QuantAlpsAn ecosystem for quantum science & technologies :
From the philosopher to the industrial

Abstract: Topological phases of matter are distinguished by robust properties that are insensitive to perturbations. These include quantized responses, perfectly conducting interfaces, and exactly zero energy modes, with wide-ranging technological applications. Recent years saw the complete classification of topological band structures, revealing an abundance of topological crystalline insulators. Many questions about the robustness of these phases to disorder are, however, still open. We develop new theoretical and numerical methods based on local topological markers and effective momentum-space Hamiltonians to study topological phases in disordered systems. We introduce symmetry indicators for amorphous systems, and we also demonstrate that it is possible to construct a fully isotropic and inversion-symmetric three-dimensional medium where time-reversal symmetry is systematically broken. We propose an amorphous system with scalar time-reversal symmetry breaking, implemented by hopping through chiral magnetic clusters along the bonds. The average spatial symmetries alone protect a statistical topological insulator phase in this system, analogous to crystalline mirror Chern insulators. We also show the expected transport properties of a three-dimensional statistical topological insulator, which remains critical on the surface for odd values of the invariant.