Quantum Criticality in Topological Insulators and Superconductors: Emergence of Strongly Coupled Majoranas and Supersymmetry

TL;DR

This paper investigates quantum phase transitions in topological insulators and superconductors, revealing emergent strongly coupled Majorana modes and supersymmetry at critical points, with implications for topological quantum states.

Contribution

It uncovers how boundary modes behave at symmetry-breaking quantum critical points, demonstrating emergent supersymmetry and strongly coupled Majorana states in topological materials.

Findings

Boundary modes decouple or flow to a strongly coupled fixed point.

Critical fluctuations can be confined to the surface, leading to supersymmetry.

Majorana modes remain gapless but become strongly coupled at criticality.

Abstract

We study symmetry breaking quantum phase transitions in topological insulators and superconductors where the single electron gap remains open in the bulk. Specifically, we consider spontaneous breaking of the symmetry that protects the gapless boundary modes, so that in the ordered phase these modes are gapped. Here we determine the fate of the topological boundary modes right at the transition where they are coupled to the strongly fluctuating order parameter field. Using a combination of exact solutions and renormalization group techniques, we find that the surface fermionic modes either decouple from the bulk fluctuations, or flow to a strongly coupled fixed point which remains gapless. In addition, we study transitions where the critical fluctuations are confined only to the surface and find that in several cases the critical point is naturally supersymmetric. This allows a determination of critical exponents and points to an underlying connection between band topology and supersymmetry. Finally, we study the fate of gapless Majorana modes localized on point and line defects in topological superconductors at bulk criticality, which is analogous to a quantum impurity problem. Again, an interplay of topology and strong correlations causes these modes to remain gapless but in a strongly coupled state. Experimental candidates for realizing these phenomena are discussed.