Disorder-induced phase transitions in double HgTe quantum wells

By using the self-consistent Born approximation, we investigate topological phase transitions in double HgTe quantum wells (QWs) induced by the short-range impurities. Following the evolution of the density-of-states and the spectral function, we demonstrate multiple closings and openings of the band-gap with the increase of the disorder strength due to the mutual inversions between the first and second electron-like and hole-like subbands. We show that starting from a band insulator in the clean limit, under the influence of disorder, the double HgTe QW undergoes a transition, first into a semimetal state similar to "bilayer graphene", and then into a high-order topological insulator state with a double band inversion. We find out that all disorder-induced transitions can be fully characterized by introducing a non-Hermitian quasiparticle Hamiltonian encoding the band structure renormalization and quasiparticle decay.