Draft:Electron–phonon interaction

In condensed matter physics, electron–phonon interaction (EPI) is the basic interaction between electrons and the vibrations of the crystal lattice (phonons). EPI is the typically the dominant contribution to electrical resistivity at room temperature. It is also responsible for the emergence of various quantum phases, such as superconductivity.

Mathematical description

The Hamiltonian describing the coupling is $$H_{\text{e-ph}}={\frac {1}{\sqrt {\Omega }}}\sum _{k,q.\eta }M_{\eta }(k+q,k)(a_{q,\eta }+a_{-q,\eta }^{\dagger })c_{k+q,\sigma }^{\dagger }c_{k,\sigma },$$ where [introduce variables]. The Hamiltonian describes an electron with lattice momentum k absorbing a phonon with momentum q or emitting a phonon with momentum -q and scattering to a state with momentum k+q.

Effects

Superconductivity

Main article: BCS theory

Polaron formation

Main article: Polaron

Sources

• Mahan, Gerald D. (2011). Condensed Matter in a Nutshell. Princeton, NJ Oxford: Princeton University Press. ISBN 978-0-691-14016-2.
• Giustino, Feliciano (2017-02-16). "Electron-phonon interactions from first principles". Reviews of Modern Physics. 89 (1). doi:10.1103/RevModPhys.89.015003. ISSN 0034-6861. Retrieved 2025-09-16.
• Ziman, J.M. (1960). Electrons and Phonons. Oxford University Press. ISBN 978-0-19-850779-6. {{cite book}}: ISBN / Date incompatibility (help)
• Born, Max; Huang, Kun (1954). Dynamical Theory of Crystal Lattices. ISBN 978-0-19-267008-3. {{cite book}}: ISBN / Date incompatibility (help)
• Ashcroft, Neil W.; Mermin, N. David (1976). Solid State Physics. Cengage Learning. ISBN 0-03-083993-9.
• Kittel, Charles (2004-11-11). Introduction to Solid State Physics. Wiley. ISBN 978-0-471-41526-8.
• Kittel, Charles (2004-11-11). Introduction to Solid State Physics. Wiley. ISBN 978-0-471-41526-8.