Cancellation of quantum anomalies and bosonization of threedimensional timereversal symmetric topological insulators
Abstract
The strong timereversal symmetric topological insulator in three space dimensions features gapless surface states in the form of massless Dirac fermions. We study these surface states with the method of bosonization, and find that the resulting bosonic theory has a topological contribution due to the parity anomaly of the surface Dirac fermions. We argue that the presence of a quantum anomaly is, in fact, the main reason for the existence of a surface state, by the principle that anomalies of a surface and bulk must cancel. Inspecting other classes of topological insulators, we argue that this principle holds in general. Moving beyond purely topological considerations, we incorporate the dynamics of the surface electron states into the bosonic theory. Additionally, we discuss the thermodynamics of the bosonic theory and propose a representation of the surface Dirac fermions in terms of the bosonic fields.
 Publication:

Physical Review B
 Pub Date:
 August 2013
 DOI:
 10.1103/PhysRevB.88.085105
 arXiv:
 arXiv:1303.2644
 Bibcode:
 2013PhRvB..88h5105Z
 Keywords:

 73.43.f;
 73.20.r;
 11.10.Lm;
 11.15.Yc;
 Quantum Hall effects;
 Electron states at surfaces and interfaces;
 Nonlinear or nonlocal theories and models;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 16 pages, 2 figures. Final minor corrections