Wigner-function formalism applied to semiconductor quantum devices: Need for nonlocal scattering models

Abstract

In designing and optimizing new-generation nanomaterials and related quantum devices, dissipation versus decoherence phenomena are often accounted for via local scattering models, such as relaxation-time and Boltzmann-like schemes. Here we show that the use of such local scattering approaches within the Wigner-function formalism may lead to unphysical results, namely anomalous suppression of intersubband relaxation, incorrect thermalization dynamics, and violation of probability-density positivity. Furthermore, we propose a quantum-mechanical generalization of relaxation-time and Boltzmann-like models, resulting in nonlocal scattering superoperators that enable one to overcome such limitations.

Simulation of Electronic Quantum Devices: Failure of Semiclassical Models

“…However, within the Wigner-function picture, this local approach suffers of intrinsic limitations. The latter is highlighted in the remainder of this section, where selected examples focusing on the analysis of energy dissipation versus decoherence phenomena [61] (Section 3.1) and on the device-reservoir carrier thermalization dynamics [67] (Section 3.2) are briefly reviewed.…”

“…Such a local description is, however, intrinsically incompatible with the fully quantum-mechanical (i.e., non-local) nature of the dissipation-free carrier dynamics within the device active region. Indeed, during the last decades the intrinsic limitations of such hybrid treatments have been repeatedly pointed out, both for the case of thermalization models based on the conventional inflow-boundary-condition scheme [34,37,[45][46][47]67] and for the case of dissipation versus decoherence treatments based on the relaxation-time approximation as well as on Boltzmann-like scattering models [61,64].…”

Generalized nonequilibrium quantum transport of spin and pseudospins: Entanglements and topological phases

“…The terminology 'weak ' as used in the experimental observations is due to the fact that in Eqs. (35) - (36) or Eqs. (29)- (32) there are other important terms that contribute to quantum nonlocality and hence magnetoconductivity transport measurements, e.g.…”

“…(36) containing one Levi-Civita symbol, which describe a complex motion similar to the motion and deformation of Landau-orbits, induced by strong magnetic fields, due to the torque exerted by the electric field 34 resulting in the build-up of Hall voltage 35. There are indeed theoretical and experimental works which support this assertion, the effect is related to what is often referred to in the literature as weak localization due to Dresselhaus and Rashba spin-orbit couplings15 and weak antilocalization or supression of scattering rates due to the Dyakonov-Perel and Elliott-Yafet scattering mechanisms16,17 or entanglement of spin-orbit couplings with another torque (spin) degrees of freedom.…”

“…There are indeed theoretical and experimental works which support this assertion, the effect is related to what is often referred to in the literature as weak localization due to Dresselhaus and Rashba spin-orbit couplings15 and weak antilocalization or supression of scattering rates due to the Dyakonov-Perel and Elliott-Yafet scattering mechanisms16,17 or entanglement of spin-orbit couplings with another torque (spin) degrees of freedom. Delocalization or nonlocal scattering terms may also occur where the scattering centers have a pseudo-spin character, such as the two-level dependence of the scattering in Wigner-function quantum transport formalism recently studied by Rossi et al36,37…”