Signatures of topological phase transitions in higher Landau levels of HgTe/CdTe quantum wells from an information theory perspective

We analyze the structure of low energy Hamiltonian eigenstates in zincblende heterostructures (like HgTe/CdTe quantum wells) near the gamma point, under magnetic fields, to characterize topological phase transitions (TPT) under an information-theoretic perspective. Using information markers like entanglement, quantum fluctuations, fidelity susceptibility, participation ration, area in phase space, etc., we realize that higher Landau levels (LL) feel the topological phase transition slightly displaced with regard to the edge state, thus leading to the concept of "higher Landau level vertical bar n vertical bar > 0 TPT", as "echoes" of the standard edge state n = 0 TPT. We compute the critical magnetic field and the critical HgTe layer thickness at which these information measures of higher Landau levels undergo a structural change. (C) 2022 The Author(s). Published by Elsevier B.V.