Reconstruction of bands in metallic hydrogen

The generalized theory of normal properties of a metal for the case of the properties of the electronic band of electron–phonon systems with a variable electron density of states is used to study the normal phase of metallic hydrogen at a pressure of $500$ GPa and a temperature of $200$ K. We calculated the frequency dependence of the real $\mathrm{Re}\,\Sigma(\omega)$ and imaginary $\mathrm{Im}\,\Sigma(\omega)$ parts of the self-energy part of the electron Green's function $\Sigma(\omega)$, as well as the electron density of states $N(\varepsilon)$ of the stable phase of metallic hydrogen with the $\mathrm{I41/AMD}$ symmetry at a pressure of $500$ GPa, renormalized by the strong electron–phonon coupling. It is found that the electron conduction band of the $\mathrm{I41/AMD}$ phase of metallic hydrogen undergoes insignificant reconstruction near the Fermi level because of the renormalization by the electron–phonon coupling.