Edge States: Topological Insulators, Superconductors and QCD Chiral Bags

TL;DR

This paper explores the emergence of edge states in topological insulators, superconductors, and QCD chiral bag models, highlighting their common boundary conditions and physical properties such as spin-momentum locking.

Contribution

It demonstrates the universal role of boundary conditions in generating edge states across different physical systems, linking condensed matter and quantum chromodynamics.

Findings

Edge states occur due to boundary conditions in topological insulators and superconductors.

Similar edge phenomena are found in QCD chiral bag models.

Edge states exhibit spin-momentum locking and are associated with an incompressible bulk.

Abstract

The dynamics of the magnetic field in a superconducting phase is described by an effective massive bosonic field theory. If the superconductor is confined in a domain M with boundary \partial M, the boundary conditions of the electromagnetic fields are predetermined by physics. They are time-reversal and also parity invariant for adapted geometry. They lead to edge excitations while in comparison, the bulk energies have a large gap. A similar phenomenon occurs for topological insulators where appropriate boundary conditions for the Dirac Hamiltonian also lead to similar edge states and an 'incompressible bulk'. They give spin-momentum locking as well. In addition time-reversal and parity invariance emerge for adapted geometry. Similar edge states appear in QCD bag models with chiral boundary conditions.