Chiral Edge States in Mesoscopic Superconductors

Quantum phase transitions are studied by solving a modified Bogliubov-de Gennes model for mesoscopic metallic superconductors with nonlocal surface scatterings. It is found that the nonlocal surface scattering effect can induce a spin-orbit interaction into the model Hamiltonian. Chiral edge states can occur with the appropriate spin-orbit coupling strength. The competitions between the chiral edge states and the spin singlet superconducting states can result in a series of quantum phase transitions with the applied axial magnetic field. The magnetization moment is found to be a constant of one quarter Bohr magneto when the phase transition between states with different angular quantum numbers occurs.