Violation of Kirchhoff's Laws for a Coherent RC Circuit

TL;DR

This paper reports a mesoscopic quantum effect where Kirchhoff's laws are violated in a coherent RC circuit at GHz frequencies, revealing that charge relaxation resistance differs from classical predictions and is universally half the resistance quantum.

Contribution

It demonstrates that in a fully coherent quantum RC circuit, the charge relaxation resistance deviates from classical expectations and is universally half the resistance quantum, challenging traditional circuit laws.

Findings

Charge relaxation resistance is half the resistance quantum.

Kirchhoff's laws do not hold in the quantum coherent regime.

The effect is universal for single mode conductors.

Abstract

What is the complex impedance of a fully coherent quantum resistance-capacitance (RC) circuit at GHz frequencies in which a resistor and a capacitor are connected in series? While Kirchhoff's laws predict addition of capacitor and resistor impedances, we report on observation of a different behavior. The resistance, here associated with charge relaxation, differs from the usual transport resistance given by the Landauer formula. In particular, for a single mode conductor, the charge relaxation resistance is half the resistance quantum, regardless of the transmission of the mode. The new mesoscopic effect reported here is relevant for the dynamical regime of all quantum devices.