Silicene is a monolayer of silicon atoms forming a honeycomb lattice. The
lattice is actually made of two sublattices with a tiny separation. Silicene is
a topological insulator, which is characterized by a full insulating gap in the
bulk and helical gapless edges. It undergoes a phase transition from a
topological insulator to a band insulator by applying external electric field.
Analyzing the spin Chern number based on the effective Dirac theory, we find
their origin to be a pseudospin meron in the momentum space. The peudospin
degree of freedom arises from the two-sublattice structure. Our analysis makes
clear the mechanism how a phase transition occurs from a topological insulator
to a band insulator under increasing electric field. We propose a method to
determine the critical electric field with the aid of diamagnetism of silicene.
Diamagnetism is tunable by the external electric field, and exhibits a singular
behaviour at the critical electric field. Our result is important also from the
viewpoint of cross correlation between electric field and magnetism. Our
finding will be important for future electro-magnetic correlated devices.Comment: 4 pages,5 figure
