Yu-Cheng Zhu, Jia-Xi Zeng and Xin-Zheng Li of Peking University report the discovery of a previously unknown lattice quantum disordered phase within superconductors. Their work reveals this phase occupies a triangular region in the P-T phase diagram, with its left boundary aligning precisely with the critical temperature where superconductivity begins on a material’s “left flank.” Identifying this alignment, the researchers establish lattice quantum disorder as a key component of the superconducting pairing mechanism and a unifying framework for both predicting new superconductors and understanding condensed matter physics more broadly.

Nuclear Quantum Effects Redefine Superconducting Phase Diagrams

Prevailing models of superconductivity have long centered on electron behavior. But new calculations reveal a previously unrecognized lattice quantum disordered (LQD) phase that precisely defines the onset of superconductivity on one side of the material’s performance range. This phase, discovered through first-principles calculations incorporating nuclear quantum many-body effects, manifests as a triangular region within the pressure-temperature (P-T) phase diagram of certain superconductors.

The discovery challenges conventional phonon theory, which traditionally omits the complex quantum interactions of atomic nuclei, leading to inaccurate structural phase diagrams and a flawed foundation for understanding superconductivity. Researchers found that the LQD phase arises from quantum fluctuations stabilizing a disordered state, resulting in lattice dynamics beyond the conventional description of atomic vibrations as simple phonons.

This quantum disorder isn’t merely a side effect. The work demonstrates that the superconducting transition on the left flank of the dome originates from the structural transition into this LQD phase, suggesting a direct link between nuclear quantum effects and the emergence of superconductivity. The team employed path-integral molecular dynamics (PIMD) to rigorously account for these nuclear quantum many-body effects from first principles, a method that goes beyond standard molecular dynamics by treating nuclei as quantum objects rather than classical particles.

This approach allowed for a more accurate determination of structural phase boundaries and the identification of the LQD phase itself. The researchers determined the true phase transition point by examining the curvature of the free energy surface, which fully accounts for both thermal and quantum effects, offering a broadly applicable criterion for structural instability.

The newly identified LQD phase is delineated by a triangular region on the P-T phase diagram, bounded by a classical boundary determined via molecular dynamics and a quantum boundary calculated using PIMD. The intersection of these boundaries defines the temperature at which quantum effects are overwhelmed by thermal fluctuations.

The impact of isotopic composition is also apparent. Deuterium, with its greater mass and weaker quantum effects, exhibits a higher-pressure quantum phase boundary and a lower temperature of approximately 160 Kelvin, compared to the 220 Kelvin observed for hydrogen. The alignment of the LQD phase’s left boundary with the superconducting dome’s left flank isn’t coincidental; the calculations show that as temperature increases, the boundary of the LQD phase shifts to higher pressure, mirroring the steepness of the superconducting dome.

This correspondence strongly suggests a causal relationship, indicating that the transition into the LQD phase is fundamental to initiating superconductivity on that side of the dome. This new understanding could allow for the design of materials with enhanced superconducting properties and a deeper comprehension of the complex interplay between nuclear and electronic behavior in these materials.

Path-Integral Molecular Dynamics Reveals Lattice Quantum Disorder

This finding challenges conventional models that prioritize electron behavior, instead highlighting the important role of the lattice structure in facilitating superconductivity. This interruption suggests that the LQD phase actively promotes superconductivity, rather than simply being a passive bystander. The implications extend beyond simply refining existing models of superconductivity. The energy scale of lattice dynamics, ranging from tens to hundreds of Kelvin, is comparable to the $T_{c}$ of high-temperature superconductors, meaning that thermal effects influencing nuclear quantum fluctuations cannot be ignored.

The researchers emphasize that superconductivity should be viewed as a macroscopic quantum state of both electronic and lattice degrees of freedom. The discovery of this LQD phase represents a departure from conventional understanding, as quantum disorder, in this context, is distinct from the dynamically or spatially disordered local moments observed in other systems.

While previous studies incorporated essential quantum corrections, they did not fully address the many-body nature of the interacting nuclei, leaving a gap in the understanding of structural phase transitions and their relationship to superconductivity. The recent emergence of nickel-based superconductors, coupled with enhanced structural characterization under pressure, provided a timely platform for validating this new picture of quantum lattice disorder and its role in facilitating superconductivity.

Lattice Quantum Disordered Phase Aligns with Superconducting Left Flank

This transition stems from a structural shift from a low-symmetry phase into the LQD phase, a finding supported by path-integral molecular dynamics (PIMD) used to accurately model the quantum behavior of the nuclei. The consistency of this alignment across different exchange-correlation functionals further strengthens the connection between the LQD phase and the superconducting mechanism. The location of the LQD phase’s boundary is not merely correlated with the superconducting dome’s peak $T_{c}$ ; it coincides with it, indicating that the quantum disorder actively contributes to, rather than simply accompanies, superconductivity.

This finding refutes earlier interpretations suggesting superconductivity occurred within a two-phase region, instead positioning it entirely within the high-symmetry phase. This behavior is distinct from classical phase transitions, where the boundary would remain relatively stable. The intersection of the quantum and classical transition lines defines a multicritical point, a specific condition where the two transitions converge.

This point aligns precisely with the observed peak $T_{c}$ , further solidifying the role of the LQD phase in initiating superconductivity. The discovery of this LQD phase is particularly relevant given the recent advancements in characterizing nickel-based superconductors under pressure. These materials provide a valuable platform for validating the theoretical framework, as first-principles calculations are important for interpreting their superconducting mechanisms. Correctly determining the structural phase diagram is therefore paramount, and the inclusion of nuclear quantum many-body effects proves essential for achieving accurate results.

The researchers suggest that future experiments should focus on tracking changes in lattice parameters at lower temperatures, particularly near the maximum superconducting $T_{c}$ , to pinpoint the boundaries of the LQD phase. The team’s findings suggest that a complete understanding of superconductivity requires considering the interplay between electron behavior and the quantum dynamics of the lattice itself, a perspective that has been largely overlooked in prevailing theoretical approaches.

Nickel-Based Superconductors Validate Quantum Lattice Disorder Origin

A newly detailed phase diagram reveals a triangular region of lattice quantum disorder (LQD) directly linked to the onset of superconductivity in nickel-based materials, challenging long-held assumptions about the primary drivers of this phenomenon. This finding reframes the understanding of high-temperature superconductivity, suggesting that the behavior of atomic nuclei within the material’s lattice is as important as electron interactions. This precise alignment, researchers argue, is not coincidental, but indicative of a fundamental connection between quantum fluctuations within the lattice and the emergence of the superconducting state.

The LQD phase, described as a competition between localized quantum fluctuations and a tendency toward long-range structural order, necessitates a treatment that captures the many-body nature of the quantum nuclei. The conventional approach to understanding superconductivity has historically prioritized electron behavior, often overlooking the complex physics inherent in the lattice structure.

This emphasis, researchers note, has led to structural phase diagrams that can be misleading and an incomplete foundation for superconducting theory. The team’s calculations reveal that the LQD phase arises from a quantum order-disorder transition, governed by the balance between quantum fluctuations and inter-site interactions within the lattice. While a BCS-like mechanism might explain the gradual increase in $T_{c}$ with decreasing pressure on the right flank, it fails to account for the abrupt interruption of this rise and the precise alignment with the LQD phase boundary.

“We instead propose that the right flank of the dome extends from the multicritical point, indicating a profound connection between LQD and the unconventional superconducting mechanism, with the LQD phase playing a decisive role in determining the maximum superconducting transition temperature,” they write. By accurately modeling the behavior of nuclei within the lattice, researchers can gain a more complete understanding of the mechanisms driving superconductivity and potentially unlock new pathways for designing materials with even higher transition temperatures.

👉 More information
🗞 Unconventional Superconductivity from Lattice Quantum Disorder
✍️ Yu-Cheng Zhu, Jia-Xi Zeng and Xin-Zheng Li
🧠 DOI: http://link.aps.org/doi/10.1103/r8fj-4t94

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