Boundary and defect criticality in topological insulators and superconductors

TL;DR

This paper investigates the unique boundary critical phenomena in topological insulators and superconductors, revealing new universality classes and phase transitions influenced by boundary fermions and bulk interactions.

Contribution

It introduces novel boundary universality classes, including boundary Gross-Neveu-Yukawa and BKT transitions, in topological phases using advanced analytical techniques.

Findings

Discovery of boundary Gross-Neveu-Yukawa critical point

Identification of boundary BKT transition in topological phases

Comprehensive phase diagram with critical exponents

Abstract

We study the boundary criticality enriched by boundary fermions, which ubiquitously emerge in topological phases of matter, with a focus on topological insulators and topological superconductors. By employing dimensional regularization and bosonization techniques, we uncover several unprecedented boundary universality classes. These include the boundary Gross-Neveu-Yukawa critical point and the special Berezinskii-Kosterlitz-Thouless (BKT) transition, both resulting from the interplay between edge modes and bulk bosons. We present a comprehensive sketch of the phase diagram that accommodates these boundary criticalities and delineate their critical exponents. Additionally, we explore a 1+1D conformal defect decorated with fermions, where a defect BKT transition is highlighted. We conclude with a discussion on potential experimental realizations of these phenomena.