Boundary criticality in topological insulators

In the presence of an edge or a surface, quantum critical phenomena are enriched through the interplay between the bulk and boundary around phase transitions. Depending on whether the surface orders after or ahead of the bulk, the boundary transition is classified as either ordinary or extraordinary, with a special transition occurring between the two. These critical points exhibit unique boundary critical exponents, distinct from those of the bulk or boundary individually.

The nontrivial boundary states featured in topological phases of matter provides a breeding ground for a variety of boundary critical phenomena, due to their distinct boundary physics. Based on the Kane-Mele model of topological insulators, we present a large scale quantum Monte Carlo study of a lattice model that exhibits all three types of boundary criticality. Our model includes a Hubbard repulsion U that drives the system to order antiferromagnetically, and a Rashba interaction that breaks the S_z symmetry. We map out the phase diagram of different surface transitions where the electrons order at the boundary and/or in the bulk, depending on the ratio of U_bulk/U_bdy. Further, along the ordinary transition, the critical antiferromagnetic fluctuation is coupled to the helical edge, exhibiting a continuous boundary critical exponent, which terminates at a special Berezinskii-Kosterlitz-Thouless transition. To the best of our knowledge, this is the first time a complete surface transition phase diagram has been uncovered nonperturbatively and unbiasedly in a lattice model of a topological insulator.