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Silicene is a monolayer of silicon atoms forming a honeycomb lattice. Thelattice is actually made of two sublattices with a tiny separation. Silicene isa topological insulator, which is characterized by a full insulating gap in thebulk and helical gapless edges. It undergoes a phase transition from atopological insulator to a band insulator by applying external electric field.Analyzing the spin Chern number based on the effective Dirac theory, we findtheir origin to be a pseudospin meron in the momentum space. The peudospindegree of freedom arises from the two-sublattice structure. Our analysis makesclear the mechanism how a phase transition occurs from a topological insulatorto a band insulator under increasing electric field. We propose a method todetermine the critical electric field with the aid of diamagnetism of silicene.Diamagnetism is tunable by the external electric field, and exhibits a singularbehaviour at the critical electric field. Our result is important also from theviewpoint of cross correlation between electric field and magnetism. Ourfinding will be important for future electro-magnetic correlated devices.

Topological Phase Transition and Electrically Tunable Diamagnetism in Silicene