Snaking states on a cylindrical surface in a perpendicular magnetic field

摘要

We calculate electronic states on a closed cylindrical surface as a model ofa core-shell nanowire. The length of the cylinder can be infinite or finite. Wedefine cardinal points on the circumference of the cylinder and consider aspatially uniform magnetic field perpendicular to the cylinder axis,in thedirection South-North. The orbital motion of the electrons depends on theradial component of the field which is not uniform around the circumference: itis equal to the total field at North and South, but vanishes at the West andEast sides. For a strong field, when the magnetic length is comparable to theradius of the cylinder, the electronic states at North and South becomelocalized cyclotron orbits, whereas at East and West the states become long andnarrow snaking orbits propagating along the cylinder. The energy of thecyclotron states increases with the magnetic field whereas the energy of thesnaking states is stable. Consequently, at high magnetic fields the electrondensity vanishes at North and South and concentrates at East and West. Weinclude spin-orbit interaction with linear Rashba and Dresselhaus models. For acylinder of finite length the Dresselhaus interaction produces an axial twistof the charge density relative to the center of the wire, which may beamplified in the presence of the Rashba interaction.