We show examples where the electrical and thermal conductances and the thermoelectric power factor exhibit huge peaks at critical coupling, while the thermoelectric figure of merit grows as the coupling approaches the critical coupling, with a small dip when reaching it.