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 electronlike and holelike 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.