Photon-assisted resonant Andreev reflections: Yu-Shiba-Rusinov and Majorana states

Abstract

Photon-assisted tunneling frequently provides detailed information on the underlying chargetransfer process. In particular, the Tien-Gordon approach and its extensions predict that the sideband spacing in bias voltage is a direct fingerprint of the number of electrons transferred in a single tunneling event. Here, we analyze photon-assisted tunneling into subgap states in superconductors in the limit of small temperatures and bias voltages where tunneling is dominated by resonant Andreev processes and does not conform to the predictions of simple Tien-Gordon theory. Our analysis is based on a systematic Keldysh calculation of the subgap conductance and provides a detailed analytical understanding of photon-assisted tunneling into subgap states, in excellent agreement with a recent experiment. We focus on tunneling from superconducting electrodes and into Yu-Shiba-Rusinov states associated with magnetic impurities or adatoms, but we also explicitly extend our results to include normal-metal electrodes or other types of subgap states in superconductors. In particular, we argue that photon-assisted Andreev reflections provide a high-accuracy method to measure small, but nonzero energies of subgap states which can be important for distinguishing conventional subgap states from Majorana bound states.

Subgap dynamics of double quantum dot coupled between superconducting and normal leads

“…For specific discussion we consider (i) abrupt detuning of the chemical potentials by the source-drain voltage, (ii) quench of the quantum dot energy levels, and (iii) their periodic driving. The latter effect has been recently achieved experimentally in the microwave-assisted tunneling via the single quantum dot in the Josephson-type junctions 47 – 49 , but similar measurements should be feasible using N-DQD-S heterostructures as well. Our calculations of the time-dependent electron occupancy and charge currents reveal the damped quantum oscillations whose frequencies coincide with the energies of in-gap bound sates.…”

Subgap Dynamics of Double Quantum Dot Coupled Between Superconducting and Normal Leads

“…For specific discussion we consider (i) abrupt detuning of the chemical potentials by the source-drain voltage, (ii) quench of the quantum dot energy levels, and (iii) their periodic driving. The latter effect has been recently achieved experimentally in the microwave-assisted tunneling via the single quantum dot in the Josephson-type (S-QD-S) junctions [45][46][47] , but similar measurements should be feasible using the N-DQD-S heterostructures as well. Our calculations of the time-dependent electron occupancy and charge currents reveal the damped quantum oscillations whose frequencies coincide with the energies of in-gap bound sates.…”

Engineered platforms for topological superconductivity and Majorana zero modes

“…With superconducting tips, identification of zero-energy states generally requires accurate knowledge of the tip gap. The energy of subgap states can, however, be measured directly as a line splitting in photon-assisted tunneling experiments [99].…”

“…Experiments probing the system by electromagnetic waves, measuring for example absorption or reflection, couple only to excitations that conserve the number of electrons and therefore do not probe ground state degeneracies. Photon-assisted tunneling in transport experiments are different and provide additional energy resolution [99,115], but do not give fundamentally different information from dc transport experiments.…”