Energy dissipation in a dc-field-driven electron lattice coupled to fermion baths

Jong E. Han and Jiajun Li
Phys. Rev. B 88, 075113 – Published 7 August 2013

Abstract

Electron transport in electric-field-driven tight-binding lattice coupled to fermion baths is comprehensively studied. We reformulate the problem by using the scattering-state method within the Coulomb gauge. Calculations show that the formulation justifies direct access to the steady state bypassing the time-transient calculations, which then makes the steady-state methods developed for quantum dot theories applicable to lattice models. We show that the effective temperature of the hot-electron induced by a dc electric field behaves as Teff=Cγ(Ω/Γ) with a numerical constant C, tight-binding parameter γ, the Bloch oscillation frequency Ω, and the damping parameter Γ. In the small damping limit Γ/Ω0, the steady state has a singular property with the electron becoming extremely hot in an analogy to the short-circuit effect. This leads to the conclusion that the dissipation mechanism cannot be considered as an implicit process, as treated in equilibrium theories. Finally, using the energy flux relation, we derive a steady-state current for interacting models where only on-site Green's functions are necessary.

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  • Received 15 April 2013

DOI:https://doi.org/10.1103/PhysRevB.88.075113

©2013 American Physical Society

Authors & Affiliations

Jong E. Han and Jiajun Li

  • Department of Physics, State University of New York at Buffalo, Buffalo, New York 14260, USA

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Issue

Vol. 88, Iss. 7 — 15 August 2013

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