# Electron-phonon coupling and the metalization of solid helium at terapascal pressures

B. Monserrat, N. Drummond, C. Pickard, R. Needs

*Physical Review Letters* 112, 5 (2014)

#materials#highpressure#condensedmatter

Phase diagram of He at the pressure- temperature range relevant for cool WDs.

Solid He is studied in the pressure and temperature ranges 1–40 TPa and 0–10,000 K using first- principles methods. Anharmonic vibrational properties are calculated within a self-consistent field framework, including the internal and free energies, density-pressure relation, stress tensor, thermal expansion, and the electron-phonon coupling renormalization of the electronic band gap. We find that an accurate description of electron-phonon coupling requires us to use a non-perturbative approach. The metalization pressure of 32.9 TPa at 0 K is larger than found previously. The vibrational effects are large; for example at P = 30 TPa the band gap is increased by 2.8 eV by electron-phonon coupling and a further 0.1 eV by thermal expansion compared to the static value. The implications of the calculated metalization pressure for the cooling of white dwarfs are discussed.

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