Effective hydrodynamic field theory and condensation picture of topological insulators

Abstract

While many features of topological band insulators are commonly discussed at the level of single-particle electron wave functions, such as the gapless Dirac spectrum at their boundary, it remains elusive to develop a {\it hydrodynamic} or {\it collective} description of fermionic topological band insulators in 3+1 dimensions. As the Chern-Simons theory for the 2+1-dimensional quantum Hall effect, such a hydrodynamic effective field theory provides a universal description of topological band insulators, even in the presence of interactions, and that of putative fractional topological insulators. In this paper, we undertake this task by using the functional bosonization. The effective field theory in the functional bosonization is written in terms of a two-form gauge field, which couples to a $U(1)$ gauge field that arises by gauging the continuous symmetry of the target system (the $U(1)$ particle number conservation). Integrating over the $U(1)$ gauge field by using the electromagnetic duality, the resulting theory describes topological band insulators as a condensation phase of the $U(1)$ gauge theory (or as a monopole condensation phase of the dual gauge field). The hydrodynamic description, and the implication of its duality, of the surface of topological insulators are also discussed. We also touch upon the hydrodynamic theory of fractional topological insulators by using the parton construction.

References in corpus (9)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Fractional topological insulators in three dimensions
• Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator
• SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
• Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
• $S$-duality of $u(1)$ gauge theory with $\theta =\pi$ on non-orientable manifolds: Applications to topological insulators and superconductors
• Effective Field Theory for a p-wave Superconductor in the Subgap Regime
• Dualities in 3D Large $N$ Vector Models

Cited by in corpus (20)

• Hydrodynamic approach to electronic transport in graphene
• Revealing tensor monopoles through quantum-metric measurements
• Braiding with Borromean Rings in (3+1)-Dimensional Spacetime
• Wilson operator algebras and ground states for coupled BF theories
• Tensor Berry connections and their topological invariants
• Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order
• Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene
• Quantum field theory of topological spin dynamics
• Lattice Boltzmann method for semiclassical fluids
• Theory of oblique topological insulators
• Three-dimensional Topological Insulators and Bosonization
• Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks
• Non-local order parameters for states with topological electromagnetic response
• Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals
• Duality of a compact topological superconductor model and the Witten effect
• Boson-fermion duality in a gravitational background
• Quantization of a Self-dual Conformal Theory in (2+1) Dimensions
• Relativistic hydrodynamics with the parity anomaly
• Field Theoretic Aspects of Condensed Matter Physics: An Overview
• An exceptional surface and its topology