Simulating the spectral response of a Majorana-transmon device

We perform a numerical study of a toy-model for the Majorana-transmon device, obtaining its spectral response across the topological phase transition. To this end, we employ the DMRG and TEBD techniques. We model the superconducting wires on either end of the Josephson junction as spinful fermions hopping on a 1D lattice with Rashba spin-orbit coupling in a Zeeman field perpendicular to the spin-orbit direction. As the Zeeman field is increased and the superconducting wires are driven across the topological phase transition, we observe the splitting of the plasma mode due to the zero-energy Majorana modes forming at the ends of the wires. Interestingly, the spectral function is largely unaffected by the gap closing in the bulk of the superconducting wires. When the length of the junction is finite, additional Andreev bound states can form. We show that the appearance of these states gives rise to additional spectral lines, obscuring the signatures of the topological phase.