Agenda

Résumé : Almost two decades after the theoretical formulation of the quantum spin Hall insulating phase (QSHI), the number of real two-dimensional (2D) QSHI materials which have been confirmed experimentally is relatively limited, often exhibiting poor performances. Indeed, the intrinsic robustness advocated by topological protection can still suffer by the presence of defects or temperature effects, as most real QSHI can be easily perturbed into a metallic or trivial state. In addition, theoretical predictions of QSHIs can be very sensitive to the accuracy of the electronic-structure methods employed. Hence, fundamental research and potential technological applications of QSHIs are hindered both by the rarity of high-performance topological materials and by the lack of predictive modelling in complex settings, ranging from strong correlations to disorder, to finite temperature. In this talk, I will first present some achievements in the discovery and design of novel QSHI with first-principles simulations. In particular, I will discuss our discovery of jacutingaite, a naturally-occurring dual topological insulator made by potentially-exfoliable monolayers. 2D jacutingaite realizes graphene’s Kane-Mele model with a large band gap and a nice interplay between spin-orbit coupling, crystal-symmetry breaking, and dielectric response. Beyond materials discovery, I will provide an example of materials design and discuss our prediction of robust ferroelectric QSHI states in van-der-Waals heterobilayers made by two non-topological monolayers.  Finally, I will present more recent efforts towards ab-initio modelling of disorder and temperature in QSHIs. In particular, I will introduce single-point and space-resolved frameworks to calculate the Z2 topological invariant and other geometrical quantities for non-crystalline systems. These latest efforts are being released in a dedicated software package, SPInv, which is designed to work both with model Hamiltonians and first-principles simulations, operating in the Wannier function software ecosystem.