Abstract
We develop an approximate theory of phonon-induced topological insulation in Dirac materials. In the weak coupling regime, long wavelength phonons may favor topological phases in Dirac insulators with direct and narrow bandgaps. This phenomenon originates from electron-phonon matrix elements, which change qualitatively under a band inversion. A similar mechanism applies to weak Coulomb interactions and spin-independent disorder; however, the influence of these on band topology is largely independent of temperature. As applications of the theory, we evaluate the temperature-dependence of the critical thickness and the critical stoichiometric ratio for the topological transition in CdTe/HgTe quantum wells and in BiTl(S$_{1-\delta}$Se$_{\delta})_2$, respectively.
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