Universal resistances of the quantum resistance-capacitance circuit

Mesoscopic circuits cooled down to low temperatures witness marked non-local effects in their transport properties because of electron coherence—electron wavefunctions spread over the sample and correlate its different parts. One of the consequences is that, in one dimension, the maximum d.c. conductance is quantized in steps of e 2 / h . Here we extend the concept of ‘universal quantized resistance’ to the a.c. regime. We analyse the coherent quantum resistance–capacitance circuit comprising a cavity capacitively coupled to a gate and connected by means of a single spin-polarized channel to a reservoir lead. We show that, as a result of the Coulomb interaction and global phase coherence, the charge relaxation resistance R q is identical for weak and large transmissions and that it smoothly changes from h /2 e 2 to h / e 2 when the frequency exceeds the level spacing of the cavity. For large cavities, we relate the resistance h / e 2 to the Korringa–Shiba relation of the Kondo model. Finally, we introduce a larger class of models with a universal charge relaxation resistance. The properties of electric conductors change markedly once quantum phenomena become relevant. So far, work on quantum coherent electron transport has largely focused on static properties, but new theoretical work now looks at such phenomena in the regime of fast alternating currents.