Ballistic Andreev Interferometers

A Josephson junction, formed between two phase-biased superconductors and a normal metal, hosts a discrete spectrum of Andreev bound states (ABS), as theoretically investigated by Kulik, and, later, by Ishii and by Bagwell. In this paper, we develop a theory for spectroscopy of Andreev bound states (ABS) in long ballistic Andreev interferometers. We specifically demonstrate that the differential conductance can directly probe the ABS spectrum, serving as an alternative to the more complex microwave spectroscopy technique. We consider three frameworks in our theoretical analysis: (i) Perturbation theory in the tunneling amplitudes, which leads to nonstandard phase-sensitive Andreev reflections coupling the supercurrent to the nonequilibrium populations in the normal region; (ii) Nonperturbative transport theory valid for all orders in tunneling and all dimensions of the device; and (iii) Physically-motivated approximations to visualize the conductance maps in the (flux, voltage) plane. We further show that our theory can capture the results of recent experiments by Penn State and Harvard groups.