Aharonov-Bohm effect for quasiparticles around a vortex line in a d-wave superconductor

On the basis of the Bogoliubov-de Gennes theory we develop an analytical description of low-energy extended quasiparticle states around an isolated flux line in a superconductor with gap nodes. The wave functions of these excitations and the corresponding density of states are shown to be strongly influenced by the interaction with a pure gauge potential due to the Aharonov-Bohm scenario.