Electron-Phonon Coupling and the Metallization of Solid Helium at Terapascal Pressures

Abstract

Solid He is studied in the pressure and temperature ranges 1-40 TPa and 0-10,000 K using firstprinciples 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.PACS numbers: 63.20. Ry, 62.50.p Helium (He) is the second most abundant element in the Universe after hydrogen and one of the most important components of stellar bodies such as giant gaseous planets, main-sequence stars, and white dwarf (WD) stars. The large value of the first excitation energy of atomic He of 19.82 eV leads to a high metalization pressure for the solid phase, of the order of tens of terapascals. Calculations of the phase diagram of He [1,2] indicate that, in the terapascal pressure range, it remains solid up to temperatures of around 8, 000 K. He is therefore expected to be found in the solid state in the outer layers of cool WDs.The vast majority of the stars in the Universe become WDs in the final stages of their evolution, with the gravitational attraction towards the center being balanced by the electron degeneracy pressure of the high-density core. The lack of a continuous energy source means that WDs cool down until reaching thermodynamic equilibrium with their surroundings, eventually becoming black dwarfs. An understanding of the cooling process [3] is essential when calculating the ages of observed WDs, which are widely used within cosmochronology [4,5] to date stellar clusters and galaxies, and hence to provide bounds on the age of the Universe.The cores of WDs are largely isothermal due to the high thermal conductivity of degenerate electrons. Hence the cooling rate is mainly determined by the outer layers, which are composed of hydrogen, He, or a mixture of both. In this context the insulator-metal transition in solid He is central because energy transport from the degenerate core is dominated by electron transport through metallic He in the deeper layers, and by photon transport through insulating He in the outermost region [6].Recent work has focused on the study of the metalization pressure of He in the solid and fluid states [6][7][8][9][10][11]. In the solid state [6], static-lattice electronic structure calculations using both the diffusion Monte Carlo (DMC) many-body wave function technique [12,13] and the GW approximation of many-body perturbation theory [14] have shown that standard generalized gradient approx...

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Theory of Thermal Relaxation of Electrons in Semiconductors

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