Abstract
The extended Hubbard Hamiltonian on a bcc lattice is studied at half-filling and for a finite hopping between next-nearest neighbours, in mean-field approximation . An ionic insulating broken-symmetry phase is predicted for any hydrogenoid bcc solid in the density range \(1.0<r_s <2.6\). The occurrence of an ionic phase would explain the failure to achieve hydrogen metallization at high pressures . Moreover, a metal–insulator transition is expected for sodium in the 100 GPa region.
Reproduced from: F. Siringo, R. Pucci, G.G.N. Angilella, High Press. Research 15, 255 (1997), with the permission of Taylor & Francis (an imprint of Informa.com).
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Notes
- 1.
A slight change of the ratio \(t_2 /t_1\) does not affect too much the phase diagram. In general, a smaller value than 0.8 would be expected, thus giving rise to an enlargement of the ionic region in the phase diagram.
- 2.
Notice that for \(r_s \sim 2.6\), V is almost independent of the atomic size, while U is slightly smaller for larger atomic orbitals, so that the critical \(r_s\) value could be even larger for the other alkali metals.
- 3.
From the minimal basis set of Clementi and Raimondi [22], the effective 3s atomic radius is \(a_0 = 3/(z-\sigma )\) a.u., where \(z=11\) and the shield constant \(\sigma =8.4927\) for sodium, thus yielding \(a_0 =1.196\), to be compared with \(a_0 \equiv 1\) for hydrogen .
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Siringo, F., Pucci, R., Angilella, G.G.N. (2017). Are Light Alkali Metals Still Metals Under High Pressure?. In: Angilella, G., La Magna, A. (eds) Correlations in Condensed Matter under Extreme Conditions. Springer, Cham. https://doi.org/10.1007/978-3-319-53664-4_18
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