Kinetic derivation of generalized phase space Chern-Simons theory

Abstract

We study anomalous transport phenomena induced by phase-space Berry curvature. For that purpose we construct a kinetic theory in $2d$ phase space when all abelian Berry curvatures are nonzero. We derive anomalous currents by calculating the complete form of the Poisson brackets of phase space coordinates. Then we construct the low-energy effective theory to reproduce the anomalous currents obtained from the kinetic theory. Such an effective theory is given by the Chern-Simons theory in $1+2d$ dimensions. Some implications of the Chern-Simons theory are also discussed.

17pages, no figure; (v2) accepted version for publication in PRB

References in corpus (14)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Spin current and magneto-electric effect in non-collinear magnets
• Experimental discovery of Weyl semimetal TaAs
• Experimental observation of Weyl points
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Quantized Adiabatic Transport in Momentum Space
• Unified Topological Response Theory for Gapped and Gapless Free Fermions

Cited by in corpus (6)

• Adiabatically Induced Orbital Magnetization
• Chiral kinetic theory of anomalous transport induced by torsion
• Diffusive real-time dynamics of a particle with Berry curvatures
• Chiral magnetic effect of light
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• Quantum geometric tensors from sub-bundle geometry