Magnetic-Field Asymmetry of Nonlinear Mesoscopic Transport

We investigate departures of the Onsager relations in the nonlinear regime of electronic transport through mesoscopic systems. We show that the nonlinear current-voltage characteristic is not an even function of the magnetic field due only to the magnetic-field dependence of the screening potential within the conductor. We illustrate this result for two types of conductors: A quantum Hall bar with an antidot and a chaotic cavity connected to quantum point contacts. For the chaotic cavity we obtain through random matrix theory an asymmetry in the fluctuations of the nonlinear conductance that vanishes rapidly with the size of the contacts.

Figure 1

Left panel: quantum Hall conductor attached to two reservoirs with an antidot connecting two edge states. Right panel: Schematic spatial variation of the screening potential inside the bar for opposite polarities of the magnetic field.

Figure 2

Normalized probability densities for the magnetic-field asymmetry $\Phi$ of a chaotic cavity connected to two reservoirs (left inset). Right inset: fluctuations of $\Phi$ as a function of the total number of modes $N$. The dashed line is the analytical prediction for $N\gg 1$.