Accurate non-perturbation electron-vibration interactions of superconductivity under high pressures

An electron-vibration interaction has essential effects on many temperature-dependent phenomena, including superconductivity. Accurate non-perturbation calculations recently developed can provide unprecedented insights into what thermal vibrational motion does to band structures of superconductors under high pressures. It clearly shows that there are strictly necessary and sufficient conditions for electron-vibration interactions to take place. For a vibrational motion to generate electron-vibration interaction, a longitudinal mode to stretch chemical bonds is essential. Degenerate energy levels at electronic wave-vectors are also required. Only such vibration motion coupling to degenerate electronic states in energy band structures can generate electron-vibration interactions for superconductivity. These conditions reveal some unexpected physical and chemical phenomena operated by electron-vibration interactions under high pressures. Accurate non-perturbation calculations for superconductors include Nb, YBa₂Cu₃O₇, LaH₁₀, and K₃C₆₀.