Changing the Topology of Electronic Systems Through Interactions or Disorder

Abstract

Recent work on the influence of interactions or disorder on the topological properties of insulators is reviewed. We show that a purely local interaction can cause topological transitions by renormalizing kinetic energy terms alone, without phase transitions associated with order parameters. Disorder is also a mean of changing the topology of Chern insulators, as it localizes every state except for those carrying the topological invariant. With increasing disorder, states with opposite topological invariant meet and annihilate. But considering the sub-lattice degree of freedom, Chern insulators may evade localization: an anomalous Hall metal may be stabilized with strong disorder in one sublattice, while the disorder in the other sublattice remains below some critical value. Also, a ferromagnetically ordered chain of magnetic impurities on conventional singlet superconductors with spin-orbit interaction induces topological Majorana modes at the ends of the chain. A ferromagnetic chain at the surface of a superconductor with spin–orbit coupling may eliminate the helical edge states of a finite system, while localized zero modes at the edges of the chain appear. Increasing the impurity density from a magnetic chain to an island produces a finite Chern number. At half-filling small concentrations may already induce chiral modes.