Quantum phase transition of dynamical resistance in a mesoscopic capacitor
We study theoretically dynamic response of a mesoscopic capacitor, which consists of a quantum dot connected to an electron reservoir via a point contact and capacitively coupled to a gate voltage. A quantum Hall edge state with a filling factor ν is realized in a strong magnetic field applied perpendicular to the two-dimensional electron gas. We discuss a noise-driven quantum phase transition of the transport property of the edge state by taking into account an ohmic bath connected to the gate voltage. Without the noise, the charge relaxation resitance for ν > 1/2 is universally quantized at Rq = h/(2e2ν), while for ν < 1/2, the system undergoes the Kosterlitz-Thouless transition, which drastically changes the nature of the dynamical resistance. The phase transition is facilitated by the noisy gate voltage, and we see that it can occur even for an integer quantum Hall edge at ν = 1. When the dissipation by the noise is sufficiently small, the quantized value of Rq is shifted by the bath impedance.