Unconventional Superconductivity from Lattice Quantum Disorder

Unconventional superconductivity presents a defining challenge in physics. Prevailing theoretical frameworks have predominantly emphasized electrons, largely neglecting the rich physics inherent in the lattice. Conventional phonon theory omits quantum many-body effects of the nuclei, leading to misleading structural phase diagrams and an unsound foundation for superconducting theory. Here, by incorporating nuclear quantum many-body effects within first-principles calculations, we discover a lattice quantum disordered phase in superconductors H_{3}S and La_{3}Ni_{2}O_{7}. This phase occupies a triangular region in the P-T phase diagram, whose left boundary aligns precisely with T_{c} of the left flank of the superconducting dome. Its T_{c}^{max} coincides with the dome's peak, identifying this phase as both the origin of superconducting transition on the left flank and a key ingredient of the pairing mechanism. Our findings advance the understanding of unconventional superconductivity and establish lattice quantum disorder as a unifying framework, both for predicting new superconductors and for elucidating phenomena in a broader context of condensed matter physics.