Role of Disorder and Interactions on the Surface of Topological Superconductors

In this work we study the surface properties of topological systems, with a special focus on topological superconductors without inversion symmetry. These materials provide a rich playground for multiple topological phenomena, showing boundary modes with linear and (or) flat dispersion arising from complex nodal structures. A remarkable characteristic of topological phases is their robustness to local perturbations. In usual topological phases such as topological band insulators, this protection owes its existence to the presence of a pronounced energy gap separating topological sectors. In the present work, we explore the extent to which this robustness can be generalized to gapless topological phases. We numerically test the robustness of topological boundary modes against local disorder and explore the contrast between different disorder strengths and distributions. An experimental signature is proposed to detect and distinguish the exotic topological boundary modes in the limit of dilute disorder, with Fourier-transform scanning tunneling microscopy in mind. We show that each type of surface state carries a universal feature in its scattering interference pattern, hence making this surface technique particularly suitable. We further explore the consequences of strong surface disorder, which does not drastically alter the bulk’s topology. We show that two limits are of particular interest. First, we consider strong fluctuations in the surface’s electrostatic potential, which lead to the formation of a high density of Anderson localized impurity states on the surface. We show that these impurity states mediate scattering within the boundary modes due to their energy proximity. Consequently, this type of disorder is particularly harmful for topological surface states, in particular for potential fluctuations with comparable strength to the system’s bandwidth. The second limit of disorder concerns strong surface impurities, which can equivalently be regarded as lattice vacancies or surface roughness. We show that in the presence of this type of disorder, the topological states migrate to inner layers. Hence, lattice vacancies or surface roughness cannot harm the topological boundary modes of both gapped and gapless phases. It follows that the existence of the topological surface states does not depend on translational symmetry. We show that substituting one disorder regime by the other by inducing strong localized surface scatterers can lead to a sharper signal in photoemission measurements after sputtering samples of the topological insulator bismuth selenide. Additionally, we study the interplay between topology and electron-electron interactions