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.