Maximization of superconducting Tc in the intermediate-pressure regime

Determine whether the superconducting critical temperature Tc of the Fm-3m LuH2.875−δN0.125 phase is maximized in the intermediate pressure regime (approximately 1–10 GPa) where quantum nuclear effects stabilize the high-symmetry metallic structure, given that non-adiabatic vertex corrections to electron-phonon coupling may either enhance or suppress Tc.

Background

The paper proposes a pressure-dependent phase diagram for LuH2.875−δN0.125 featuring: (i) a low-pressure molecularized-hydrogen state that is semimetallic or semiconducting, (ii) an intermediate-pressure range (e.g., 1–10 GPa) where quantum nuclear effects stabilize a high-symmetry metallic phase with flat hydrogen-derived bands near the Fermi level, and (iii) a high-pressure regime with harmonically stabilized hydrogen modes. The intermediate regime is suggested as a candidate for enhanced superconductivity due to both anharmonically stabilized low-frequency modes and non-adiabatic coupling of high-frequency hydrogen modes.

However, the authors emphasize that large effective electron masses from flat bands and light hydrogen masses imply significant vertex corrections beyond Migdal-Eliashberg theory. Because vertex corrections can either increase or decrease Tc, the authors explicitly state they cannot assert that Tc is maximized in this intermediate-pressure regime, leaving the question open.