ABSTRACT

The helical edge states of 2DTIs have higher-dimensional analogues,

Dirac-like 2D states at a surface of a bulk material. A bulk system

with the Dirac surface states inside the band gap is a three-

dimensional topological insulator (3DTI). To elucidate the origin of

the surface states, in this section we introduce a microscopic model

based on the Kane k · p Hamiltonian with a nontrivial boundary condition. We shall see that out of all bulk degrees of freedom

the surface state inherits only the electron spin. Similar to the

helical edge states, the spin of the surface carrier is locked to the

direction of its momentum. In the 2D surface geometry the spin-

momentum locking gives rise to a new transport phenomenon, weak

antilocalization. We shall discuss both a simple qualitative picture

and the detailed theory of this phenomenon.