Forces, phonons and superconductivity from dynamical mean-field theory

Evgeny Plekhanov

King's College London, UK


The failure of density functional theory's (DFT)ís exchange-correlation functionals to capture strong correlation physics severely limits its use for nanoscale design of important functional materials. In contrast to DFT, great progress has been made in describing strongly correlated materials with the dynamical mean-field theory (DMFT). DMFT is a sophisticated method which offers a higher level of theoretical description than DFT and bridges the gap between DFT and Greenís function approaches. Within DMFT, the treatment of local electronic correlation effects is formally exact, although the nonlocal electronic correlation effects are neglected. DMFT can be combined with DFT, giving rise to the DFT+DMFT method. Moreover, within DFT+DMFT, a variational principle for the total free energy can be derived, and it can be shown that at self-consistency, the DFT+DMFT solution corresponds to a stationary point.
We show how to calculate analytical atomic forces within the DFT+DMFT approach in the case when ultrasoft or norm-conserving pseudopotentials are used. These force calculations are benchmarked within our implementation of DFT+DMFT within the CASTEP ab initio code. We show how to treat the nonlocal projection terms arising within the pseudopotential formalism and circumvent the problem of nonorthogonality of the Kohn-Sham eigenvectors. Our approach is, in principle, independent of the DMFT solver employed and was tested with the Hubbard-I solver.
We apply the DFT+DMFT computational framework to study the superconductivity in Hydrogen-rich superhydrides (HRS) at extreme pressures (above 200 GPa). HRS are promising high-Tc superconductors, with experimentally observed superconductivity near room temperature. Superconductivity is mediated by the highly energetic lattice vibrations associated with hydrogen and their interplay with the electronic structure, requiring fine descriptions of the electronic properties, notoriously challenging for correlated f systems.
Focusing on several HRS, we report that density functional theory provides an accurate structure and phonon frequencies, but many-body corrections lead to an increase of the critical temperature, which is associated with the spectral weight transfer of the f-states.
We also analyze how the calculation of Tc is affected by the hierarchy of many-body corrections and obtain a compelling increase in Tc at the highest level of theory, which goes in the direction of experimental observations. In this work, we propose a first-principles calculation platform with the inclusion of many-body corrections to evaluate the detailed physical properties of the LAĖH systems (where LA=La,Ce,Sm) and to understand the structure, stability, and superconductivity of these systems at ultra-high pressure.