Interaction-Induced Criticality in ${\mathbb{Z}}_2$ Topological Insulators

We study interaction effects in topological insulators with strong spin-orbit coupling. We find that the interplay of nontrivial topology and Coulomb repulsion induces a novel critical state on the surface of a three-dimensional topological insulator. Remarkably, this interaction-induced criticality, characterized by a universal value of conductivity, emerges without any adjustable parameters. Further, we predict a direct quantum-spin-Hall transition in two dimensions that occurs via a similar critical state.

Figure 1

Schematic scaling functions for the conductivity of 2D disordered systems of symplectic symmetry class. The plotted beta functions $\beta (g)=dg/d\ln L$ determine the flow of the dimensionless conductivity $g$ with increasing system size $L$ (as indicated by the arrows). The upper two panels show the beta functions for ordinary SO systems which are not topologically protected; the lower two panels demonstrate the scaling for topologically protected Dirac fermions (left: no interaction; right: Coulomb interaction included). In the interacting case the number of independent flavors is $N=1$.

Figure 2

Phase diagrams of a disordered 2D system demonstrating the QSH effect. (a) Noninteracting case. (b) Coulomb interaction included. Interaction “kills” the supermetal: the two insulators are separated by the critical line.