TKNN formula for general Hamiltonian

Abstract

Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low energy effective action for a general class of Hamiltonians bilinear in the fermion with general U(1) gauge interactions including non-minimal couplings by an explicit calculation. A series of Ward-Takahashi identities are crucial to relate the Chern-Simons level to a winding number, which could then be directly reduced to Chern character of Berry curvature by carrying out the integral over the temporal momenta.

revised version, 23 pages

References in corpus (2)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Wigner transformation, momentum space topology, and anomalous transport

Cited by in corpus (4)

• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Higher bracket structure of density operators in Weyl fermion systems and topological insulators
• Topological invariant of multilayer Haldane models with irregular stackings
• TKNN formula for general lattice Hamiltonian in odd dimensions