An approach to quantum transport based on reduced hierarchy equations of motion: Application to a resonant tunneling diode

TL;DR

This paper presents a rigorous quantum transport approach using reduced hierarchy equations of motion to analyze dissipative tunneling in double barrier structures, revealing complex current behaviors including hysteresis and self-oscillations.

Contribution

It introduces a novel application of reduced hierarchy equations of motion in Wigner space for quantum transport, incorporating non-Markovian effects and self-consistent potentials.

Findings

Observation of hysteresis and double plateau in I-V characteristics

Identification of self-excited current oscillations in NDR region

Discovery of tornado-like steady oscillation in Wigner space

Abstract

The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of a rigorous treatment for the first time. We employ a Caldeira-Leggett Hamiltonian with an effective potential calculated self-consistently, accounting for the electron distribution. With this Hamiltonian, we use the reduced hierarchy equations of motion in the Wigner space representation to study the effects of non-Markovian thermal fluctuations and dissipation at finite temperature in a rigorous manner. Hysteresis, double plateau-like behavior, and self-excited current oscillation are observed in a negative differential resistance (NDR) region of the current-voltage curve. We find that while most of the current oscillations decay in time in the NDR region, there is a steady oscillation characterized by a tornado-like rotation in the Wigner space in the upper plateau of the NDR region.