Effect of Strong Electric Fields on Material Responses: The Bloch Oscillation Resonance in High Field Conductivities

In this paper, we investigated the effect of strong electric fields on material responses and the Bloch oscillation resonance in high field conductivities. For this purpose, a high-order accurate explicit modal discontinuous Galerkin (DG) solver is employed for solving the quantum Boltzmann transport equation (BTE) in the context of electron transport at nanoscales under strongly out-of-equilibrium conditions. Here, we study the transient behavior and the convergence of a steady-state response to an external oscillating electric field switched on at time zero. We first benchmark our numerical results with known analytic steady-state responses at low fields. The computational results show that the present DG scheme is in excellent agreement with analytic solutions over the whole range of parameters and to an extremely high precision, allowing us to achieve good agreement even for the fifth-order response at low fields. We then extend the method to strong electric fields and show how the responses are deviated from the low-field ones and the transition to a dampened Bloch oscillation regime. Most importantly, we report the observation of a new regime induced by the resonance between the standard low-field response and Bloch oscillations.