Adiabatic Pumping of Chern-Simons Axion Coupling

Abstract

We study the adiabatic pumping of the Chern-Simons axion (CSA) coupling along a parametric loop characterized by a non-zero second Chern number $C^{(2)}$ from the viewpoint of the hybrid Wannier representation, in which the Wannier charge centers (WCCs) are visualized as sheets defined over a projected 2D Brillouin zone. We derive a new formula for the CSA coupling, expressing it as an integral involving Berry curvatures and potentials defined on the WCC sheets. We show that a loop characterized by a non-zero $C^{(2)}$ requires a series of sheet-touching events at which $2\pi$ quanta of Berry curvature are passed from sheet to sheet, in such a way that $e^2/h$ units of CSA coupling are pumped by a lattice vector by the end of the cycle. We illustrate these behaviors via explicit calculations on a model tight-binding Hamiltonian and discuss their implications.

References in corpus (3)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Computing topological invariants without inversion symmetry
• Wannier Center Sheets in Topological Insulators

Cited by in corpus (26)

• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
• Surfaces of Axion Insulators
• On the matter of topological insulators as magnetoelectrics
• Quantization in chiral higher order topological insulators: circular dichroism and local Chern marker
• Surface theorem for the Chern-Simons axion coupling
• Wannier representation of Floquet topological states
• Teleportation of Berry curvature on the surface of a Hopf insulator
• Axion coupling in the hybrid Wannier representation
• Smooth gauge and Wannier functions for topological band structures in arbitrary dimensions
• Local Topological Markers in Odd Dimensions
• Geometric and nongeometric contributions to the surface anomalous Hall conductivity
• The New Phase due to Symmetry Protected Piecewise Berry Phases; Enhanced Pumping and Non-reciprocity in Trimer Lattices
• Half-Quantized Helical Hinge Currents in Axion Insulators
• Gauge-discontinuity contributions to Chern-Simons orbital magnetoelectric coupling
• Effects of Dephasing on Quantum Adiabatic Pumping with Nonequilibrium Initial States
• ${\mathbb{Z}}_2$ Spin Hopf Insulator: Helical Hinge States and Returning Thouless Pump
• Quantized surface magnetism and higher-order topology: Application to the Hopf insulator
• The multi-state geometry of shift current and polarization
• Real Hopf Insulator
• Competing Adiabatic Thouless Pumps in Enlarged Parameter Spaces
• Protected Gapless Edge States In Trivial Topology
• Mirror Chern numbers in the hybrid Wannier representation
• Quantized Chern-Simons Axion Coupling in Anomalous Floquet Systems
• Exact expression for the Berry connection in the projection gauge
• Gapless hinge states from adiabatic pumping of axion coupling