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

TL;DR

This paper investigates electron transport in a lattice under a DC electric field coupled to fermion baths, revealing how dissipation and effective temperature behave, and providing a method to calculate steady-state currents.

Contribution

It introduces a scattering state formulation for steady-state analysis, linking quantum dot theories to lattice models, and derives a new expression for steady-state current using Green's functions.

Findings

Effective temperature scales with electric field and damping parameters.

Steady-state exhibits a singular hot-electron behavior in low damping limit.

Derived a steady-state current formula using only on-site Green's functions.

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 $T_{\rm eff}=C\gamma(\Omega/\Gamma)$ with a numerical constant $C$, tight-binding parameter $\gamma$, the Bloch oscillation frequency $\Omega$ and the damping parameter $\Gamma$. In the small damping limit $\Gamma/\Omega\to 0$, 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.