Electron-phonon interactions and Kohn anomalies

Electron-phonon interactions

Derivation of Hamiltonian Electron-Phonon Coupling

The Hamiltonian for the electron-phonon interaction can be described as

$H=H_{el}^{0}+H_{ph}^{0}+H_{coul}+H_{int}$

Where

$H_{el}^{0}=\sum _{k\sigma }E_{k}c_{k\sigma }^{\dagger }c_{k\sigma }$ Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H^0_{ph} = \sum_{k \lamda}E_kc^\dagger_{k \sigma}c_{k \sigma}} $H_{el}^{0}=\sum _{k\sigma }E_{k}c_{k\sigma }^{\dagger }c_{k\sigma }$

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