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Degeneracy-Projected Polarization Formulas for Hall-Type Conductivities.
1Physics Department, Technion, 32000 Haifa, Israel.
Physical Review Letters
|February 4, 2022
Summary
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.
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.
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