Evolution of Charge-Lattice Dynamics across the Kuramoto Synchronization Phase Diagram of Quantum Tunneling Polarons in Cuprate Superconductors

Abstract

Because of its sensitivity to the instantaneous structure factor, S(Q,t = 0), Extended X-ray Absorption Fine Structure (EXAFS) is a powerful tool for probing the dynamic structure of condensed matter systems in which the charge and lattice dynamics are coupled. When applied to hole-doped cuprate superconductors, EXAFS has revealed the presence of internal quantum tunneling polarons (IQTPs). An IQTP arises in EXAFS as a two-site distribution for certain Cu–O pairs, which is also duplicated in inelastic scattering but not observed in standard diffraction measurements. The Cu–Sr pair distribution has been found to be highly anharmonic and strongly correlated to both the IQTPs and to superconductivity, as, for example, in YSr2Cu2.75Mo0.25O7.54(Tc=84 K). In order to describe such nontrivial, anharmonic charge-lattice dynamics, we have proposed a model Hamiltonian for a prototype six-atom cluster, in which two Cu-apical-O IQTPs are charge-transfer bridged through Cu atoms by an O atom in the CuO2 plane and are anharmonically coupled via a Sr atom. By applying an exact diagonalization procedure to this cluster, we have verified that our model indeed produces an intricate interplay between charge and lattice dynamics. Then, by using the Kuramoto model for the synchronization of coupled quantum oscillators, we have found a first-order phase transition for the IQTPs into a synchronized, phase-locked phase. Most importantly, we have shown that this transition results specifically from the anharmonicity. Finally, we have provided a phase diagram showing the onset of the phase-locking of IQTPs as a function of the charge-lattice and anharmonic couplings in our model. We have found that the charge, initially confined to the apical oxygens, is partially pumped into the CuO2 plane in the synchronized phase, which suggests a possible connection between the synchronized dynamic structure and high-temperature superconductivity (HTSC) in doped cuprates.

Correlation of strontium anharmonicity with charge-lattice dynamics of the apical oxygens and their coupling to cuprate superconductivity

“…These experimental and theoretical results provide a critical extension to our prior EXAFS studies that demonstrated that the two-site Cu-O distributions in the dynamic structure that constitute the IQTPs are strongly coupled to the HTSC [6,8,12,13,19,30,31] as well as these overdoped, superconducting SCO and YSCO-Mo [57]. It would be expected that a phenomenon that is coupled to the HTSC mechanism would exhibit a correlation with T c .…”

“…The minimal subunit encompassing the relevant constituents consists of a pair of neighboring Cu-Oap IQTPs bridged between their copper ions by an Opl and between their Oap by the strontium of the dielectric layer (figure 1) [30,31]. The novel aspects enabled by this structure are the addition of the CuO 2 plane through the inclusion of Opl and the anharmonic structural dynamics of the Cu-Sr pair that is incorporated via the nontrivial Oap-Sr-Oap triatomic molecular structure indicated by these EXAFS results.…”

“…This local electron-phonon coupling is present only on the apical positions Oap in order to ensure polaron formation. Further details of the exact diagonalization method and the Kuramoto analysis can be found in [30,31].…”

“…The potential significance of IQTPs is that at a critical value of an anharmonic coupling between the two oxygen ions the pairwise exchange of the charge and displacement between them synchronizes, merging the wave functions to encompass the entire cluster built to model their aspects [30,31]. This correlated motion of charge and atoms makes IQTPs especially interesting from the perspective that the HTSC driver in cuprates is electron-electron interactions [32][33][34][35][36] that, as found by angle-resolved photoemission spectroscopy (ARPES), are augmented by strongly coupled phonons [37][38][39][40][41][42][43].…”

Complex quantum networks: a topical review

“…The Kuramoto model is the most important classical model displaying this phase transition. The model has been successfully used to describe arrays of coupled Josephson junctions [123] and recently is gaining further attention for study of condensed matter phenomena such as persistent entanglement in isolated quantum systems, exciton delocalization in molecular aggregates, and tunneling of polarons in cuprate superconductors [124][125][126].…”