Time-dependent manipulation of YSR states and Majorana zero modes

The realization of topological quantum computing using topological superconductors requires the ability to manipulate Majorana zero modes at the nanoscale in real time. In this talk, I present a non-equilibrium formalism that allows one to study the real time response of superconductors to external perturbations.

In particular, I will show how this formalism can be used to study the emergence and manipulation of YSR states in s-wave superconductors in response to time-dependent changes in the local magnetic environment. I will demonstrate that the latter can also be employed to drive the superconductor through a time-dependent quantum phase transition, in which the ground state changes from a singlet to a doublet state. Finally, I will show how this approach allows us to investigate the braiding of Majorana zero modes in real time and space in topological superconductors.