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1. Doping induced Mott collapse and possible density wave instabilities in (Sr1−xLax)3Ir2O7

   https://doi.org/10.1038/s41535-019-0183-y  

   Wang, Zhenyu ; Walkup, Daniel ; Maximenko, Yulia ; Zhou, Wenwen ; Hogan, Tom ; Wang, Ziqiang ; Wilson, Stephen D. ; Madhavan, Vidya ( August 2019 , npj Quantum Materials)

   The path from a Mott insulating phase to high temperature superconductivity encounters a rich set of unconventional phenomena involving the insulator-to-metal transition (IMT), such as emergent electronic orders and pseudogaps, that ultimately affect the condensation of Cooper pairs. A huge hindrance to understanding the origin of these phenomena is the difficulty in accessing doping levels near the parent state. TheJ_eff = 1/2 Mott state of the perovskite strontium iridates has revealed intriguing parallels to the cuprates, with the advantage that it provides unique access to the Mott transition. Here, we exploit this accessibility to study the IMT and the possible nearby electronic orders in the electron-doped bilayer iridate (Sr_1 − xLa_x)₃Ir₂O₇. Using spectroscopic imaging scanning tunneling microscopy, we image the La dopants in the top as well as the interlayer SrO planes. Surprisingly, we find a disproportionate distribution of La between these layers with the interlayer La being primarily responsible for the IMT. This reveals the distinct site-dependent effects of dopants on the electronic properties of bilayer systems. Electron doping also results in charge reordering. We find unidirectional electronic order concomitant with the structural distortion known to exist in this system. Intriguingly, similar to the single layer iridate, we also find local resonant states forming a checkerboard-like pattern trapped by La. This suggests that multiple charge orders may exist simultaneously in Mott systems, even with only one band crossing the Fermi energy.

    

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2. Valence transition model of the pseudogap, charge order, and superconductivity in electron-doped and hole-doped copper oxides

   https://doi.org/DOI: 10.1103/PhysRevB.98.205153  

   Mazumdar, S. ( October 2018 , Physical review. B, Condensed matter)

   We present a valence transition model for electron- and hole-doped cuprates, within which there occurs a discrete jump in ionicity Cu2+ -> Cu1+ in both families upon doping, at or near optimal doping in the conventionally prepared electron-doped compounds and at the pseudogap phase transition in the hole-doped materials. In thin films of the T' compounds, the valence transition has occurred already in the undoped state. The phenomenology of the valence transition is closely related to that of the neutral-to-ionic transition in mixed-stack organic charge-transfer solids. Doped cuprates have negative charge-transfer gaps, just as rare-earth nickelates and BaBiO3. The unusually high ionization energy of the closed shell Cu1+ ion, taken together with the dopingdriven reduction in three-dimensional Madelung energy and gain in two-dimensional delocalization energy in the negative charge transfer gap state drives the transition in the cuprates. The combined effects of strong correlations and small d-p electron hoppings ensure that the systems behave as effective 1/2-filled Cu band with the closed shell electronically inactive O2- ions in the undoped state, and as correlated two-dimensional geometrically frustrated 1/4-filled oxygen hole band, now with electronically inactive closed-shell Cu1+ ions, in the doped state. The model thus gives microscopic justification for the two-fluid models suggested by many authors. The theory gives the simplest yet most comprehensive understanding of experiments in the normal states. The robust commensurate antiferromagnetism in the conventional T' crystals, the strong role of oxygen deficiency in driving superconductivity and charge carrier sign corresponding to holes at optimal doping are all manifestations of the same quantum state. In the hole-doped pseudogapped state, there occurs a biaxial commensurate period 4 charge density wave state consisting of O1- -Cu l(1+)-O1- spin singlets that coexists with broken rotational C-4 symmetry due to intraunit cell oxygen inequivalence. Finite domains of this broken symmetry state will exhibit twodimensional chirality and the polar Kerr effect. Superconductivity within the model results from a destabilization of the 1/4-filled band paired Wigner crystal [Phys. Rev. B 93, 165110 (2016) and ihid. 93, 205111 (2016)]. We posit that a similar valence transition, Ir4+ -> Ir3+, occurs upon electron doping Sr2IrO4. We make testable experimental predictions in cuprates including superoxygenated La2CuO4+delta and iridates. Finally, as indirect evidence for the valence bond theory of superconductivity proposed here, we note that there exist an unusually large number of unconventional superconductors that exhibit superconductivity proximate to exotic charge ordered states, whose band fillings are universally 1/4 or 3/4, exactly where the paired Wigner crystal is most stable. 

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3. Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity

   https://doi.org/10.1073/pnas.2002429117  

   Choubey, Peayush ; Joo, Sang Hyun ; Fujita, K. ; Du, Zengyi ; Edkins, S. D. ; Hamidian, M. H. ; Eisaki, H. ; Uchida, S. ; Mackenzie, A. P. ; Lee, Jinho ; et al ( June 2020 , Proceedings of the National Academy of Sciences)

   null (Ed.)

   The defining characteristic of hole-doped cuprates is d -wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d -symmetry form factor, pair density wave (PDW) state coexisting with d -wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states N r , E is predicted at the terminal BiO surface of Bi 2 Sr 2 CaCu 2 O 8 and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of N r , E , the modulations of the coherence peak energy Δ p r , and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space q - space . Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi 2 Sr 2 CaCu 2 O 8 does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p *, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p * ≈ 19% occurs due to disappearance of this PDW. 

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4. Emergence of nodal Bogoliubov quasiparticles across the transition from the pseudogap metal to the d-wave superconductor

   https://doi.org/10.1038/s41535-023-00608-0  

   Christos, Maine ; Sachdev, Subir ( January 2024 , npj Quantum Materials)

   We model the pseudogap state of the hole- and electron-doped cuprates as a metal with hole and/or electron pocket Fermi surfaces. In the absence of long-range antiferromagnetism, such Fermi surfaces violate the Luttinger requirement of enclosing the same area as free electrons at the same density. Using the Ancilla theory of such a pseudogap state, we describe the onset of conventionald-wave superconductivity by the condensation of a chargeeHiggs boson transforming as a fundamental under the emergent SU(2) gauge symmetry of a backgroundπ-flux spin liquid. In all cases, we find that thed-wave superconductor has gapless Bogoliubov quasiparticles at 4 nodal points on the Brillouin zone diagonals with significant velocity anisotropy, just as in the BCS state. This includes the case of the electron-doped pseudogap metal with only electron pockets centered at wavevectors (π, 0), (0, π), and an electronic gap along the zone diagonals. Remarkably, in this case, too, gapless nodal Bogoliubov quasiparticles emerge within the gap at 4 points along the zone diagonals upon the onset of superconductivity.

    

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5. Bogoliubov quasiparticle on the gossamer Fermi surface in electron-doped cuprates

   https://doi.org/10.1038/s41567-023-02209-x  

   Xu, Ke-Jun ; Guo, Qinda ; Hashimoto, Makoto ; Li, Zi-Xiang ; Chen, Su-Di ; He, Junfeng ; He, Yu ; Li, Cong ; Berntsen, Magnus H. ; Rotundu, Costel R. ; et al ( September 2023 , Nature Physics)

   Electron-doped cuprates consistently exhibit strong antiferromagnetic correlations, leading to the prevalent belief that antiferromagnetic spin fluctuations mediate Cooper pairing in these unconventional superconductors. However, early investigations showed that although antiferromagnetic spin fluctuations create the largest pseudogap at hot spots in momentum space, the superconducting gap is also maximized at these locations. This presented a paradox for spin-fluctuation-mediated pairing: Cooper pairing is strongest at momenta where the normal-state low-energy spectral weight is most suppressed. Here we investigate this paradox and find evidence that a gossamer—meaning very faint—Fermi surface can provide an explanation for these observations. We study Nd2–xCexCuO4 using angle-resolved photoemission spectroscopy and directly observe the Bogoliubov quasiparticles. First, we resolve the previously observed reconstructed main band and the states gapped by the antiferromagnetic pseudogap around the hot spots. Within the antiferromagnetic pseudogap, we also observe gossamer states with distinct dispersion, from which coherence peaks of Bogoliubov quasiparticles emerge below the superconducting critical temperature. Moreover, the direct observation of a Bogoliubov quasiparticle permits an accurate determination of the superconducting gap, yielding a maximum value an order of magnitude smaller than the pseudogap, establishing the distinct nature of these two gaps. We propose that orientation fluctuations in the antiferromagnetic order parameter are responsible for the gossamer states. 

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