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Electric polarization in a Chern insulator.

Sinisa Coh1, David Vanderbilt

  • 1Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA. sinisa@physics.rutgers.edu

Physical Review Letters
|April 28, 2009
PubMed
Summary

This study extends the Berry-phase concept to Chern insulators, relating bulk current and surface charge to bulk polarization. It addresses challenges posed by partially occupied chiral edge states for accurate polarization calculations.

Area of Science:

  • Condensed Matter Physics
  • Topological Materials
  • Quantum Mechanics

Background:

  • The Berry-phase concept is crucial for understanding electric polarization in insulators.
  • Chern insulators, characterized by a nonzero Chern invariant, exhibit unique topological properties including chiral edge states.
  • Partial occupation of these edge states complicates the direct application of standard polarization theories.

Purpose of the Study:

  • To generalize the Berry-phase concept of polarization to insulators with a nonzero Chern invariant (Chern insulators).
  • To establish a relationship between bulk current, surface charge, and bulk polarization in these topological materials.
  • To provide analytical and numerical support for the developed theoretical framework.

Main Methods:

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  • Extension of the Berry-phase formalism to address partial occupation of chiral edge states.
  • Relating integrated bulk current to differences in bulk polarization via adiabatic evolution.
  • Connecting surface charge to bulk polarization, contingent on identifying specific wave vectors for edge state occupancy discontinuity.
  • Numerical calculations using a model Hamiltonian.

    • Main Results:

    • An analytical method is presented to calculate polarization in Chern insulators, accounting for edge state complexities.
    • The integrated bulk current is shown to be equivalent to a difference in bulk polarizations.
    • Surface charge is linked to bulk polarization, with a condition on the wave vector of edge state discontinuity.
    • Numerical simulations corroborate the analytical findings.

    Conclusions:

    • The generalized Berry-phase concept provides a robust framework for defining and calculating polarization in Chern insulators.
    • The findings offer new insights into the relationship between bulk and edge properties in topological insulators.
    • This work facilitates a deeper understanding and potential applications of topological materials in condensed matter physics.