Leveraging structural disorder to enhance topological phases

Abstract

On-site disorder can be leveraged to induce a transition from a trivial to a topological insulator. However it is unclear if structural disorder in the absence of on-site disorder can aid a similar transition and, if so, which kind of structural disorder is more favourable. We numerically show that structural disorder can enhance and sustain a topological phase up to strong disorder in two dimensions provided that one penalises atomic sites from being close to one another. However, we find this effect is absent in three dimensions, where structural disorder appears generically detrimental to the phase. In our calculations we include disorder that can scramble the global spin-reference frame, an overlooked type of disorder expected to exist in strongly disordered solids. This disorder fatally scrambles the information necessary for the spin-Bott and the spin-Chern marker to correctly diagnose a topological phase. By using the spectral localizer, a local marker directly defined using the time-reversal symmetry operator rather than a spin-projection, we show how one can circumvent this limitation, providing a basis-indifferent theory for calculating Z2 invariants. Our work showcases that not all structural disorders are equally beneficial to topology, and highlights guiding principles to enhance and detect topological phases in both solid-state and metamaterial realisations.