Transport in magnetized nanocylindrical topological insulators

Abstract

In this work we study the surface states of a topological insulator (TI) cylinder with a magnetization in the radial, azimuthal and axial directions. We derive the eigenenergies and eigenstates, and show that a state with a quantum number associated with the orbital angular momentum incident at a junction between a source TI cylinder and a coaxial drain TI cylinder can only be transmitted and reflected into states with the same quantum number. For cylinders magnetized only in the radial direction, this leads to markedly different behavior in the transmission depending on whether the source magnetization is smaller or larger than the drain magnetization. For azimuthal magnetizations, it results in perfect transmission between two cylinders magnetized to different extents in the azimuthal direction. The restriction of transmission and reflection to states with the same quantum number gives rise to a step-like increment in the transmission from an unmagnetized cylinder to one with an axial magnetization as the energy and magnetization are varied.