Unconventional superconductivity from lattice quantum disorder

Abstract

Unconventional superconductivity presents a defining and enduring challenge in condensed matter physics. Prevailing theoretical frameworks have predominantly emphasized electronic degrees of freedom, largely neglecting the rich physics inherent in the lattice. Although conventional phonon theory offers an elegant description of structural phase diagrams and lattice dynamics, its omission of nuclear quantum many-body effects results in misleading phase diagram interpretations and, consequently, 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 H3S and La3Ni2O7. This phase occupies a triangular region in the pressure-temperature phase diagram, whose left boundary aligns precisely with Tc of the left flank of the superconducting dome. The Tcmax of this quantum disordered phase coincides with the maximum of superconducting Tc, indicating this phase as both the origin of superconductivity on the dome's left flank and a key ingredient of its pairing mechanism. Our findings advance the understanding of high-temperature superconductivity and establish the lattice quantum disordered phase as a unifying framework, both for predicting new superconductors and for elucidating phenomena in a broader context of condensed matter physics.

Figures (10)

• Figure 1: Lattice quantum disordered phase in $\textup{H}_3\textup{S}$ and $\textup{D}_3\textup{S}$ from first-principles calculation.a, A schematic diagram of a 1-D double-well chain, which describes the LQD phase. The nucleus on each lattice site (the ball) lies on a double-well potential (red curve) connected to the neighboring sites by spring interactions (zigzag lines). The many-body nuclear quantum states are determined by the competition between the on-site tunneling effects and the inter-site interactions. In Ref. zhu_quantum_2025, we have a detailed description of the LQD phase described by this model and the PIMD method. b, The dispersion relation of lattice dynamics of $\textup{Im}\bar{3}\textup{m}$$\textup{H}_3\textup{S}$ ($T=200$ K, $P=141$ GPa) by PIMD (solid lines) in comparison with the harmonic phonon spectra (dashed lines). The structural instability indicated by the soft phonon mode is suppressed. c, PIMD frequency at $\Gamma$ point for the soft mode defined in (b), as a function of temperature and pressure. The open black and red circles correspond to $\textup{H}_3\textup{S}$ and $\textup{D}_3\textup{S}$, respectively. The structural phase transition is defined by the point at which this frequency changes sign. d, The triangular region of the LQD phase on the $P-T$ phase diagram is bounded by the quantum (PIMD) and classical (MD) phase boundaries. The solid symbols represent the experimental superconducting $T_{c,\textup{SC}}$ from Refs. drozdov_conventional_2015einaga_crystal_2016D3S2020. Notably, the left boundary of the LQD phase (the PIMD line) aligns with the left flank of the superconducting dome, and $T_{c,\textup{LQD}}^{\textup{max}}$ coincides with $T_{c,\textup{SC}}^{\textup{max}}$ for both $\textup{H}_3\textup{S}$ and $\textup{D}_3\textup{S}$.
• Figure 1: LQD phase and the SSCHA phase boundary in $\textup{H}_3\textup{S}$ by different functionals. The structural phase boundary between $\textup{Im}\bar{3}\textup{m}$ (high-pressure) and $\textup{R3m}$ (low-pressure) by the stochastic self-consistent harmonic approximation (SSCHA) methodmonacelli2021 is shown by the cyan line. SSCHA predicts a much lower transition pressure compared to PIMD. In comparison with PBE, the structural phase boundary by R2SCAN functional shifts to higher pressure because, at the same pressure, R2SCAN predicts a higher potential barrier hence weaker quantum fluctuation.
• Figure 2: Lattice quantum disordered phase in $\textup{La}_3\textup{Ni}_2\textup{O}_7$ from first-principles calculation. The solid symbols represent the experimental superconducting $T_{c,\textup{SC}}$ from Refs. sun_signatures_2023Hou_2023. On the left flank of the superconducting dome (below 14 GPa), $T_{c,\textup{SC}}$ is marked by a sudden and rapid decrease. The quantum structural phase boundary by PIMD aligns with the left flank, and $T_{c,\textup{LQD}}^{\textup{max}}\approx77$ K is in consistence with the experimental $T_{c,\textup{SC}}^{\textup{max}}=80$ K.
• Figure 2: Classical structural phase boundaries by MD.a-f, S-H pair distribution function for $\textup{H}_3\textup{S}$ at different temperatures and pressures. The PDFs obtained from MD are identical for $\textup{D}_3\textup{S}$ and $\textup{H}_3\textup{S}$. g, pair distribution function for $\textup{La}_3\textup{Ni}_2\textup{O}_7$. h, derivative of the lattice parameter ratio $c/a$ with respect to pressure. i, PIMD predicts a higher pressure than MD at the same volume. j, the classical transition pressure was determined by $\textup{d}(\frac{c}{a})/\textup{d}P_{\textup{MD}}=0$.
• Figure 3: Schematic phase diagram of lattice quantum disorder and unconventional superconductivity. The quantum order-disorder transition boundary (solid red line), dominant at low temperatures, is shifted to lower pressures compared to the classical transition boundary (dashed black line). Their intersection defines $T_{c,\textup{LQD}}^{\textup{max}}$——a tricritical point (red point). The region enclosed by these two boundaries is the LQD phase (shaded orange area). Experimentally observed superconductivity forms a dome (orange area). Crucially, the left flank of the superconducting dome coincides with the left boundary of the LQD phase, and $T_{c,\textup{SC}}^{\textup{max}}$ aligns precisely with the tricritical point ($T_{c,\textup{LQD}}^{\textup{max}}$ ). We contend that this unequivocally points to a superconducting mechanism inherent to the LQD phase, with the tricritical point determining the maximum superconducting transition temperature.