Berry connection and Wilson loop in topological insulators (part 2)

Author: George Tsitsishvili
Co-authors: Merab Eliashvili
Keywords: Topological insulator, Berry connection, Wilson Loop
Annotation:

The U(N) non-Abelian Berry connections are constructed by use of the eigenstates of the matrix Hamiltonian associated with 2D tight-binding model. It is shown that the corresponding strength tensor vanishes everywhere in the Brillouin zone except certain isolated points where the tensor exhibits singular behavior. Such points are usually related to edge-bulk phase transition points and can be described/characterized by the Wislon loop eigenvalues which are gauge-invariant objects. For the matrix Hamiltonian we use the so-called singular value decomposition which allows to calculate the Wilson loop and its eigenvalues in the closed analytic form.