Gauge Dynamics and Topological Insulators

Abstract

A non-abelian magnetic field in Yang-Mills theory induces the formation of a "W-boson" vortex lattice. We study the propagation of fundamental fermions in the presence of this lattice in 2+1 dimensions. We show that the spectrum for massless fermions contains four topologically-protected Dirac points with non-zero Bloch momentum. For massive fermions, we compute topological invariants of the band structure and show that it is possible to realise a Z2 topological insulator within Yang-Mills theory.

28 pages + appendices, 5 figures. v2: Added comments on stability of lattice. Emphasised role of Higgs field. Added references v3: Further reference added. v4: Version to appear in JHEP

References in corpus (10)

• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• On the $Z_2$ classification of Quantum Spin Hall Models
• Topological aspects of quantum spin Hall effect in graphene: Z${}_2$ topological order and spin Chern number
• Magnetic field induced lattice ground states from holography
• QCD as a topologically ordered system
• Monopoles and Holography
• Electromagnetic superconductivity of vacuum induced by strong magnetic field

Cited by in corpus (1)

• Fermion zero modes in a chromomagnetic vortex lattice