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

Abstract

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 is known to show an abrupt transition as the dot-reservoir coupling is increased into the strong-coupling regime for a broad class of band structures. This transition involves an infinite-lifetime bound state appearing in the band gap. We find a signature of this transition in the continuum states of the model, visible as a discontinuous behaviour of the dot's transmission function. This can result in the steady-state DC electric and thermoelectric responses having a very strong dependence on coupling close to critical coupling. We give examples where the conductances and the thermoelectric power factor exhibit huge peaks at critical coupling, while the thermoelectric figure of merit ZT grows as the coupling approaches critical coupling, with a small dip at critical coupling. The critical coupling is thus a sweet spot for such thermoelectric devices, as the power output is maximal at this point without a significant change of efficiency.

Non-equilibrium boundary driven quantum systems: models, methods and properties

“…which has strict finite support. It should be noted that whereas non-vanishing spectral densities (Schaller et al, 2009;Topp et al, 2015) can be used to model non-Markovian effects , a spectral density with strict finite support can even lead to phenomena like bound states that may persist even in the long-term limit (Jussiau et al, 2019). To invert the Laplace transform, we can then analytically calculate expressions like…”

Transport in spinless superconducting wires

“…To derive these expressions we have to assume the existence of a nonequilibrium steady state and this is related to the existence of bound states (discrete energy levels) in the spectrum of the entire coupled system of the superconducting wire and the baths (non-interacting normal electrons). The role of bound states on the existence of steady states is known for normal systems 24,[28][29][30] and has recently been investigated for the case of superconductors in Ref. [22].…”

“…Using Eqs. (29,30,33) and the correlation properties of the noise terms we finally obtain the following expression for current:…”

Broadband frequency filters with quantum dot chains

“…that allows perfect energy transfers in the transmission window [ω min , ω max ] and blocks transfers anywhere else, one may reach a situation yielding a finite matter current I M with negligible noise S M (note that we only discuss the contributions rising linearly in time and thereby neglect features such as bound states 58 or any constant finite contributions) that saturates the FTUR bound (11). In the current and noise integrals (2), the integration boundary will then be limited to the interval [ω min , ω max ] for a rectangular transmission function.…”