The discovery of topological materials represents a milestone in condensed matter physics. It twisted the way we look at the band structure of solids classifying them in terms of well-defined global invariants of their bulk wave function electronic space. When non-trivial, these invariants are associated to the emergence of boundary modes which, because of their topological origin, are protected against weak disorder. In my talk, I will provide an overview of universal trends which emerge in topological materials once the symmetries which guarantee their existence are lifted.
I will start by discussing topological insulators interacting with time-reversal symmetry breaking perturbations. I will demonstrate that, contrary to the general belief, magnetic order and gapless states can coexist. By analyzing the quantum anomalous Hall effect platform, I will show that this apparent paradox is associated to a dual nature of the dopants which gives rise to a two fluid behavior with opposite and competing trends, i.e. gap opening vs. gap closing.
I will then move on topological crystalline insulators where I will report on the discovery of robust 1D spin-polarized channels naturally emerging at TCI surfaces once translational invariance is broken. I will illustrate how these 1D channels can be easily obtained in the prototypical TCI Pb1−xSnxSe compound without the need of any sophisticated preparation technique and demonstrate how, contrary to 1D topological states known so far, their protection mechanisms result in a striking robustness to defects, strong magnetic fields, and elevated temperature.
Finally, I will discuss more recent results on Weyl semimetals, showing how their interaction with atomic scale perturbations give rise to strong and universal spectroscopic signatures associates to their topological states, i.e. Weyl points and Fermi arcs. These signatures are found to be stoichiometry independent, providing a unifying picture of the Weyl phase diagram.