I'm studying 3D topological insulators and more in particular, weak antilocalization (WAL) effects, so I know that they are characterized by a $\pi$ Berry phase that gives rise to destructive interferences in closed paths between time reversal paths producing WAL. In surface carriers this seems to be logical to me. However, I'm not sure about this in the bulk. In the bulk, you have time reversal symmetry (TRS) and inversion symmetry (IR) (most of time), so the spin degeneracy must hold (I'm using + for spin up and - for spin down): $$ TRS: E(+, k)=E(-, -k) $$ $$ IS: E(+, k)=E(+, -k) $$ If these two relations hold, then we have: $$ E(+, k)=E(-, k) $$ At the boundaries, inversion symmetry is broken, so the spin degeneracy can be lifted and we end up with spin momentum locking. However in the bulk, this is not the case. So the spin of the electron is not well defined as far as I understand. So I cannot see where the $\pi$ Berry phase comes form in bulk carriers. Consequently, WAL should not be possible in bulk carriers. Am I wrong?


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