Signature of the transition to a bound state in thermoelectric quantum transport

Étienne Jussiau, Masahiro Hasegawa, Robert S. Whitney

Published 2018-11-28Version 1

We study 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. This is modelled with an exactly solvable Hamiltonian without interactions (the Fano-Anderson model). The model shows an abrupt transition in its physics as the dot-reservoir coupling is increased, if the band's density of states goes to zero at the band edge. Then an infinite-lifetime bound state appears in the band gap, when the coupling is stronger than a critical value. We study the signature of this transition in the electric and thermoelectric responses, showing that they change very rapidly when the dot-reservoir coupling is close to its critical value. Typically, the thermoelectric figure of merit $ZT$ grows as the coupling approaches its critical value, but then drops sharply at the critical point.