Pseudo-relativistic fermions and topological states in zinc-blende semiconductors and their heterostructures (Habilitation thesis)

Abstract

Tracing my scientific path from many-body physics in semiconductor nanostructures to topological quantum matter, this Habilitation à diriger des recherches (HDR) memoir presents only part of my research since defending two PhD theses in Toulouse and Nizhny Novgorod in 2011. Focusing on pseudo-relativistic fermions and topological states in zinc-blende semiconductors and their heterostructures, it highlights my independent research program: identifying physical problems, developing predictive theories, and initiating new directions with experimentalists. The first part addresses Kane fermions in bulk HgCdTe: temperature-driven band inversion, domain-wall states, the collapse of Landau levels in crossed electric and magnetic fields, and disorder-induced topological transitions. The second examines pressure-, temperature-, and disorder-driven phase transitions in single and double HgTe quantum wells (QWs), including bilayer-graphene-like semimetals and a two-dimensional higher-order topological insulator (2D HOTI) phase beyond the minimal BHZ model. The third develops three-layer InAs/Ga(In)Sb QWs as a III-V platform for massless Dirac fermions, large-gap quantum spin Hall insulators, 2D HOTI phases, and semimetals with quadratic band touching, and discusses InAs$_{x}$Sb$_{1-x}$/InAs$_{y}$Sb$_{1-y}$ heterostructures as a promising alternative. Several of these predictions are supported by experimental observations, including quantized helical edge transport up to 60 K and the unconventional quantum Hall effect. Defended on March 25, 2026, at the University of Montpellier. Jury: Michel GOIRAN (chair and rapporteur, LNCMI-CNRS, Toulouse); Alexey KAVOKIN (rapporteur, Westlake University, Hangzhou); Robson FERREIRA (rapporteur, LPENS-CNRS, Paris); Alexei BARANOV (member, IES-CNRS, Montpellier); Benoit JOUAULT and Frédéric TEPPE (members, L2C-CNRS, Montpellier).