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Abstract:

Quantum Matter and Optic

Abstract:

A Kondo lattice is often electrically insulating at low temperatures. However, several recent experiments have detected signatures of bulk metallicity within this Kondo insulating phase. In this study, we visualized the real-space charge landscape within a Kondo lattice with atomic resolution using a scanning tunneling microscope. We discovered nanometer-scale puddles of metallic conduction electrons centered around uranium-site substitutions in the heavy-fermion compound uranium ruthenium silicide (URu₂Si₂) and around samarium-site defects in the topological Kondo insulator samarium hexaboride (SmB₆). These defects disturbed the Kondo screening cloud, leaving behind a fingerprint of the metallic parent state. Our results suggest that the three-dimensional quantum oscillations measured in SmB₆ arise from Kondo-lattice defects, although we cannot exclude other explanations. Our imaging technique could enable the development of atomic-scale charge sensors using heavy-fermion probes.

Abstract:

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 [Formula: see text], generate "superexchange" spin-spin interactions of energy [Formula: see text] 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 [Formula: see text]. To explore this hypothesis directly at atomic scale, we combine single-electron and electron-pair (Josephson) scanning tunneling microscopy to visualize the interplay of [Formula: see text] and the electron-pair density n_P in Bi₂Sr₂CaCu₂O_8+x. The responses of both [Formula: see text] 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.

Abstract:

Electron-pair density wave (PDW) states are now an intense focus of research in the field of cuprate correlated superconductivity. PDWs exhibit periodically modulating superconductive electron pairing that can be visualized directly using scanned Josephson tunneling microscopy (SJTM). Although from theory, intertwining the d-wave superconducting (DSC) and PDW order parameters allows a plethora of global electron-pair orders to appear, which one actually occurs in the various cuprates is unknown. Here, we use SJTM to visualize the interplay of PDW and DSC states in Bi₂Sr₂CaCu₂O_8+x at a carrier density where the charge density wave modulations are virtually nonexistent. Simultaneous visualization of their amplitudes reveals that the intertwined PDW and DSC are mutually attractive states. Then, by separately imaging the electron-pair density modulations of the two orthogonal PDWs, we discover a robust nematic PDW state. Its spatial arrangement entails Ising domains of opposite nematicity, each consisting primarily of unidirectional and lattice commensurate electron-pair density modulations. Further, we demonstrate by direct imaging that the scattering resonances identifying Zn impurity atom sites occur predominantly within boundaries between these domains. This implies that the nematic PDW state is pinned by Zn atoms, as was recently proposed [Lozano ���������., Phys. Rev. B 103, L020502 (2021)]. Taken in combination, these data indicate that the PDW in Bi₂Sr₂CaCu₂O_8+x is a vestigial nematic pair density wave state [Agterberg ���������. Phys. Rev. B 91, 054502 (2015); Wardh and Granath arXiv:2203.08250].