Year: 2012
Type: article
Abstract: We discuss (2+1)-dimensional topological superconductors with ${N}_{f}$ left- and right-moving Majorana edge modes and a ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry. In the absence of interactions, these phases are distinguished by an integral topological invariant ${N}_{f}$. With interactions, the edge state in the case of ${N}_{f}=8$ is unstable against interactions, and a ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ invariant mass gap can be generated dynamically. We show that this phenomenon is closely related to the modular invariance of type II superstring theory. More generally, we show that the global gravitational anomaly of the nonchiral Majorana edge states is the physical manifestation of the bulk topological superconductors classified by ${\mathbb{Z}}_{8}$.
Source: Physical Review B
Authors: Shinsei Ryu, Shou-Cheng Zhang
Institutions: University of Illinois Urbana-Champaign, Stanford University
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1984334615