On the Electron Pairing Mechanism of Copper-Oxide High Temperature Superconductivity

The elementary CuO₂ plane sustaining cuprate high-temperature superconductivity occurs typically at the base of a periodic array of edge-sharing CuO₅ pyramids. Virtual transitions of electrons between adjacent planar Cu and O atoms, occurring at a rate t/ℏ and across the charge-transfer energy gap ε, generate “superexchange” spin–spin interactions of energy J ≈ 4t⁴/ε³ in an antiferromagnetic correlated-insulator state. However, hole doping this CuO₂ plane converts this into a very-high-temperature superconducting state whose electron pairing is exceptional. A leading proposal for the mechanism of this intense electron pairing is that, while hole doping destroys magnetic order, it preserves pair-forming superexchange interactions governed by the charge-transfer energy scale ε. To explore this hypothesis directly at atomic scale, we combine single-electron and electron-pair (Josephson) scanning tunneling microscopy to visualize the interplay of ε and the electron-pair density n_p in Bi₂Sr₂CaCu₂O_8+x. The responses of both ε and n_p to alterations in the distance δ between planar Cu and apical O atoms are then determined. These data reveal the empirical crux of strongly correlated superconductivity in CuO₂, the response of the electron-pair condensate to varying the charge-transfer energy. Concurrence of predictions from strong-correlation theory for hole-doped charge-transfer insulators with these observations indicates that charge-transfer superexchange is the electron-pairing mechanism of superconductive Bi₂Sr₂CaCu₂O_8+x.

Published Article - Proc. Nat'l Acad. Sci. 119, 2207449119 - September 2022

Imaging the Energy Gap Modulations of the Cuprate Pair Density Wave State

The defining characteristic of Cooper pairs with finite center-of-mass momentum is a spatially modulating superconducting energy gap Δ(r). Recently, this concept has been generalized to the pair density wave (PDW) state predicted to exist in high temperature superconducting cuprates (ARCMP 11, 231 (2020) ). Although the existence of a PDW in cuprates was discovered by using Cooper-pair tunneling (Nature 532, 343 (2016) ), its signature in single-electron tunneling of periodic Δ(r) modulations, proved elusive. Now, by using a new approach, we detect strong Δ(r) modulations in Bi₂Sr₂CaCu₂O_8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ 2π/a₀ (1/8,0); 2π/a₀ (0,1/8). Simultaneous imaging of the local-density-of-states N(r,E) reveals electronic modulations with wavevectors Q and 2Q, as anticipated for a coexisting superconductor and PDW. Overall, this provides strong confirmation that a PDW state coexists with superconductivity in the canonical cuprate Bi₂Sr₂CaCu₂O_8+δ.

Published Article - Nature 580, 65-70 - April 2020

Machine Learning in Electronic-Quantum-Matter Imaging Experiments

A collaboration of experimental physicists led by Prof. JC Séamus Davis (University of Oxford), theoretical physicists led by Prof. Eun-Ah Kim (Cornell University), and computer scientists led by Prof. E. Kathami (San Jose State University), developed and trained a new Machine Learning (ML) protocol, based on a suite of artificial neural networks (ANN), that is designed to recognize different types of electronic ordered states which are hidden within electronic quantum matter image-arrays.
Electronic quantum matter studies using automated scientific instrumentation and large-scale data acquisition are now generating data sets of such volume and complexity as to defy human analysis. For example modern scanning tunneling microscopy (STM) visualization of electronic quantum matter (EQM) yields dense arrays of atomic-scale, electronic-structure images, that are often astonishingly complex.
The ANN suite analyzed one of the Davis Group experimental EQM image archives, spanning a wide range of electron densities and energies, in carrier-doped cuprate Mott insulators. The ANN suite discovered, throughout all the noisy and complex data, the features of a very specific ordered state of EQM: a Vestigial Nematic State. This is a milestone for general scientific technique in that ANN's can process and identify specific broken symmetries of highly complex image-arrays from non-synthetic experimental EQM data. It opens the immediate prospect of additional ML-driven scientific discovery in EQM studies.

Published Article - Nature 570, 484 - June 2019

Magnetic-Field Induced Pair Density Wave State in the Cuprate Vortex Halo

Superconductivity occurs when electrons form pairs of opposite spin and opposite momentum, and these "Cooper pairs" condense into a homogeneous electronic fluid. However, theorists have recently realized that these electron pairs might also crystallize into a “pair density wave” (PDW) state where the density of pairs modulates periodically in space. Intense theoretical interest has emerged in whether such a PDW is the competing phase in cuprates. To search for evidence of such a PDW state we suppress the homogeneous superconductivity using high magnetic field and visualize the electronic structure of the new phase which appears. Under these circumstances we discovered modulations in the density of electronic states containing multiple signatures of a PDW state. The phenomena are in detailed and excellent agreement with theoretical predictions for a field-induced primary PDW state. These data indicate that it is a PDW state which competes with superconductivity in cuprates and that it dominates in the high-field regime.

Published Article - Science 364, 976 - June 2019

Evidence for a Vestigial Nematic State in the Cuprate Pseudogap Phase

In the cuprate pseudogap phase, an energy gap of unknown mechanism opens, and both an electronic nematic phase (NE) and a density-wave (DW) phase appear. Perplexingly, the DW, which should generate an energy gap, appears without any new gap opening; and the NE, which should be incapable of opening an energy gap, emerges coincident with the pseudogap opening. Recently, however, it was demonstrated theoretically that a disordered unidirectional DW can generate a vestigial nematic (VN) phase. If the cuprate pseudogap phase were in such a VN state, the energy gap of the NE and DW should be identical to each other and to the pseudogap. We report discovery of such a phenomenology throughout the phase diagram of underdoped Bi₂Sr₂CaCu₂O₈.

Published Article - Proc. Nat'l Acad. Sci. 116, 13249 - June 2019