Junction between surfaces of two topological insulators

Abstract

We study the properties of a line junction which separates the surfaces of two three-dimensional topological insulators. The velocities of the Dirac electrons on the two surfaces may be unequal and may even have opposite signs. For a time reversal invariant system, we show that the line junction is characterized by an arbitrary parameter \alpha which determines the scattering from the junction. If the surface velocities have the same sign, we show that there can be edge states which propagate along the line junction with a velocity and orientation of the spin which depend on \alpha and the ratio of the velocities. Next, we study what happens if the two surfaces are at an angle \phi with respect to each other. We study the scattering and differential conductance through the line junction as functions of \phi and \alpha. We also find that there are edge states which propagate along the line junction with a velocity and spin orientation which depend on \phi. Finally, if the surface velocities have opposite signs, we find that the electrons must transmit into the two-dimensional interface separating the two topological insulators.