Quantum-critical dynamics of a Josephson junction at the topological transition

A semiconducting nanowire proximitized by a superconductor is emerging as a building block of a topological qubit. Magnetic field applied to a proximitized nanowire drives it through the critical point into a topological state. We investigate signatures of this quantum phase transition in the microwave response of a nanowire Josephson junction. To this end, we compute the finite-frequency admittance Y(ω) of the junction at the transition and in its vicinity. At the critical point, the dependence of the admittance on frequency and temperature is universal and determined by the symmetries of the system. We find that, despite the closing of the spectral gap at the transition, the dissipative response may remain weak: ReY(ω) ~ max(ω, T)². This behavior is markedly different from the conventional transition between the superconducting and normal states. We also establish scaling functions for the frequency-dependence of the admittance near the transition. Our work paves the way towards the microwave detection of the topological phase transition in proximitized semiconducting nanowires.