Rectification and nonlinear transport in chaotic dots and rings

TL;DR

This paper studies nonlinear and rectified currents in mesoscopic conductors, highlighting the effects of Coulomb interactions, bias modes, and magnetic fields, with a focus on chaotic rings and quantum dots.

Contribution

It introduces a comprehensive model for nonlinear transport in chaotic quantum rings and dots, accounting for interactions, bias modes, and magnetic field effects, with experimental relevance.

Findings

Nonlinear conductance fluctuations decrease with frequency.

Antisymmetric conductance is suppressed more than symmetric conductance.

Phase rigidity is lost in nonlinear Aharonov-Bohm oscillations.

Abstract

We investigate the nonlinear current-voltage characteristic of mesoscopic conductors and the current generated through rectification of an alternating external bias. To leading order in applied voltages both the nonlinear and the rectified current are quadratic. This current response can be described in terms of second order conductance coefficients and for a generic mesoscopic conductor they fluctuate randomly from sample to sample. Due to Coulomb interactions the symmetry of transport under magnetic field inversion is broken in a two-terminal setup. Therefore, we consider both the symmetric and antisymmetric nonlinear conductances separately. We treat interactions self-consistently taking into account nearby gates. The nonlinear current is determined by different combinations of second order conductances depending on the way external voltages are varied away from an equilibrium reference point (bias mode). We discuss the role of the bias mode and circuit asymmetry in recent experiments. In a photovoltaic experiment the alternating perturbations are rectified, and the fluctuations of the nonlinear conductance are shown to decrease with frequency. Their asymptotical behavior strongly depends on the bias mode and in general the antisymmetric conductance is suppressed stronger then the symmetric conductance. We next investigate nonlinear transport and rectification in chaotic rings. To this extent we develop a model which combines a chaotic quantum dot and a ballistic arm to enclose an Aharonov-Bohm flux. In the linear two-probe conductance the phase of the Aharonov-Bohm oscillation is pinned while in nonlinear transport phase rigidity is lost. We discuss the shape of the mesoscopic distribution of the phase and determine the phase fluctuations.