Three-dimensional Topological Insulators and Bosonization

Abstract

Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF gauge theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.

54 pages, 11 figures

References in corpus (14)

• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• On the $Z_2$ classification of Quantum Spin Hall Models
• Fractional topological insulators in three dimensions
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding
• More Abelian Dualities in 2+1 Dimensions
• Layer construction of 3D topological states and string braiding statistics
• Universal Topological Data for Gapped Quantum Liquids in Three Dimensions and Fusion Algebra for Non-Abelian String Excitations
• Partition Functions of Non-Abelian Quantum Hall States

Cited by in corpus (10)

• Revealing tensor monopoles through quantum-metric measurements
• Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order
• Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks
• Holographic Projection of Electromagnetic Maxwell Theory
• Bosonization of Majorana modes and edge states
• Fermion-fermion duality in 3+1 dimensions
• Microscopic states of Kerr black holes from boundary-bulk correspondence
• Induced parity-odd effective action for a Dirac field on $S^2\times S^1$
• Quantization of a Self-dual Conformal Theory in (2+1) Dimensions
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates