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Degeneracy-Projected Polarization Formulas for Hall-Type Conductivities.

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Simplified Kubo formulas offer economical calculations for Hall, transverse thermoelectric, and thermal Hall conductivities. These new expressions apply to general Hamiltonians and reveal gapless chiral excitations carrying Hall currents.

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Area of Science:

  • Condensed matter physics
  • Quantum transport phenomena

Background:

  • Kubo formulas are essential for calculating transport coefficients.
  • Existing methods can be computationally intensive and may require a band gap.

Purpose of the Study:

  • To simplify Kubo formulas for Hall, transverse thermoelectric, and thermal Hall conductivities.
  • To develop computationally economical expressions applicable to general Hamiltonians.
  • To investigate the nature of Hall currents in open boundary systems.

Main Methods:

  • Derivation of simplified Kubo formulas using on-shell commutators of degeneracy projected polarizations.
  • Application to general Hamiltonians, including those without a gap.
  • Demonstration using finite lattice calculations extrapolated to the dc-thermodynamic limit for a disordered metal.

Main Results:

  • New, computationally economical expressions for Hall, transverse thermoelectric, and thermal Hall conductivities.
  • Demonstration that Hall currents in open boundaries are carried by gapless chiral excitations.
  • Successful extrapolation of finite lattice calculations to the dc-thermodynamic limit.

Conclusions:

  • The simplified Kubo formulas provide a more efficient approach to calculating key transport properties.
  • Gapless chiral excitations are identified as the carriers of Hall currents in open systems.
  • The method is validated for disordered metals, showing its applicability to complex systems.