Probing Majorana bound states through an inhomogeneous Andreev double dot interferometer

In modern experiments with hybrid superconducting (SC)/semiconducting nanowires the presence of zero-energy Andreev bound states (ABSs), characterized by a partial overlap of the Majorana wave functions, is a common problem that significantly complicates the detection of a genuine Majorana bound state (MBS). In this article, taking into account spatial inhomogeneity of experimentally investigated nanowire samples, we study interference transport features of a curved heterostructure in which two normal wires (or arms) are separated by a superconducting wire. Since Andreev reflection on the two N/S interfaces with smoothly changing electrostatic and SC pairing potentials results in the emergence of bound states, the low-energy interference transport is described in the framework of the model of two noninteracting Andreev levels or the Andreev double quantum dot. A set of limiting cases is analyzed allowing us to highlight the interference properties that are unique for the different types of ABSs, such as bulk ABS, inhomogeneous ABS, and MBS. In particular, considerable attention is paid to the features of the Aharonov-Bohm (AB) effect. It is shown that the response of each state can be recognized analyzing both AB period and extrema positions of the conductance oscillations which take place without any fine-tuning of the system parameters.