Fine energy splitting of overlapping Andreev bound states in multiterminal superconducting nanostructures

Abstract

The recent proposals of experiments with single Andreev bound states make relevant a detailed analysis of these states in multiterminal superconducting nanostructures. We evaluate the energy splitting of degenerate Andreev bound states that overlap in a superconducting lead, and find that the splitting is reduced in comparison with their energy by a small factor sqrt[RG_{Q}], with RG_{Q} being the dimensionless resistance of the overlap region in the normal state. This permits quantum manipulation of the quasiparticles in these states. We provide a simple scheme of such manipulation.