Recent development in the high-pressure physics provides us with a new class of the superconducting materials, namely with the hydrogen-rich materials, such as silane (transition temperature Tc = 17 K at pressure p = 96 GPa), hydrogen sulphide (Tc = 203K, p = 150 GPa) or hydrogen lanthanide (Tc = 274-286 K, p = 210 GPa).
We will discuss the versatility of the molecular-to-atomic transitions in one-, two-, and quasi-three-dimensional hydrogen systems, using our own original approach - the Exact Diagonalization Ab-Initio (EDABI) method. Starting from the extended Hubbard model, we examine an electron-correlation-driven conductivity connected with the creation of high-symmetry hydrogen molecular and atomic planes, as well as a series of both structural and electronic-in-nature quantum phase transitions.
We discuss the suppression of molecular nature in a reversed Peierls-like transition under high pressure, as well as the proper van-der-Waals-like effective interaction derived from the first principles of quantum mechanics.
We obtain an effective electron-phonon Hamiltonian for which we estimate the lattice dynamics using the density functional theory. Finally, using the McMillan formula we predict the superconducting transition temperature versus the effective pressure (external and/or chemical).
We acknowledge the support of Grant Agency of the Czech Republic (GAČR) No. 20-18392S and the National Science Centre (NCN) grant OPUS, No. UMO-2018/29/B/ST3/02646.