The evaluation of non-topological components in Berry phase and momentum relaxation time in a gapped 3D topological insulator

The zero gap surface states of a 3D-topological insulator host Dirac fermions with spin locked to the momentum. The gap-less Dirac fermions exhibit electronic behaviour different from those predicted in conventional materials. While calculations based on a simple linear dispersion can account for observed experimental patterns, a more accurate match is obtained by including higher order \( \overrightarrow{k}\) terms in the Hamiltonian. In this work, in presence of a time reversal symmetry breaking external magnetic field and higher order warping term, alteration to the topologically ordained Berry phase of \( (2n + 1)\pi \), momentum relaxation time, and the magneto-conductivity tensors is established.