Magnetic impurities on superconducting surfaces: Shiba and Majorana states studied with the STM

Abstract

A magnetic impurity on a superconductor can create a bound state. The state is localized to the magnetic impurity but it extends well into the superconductor and along the surface. Its energy is within the superconductor's gap. This state is not an electronic state. It is a complex state caused by the weakening of Cooper pairs due to the magnetic exchange field produced by the impurity. Its total spin is 1/2, but it is shared between electrons and holes. This state is known as Shiba state, also Yu-Shiba-Rusinov state. If another magnetic impurity is approached, the Shiba states can start interacting. If their spins are aligned, they can form bonding and antibonding states. As the number of impurities increases forming a chain of impurities, the Shiba states also increase forming Shiba bands. Under certain conditions, some of these bands can cross the Fermi energy, closing the superconducting gap. This can give rise to change in the topological electronic structure of the system. As a consequence, if the chain is not infinite, bound states at the edges of the chain are actually Majorana fermions. These Majorana fermions have strange properties when they are mutually exchanged, leading to complex operations that can eventually be used for quantum computations. I will give a pedagogical introduction to these matters, and I will exemplify them with some calculations done for the case of Cr chains on a ß-Bi2Pd superconductor.