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Continuous Kubo-Greenwood formula: Theory and numerical implementation
G S Demyanov1, D V Knyazev1, P R Levashov1
1Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia and Moscow Institute of Physics and Technology, Institutskiy Pereulok 9, Dolgoprudny, Moscow Region 141700, Russia.
A new continuous Kubo-Greenwood formula offers a detailed analysis of dynamic electrical conductivity by integrating over all energy ranges. This method enhances understanding of electron spectrum contributions to material properties.
Area of Science:
- Condensed Matter Physics
- Computational Materials Science
Background:
- The Kubo-Greenwood formula is a standard method for calculating dynamic Onsager coefficients and electrical conductivity.
- Traditional methods involve summations over discrete energy levels, limiting detailed spectral analysis.
Purpose of the Study:
- To introduce and validate a continuous Kubo-Greenwood formula for numerical calculations.
- To enable detailed analysis of electron energy spectrum contributions to material properties.
Main Methods:
- Formulation of a continuous Kubo-Greenwood formula as an integral over the energy range.
- Development of a smoothing procedure for matrix element functions D(ɛ,ɛ+ℏω).
- Implementation in the parallel code 'cubogram' for simulations.
Main Results:
- The continuous formula provides an alternative to the discrete version, yielding comparable results.
- Demonstrated the influence of technical parameters and matrix element computation methods on dynamic electrical conductivity simulations for liquid aluminum.
- Enabled analysis of contributions from different parts of the electron spectrum.
Conclusions:
- The continuous Kubo-Greenwood formula offers enhanced analytical capabilities for understanding material properties.
- The 'cubogram' code facilitates efficient simulation and analysis of dynamic electrical conductivity.
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