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

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 eff = 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/Ω → 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.

Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach

“…Han has later shown that the inclusion of a fermionic bath is sufficient to reproduce a semiclassical Ohm-expression in the conductivity despite the lack of explicit momentum scattering [561], confirming that this bath can lead to a proper dissipation despite its intrinsic simplifications. Only in the limit of small dissipation the steady state displays a divergent effective temperature as long as the Bloch oscillation frequency remains finite [562].…”

Microscopic Theory of Resistive Switching in Ordered Insulators: Electronic versus Thermal Mechanisms

“…We divide the Hamiltonian Ĥ into (i) Ĥ Hub , the correlated electronic sample itself, given by a Hubbard model on a finite 2d square lattice, (ii) Ĥ bath+leads , the two leads and the dissipative environment, given by reservoirs of Fermions, and (iii) Ĥ E , the electric-field induced electrostatic potential, originating from our choice to work with the Coulomb gauge. , We have where d r σ † is the Fermionic creation operator in the orbital at site r with spin σ = ↑,↓ and Δn r σ ≡ d r σ † d r σ –1/2. The hopping integrals given by t are limited to nearest neighbors, while U controls the on-site Coulombic interaction.…”

Correlated Insulator Collapse due to Quantum Avalanche via In-Gap Ladder States

“…with the coupling constant g ep . We use a Schwinger-Keldysh formulation of the dynamical mean-field theory (DMFT [28,30,31]) which bypasses the transient dynamics and directly yields the homogeneous nonequilibrium steady-state of the manybody dynamics [32,33]. The fermion baths enter the computation of the electronic Green's function via local retarded and lesser self-energies at site i as…”