Institute of Fundamental Technological Research

One of the key issues in the physics of topological insulators is whether the topologically non trivial properties survive at finite temperatures and, if so, whether they disappear only at the temperature of topological gap closing. Here, we study this problem, using quantum fidelity as a measure, by means of ab-initio methods supplemented by an effective dissipative theory built on the top of the ab-initio electron and phonon band structures. In the case of SnTe, the prototypical crystal topological insulator, we reveal the presence of a characteristic temperature, much lower than the gap-closing one, that marks a loss of coherence of the topological state. The transition is not present in a purely electronic system but it appears once we invoke coupling with a dissipative bosonic bath. Features in the dependence with temperature of the fidelity susceptibility can be related to changes in the band curvature, but signatures of a topological phase transition appear in the fidelity only though the non-adiabatic coupling with soft phonons. Our argument is valid for valley topological insulators, but in principle can be generalized to the broader class of topological insulators which host any symmetry-breaking boson.

PbTe is a leading thermoelectric material at intermediate temperatures, largely thanks to its low lattice thermal conductivity. However, its efficiency is too low to compete with other forms of power generation. This efficiency can be effectively enhanced by designing nanostructures capable of scattering phonons over a wide range of length scales to reduce the lattice thermal conductivity. The presence of grain boundaries can reduce the thermal conductivity to ∼0.5 W m −1 K−1 for small acancy concentrations and grain sizes. However, grains anneal at finite temperature, and equilibrium and metastable grain size distributions determine the extent of the reduction in thermal conductivity. In the present work, we propose a phase-field model informed by molecular dynamics simulations to study the annealing process in PbTe and how it is affected by the presence of grain boundaries and voids. We find that the thermal conductivity of PbTe is reduced by up to 35% in the porous material at low temperatures. We observe that a phase transition at a finite density of voids governs the kinetics of impeding grain growth by Zener pinning.

The temperature renormalization of the bulk band structure of a topological crystalline insulator, SnTe, is calculated using first-principles methods. We explicitly include the effect of thermal-expansion-induced modification of electronic states and their band inversion on electron-phonon interaction.We show that the direct gap decreases with temperature, as both thermal expansion and electron-phonon interaction drive SnTe towards the phase transition to a topologically trivial phase as temperature increases. The band gap renormalization due to electron-phonon interaction exhibits a nonlinear dependence on temperature as the material approaches the phase transition, while the lifetimes of the conduction band states near the band edge show a nonmonotonic behawior with temperature. These effects should have important implications on bulk electronic and thermoelectric transport in SnTe and other topological insulators.