  The surface states in three-dimensional (3D) topological insulators (TIs) can
be described by a two-dimensional (2D) continuous Dirac Hamiltonian. However,
there exists the Fermion doubling problem when putting the continuous 2D Dirac
equation into a lattice model. In this letter, we introduce a Wilson term with
a zero bare mass into the 2D lattice model to overcome the difficulty. By
comparing with a 3D Hamiltonian, we show that the modified 2D lattice model can
faithfully describe the low-energy electrical and transport properties of
surface states of 3D TIs. So this 2D lattice model provides a simple and cheap
way to numerically simulate the surface states of 3D TI nanostructures. Based
on the 2D lattice model, we also establish the wormhole effect in a TI nanowire
by a magnetic field along the wire and show the surface states being robust
against disorder. The proposed 2D lattice model can be extensively applied to
study the various properties and effects, such as the transport properties,
Hall effect, universal conductance fluctuations, localization effect, etc.. So
it paves a new way to study the surface states of the 3D topological
insulators.
