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1. 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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2. Absence of Superconductivity in the Hubbard Dimer Model for κ-(BEDT-TTF)2X

   https://doi.org/10.3390/cryst11060580  

   Roy, Dipayan; Clay, R. Torsten; Mazumdar, Sumit (June 2021, Crystals)

   null (Ed.)

   In the most studied family of organic superconductors κ-(BEDT-TTF)2X, the BEDT-TTF molecules that make up the conducting planes are coupled as dimers. For some anions X, an antiferromagnetic insulator is found at low temperatures adjacent to superconductivity. With an average of one hole carrier per dimer, the BEDT-TTF band is effectively 12-filled. Numerous theories have suggested that fluctuations of the magnetic order can drive superconducting pairing in these models, even as direct calculations of superconducting pairing in monomer 12-filled band models find no superconductivity. Here, we present accurate zero-temperature Density Matrix Renormalization Group (DMRG) calculations of a dimerized lattice with one hole per dimer. While we do find an antiferromagnetic state in our results, we find no evidence for superconducting pairing. This further demonstrates that magnetic fluctuations in the effective 12-filled band approach do not drive superconductivity in these and related materials. 

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3. Coexistence of superconductivity with partially filled stripes in the Hubbard model

   https://doi.org/10.1126/science.adh7691  

   Xu, Hao; Chung, Chia-Min; Qin, Mingpu; Schollwöck, Ulrich; White, Steven R; Zhang, Shiwei (May 2024, Science)

   The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature (T_c) superconductivity. 

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4. Ground-state phase diagram of the t-t ′ -J model

   https://doi.org/10.1073/pnas.2109978118  

   Jiang, Shengtao; Scalapino, Douglas J.; White, Steven R. (October 2021, Proceedings of the National Academy of Sciences)

   We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t- $t^{\prime }$-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative $t^{\prime }$values ( $t^{\prime }/t=\pm 0.2$) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The $t^{\prime }<0$(hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find $t^{\prime }<0$strongly suppresses superconductivity. The $t^{\prime }>0$(electron-doped) region shows the expected circular Fermi pocket of holes around the $\left(\pi ,\pi \right)$point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector $\left(\pi ,\pi \right)$induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with $t^{\prime }>0$is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region near $x=0.08$for $t^{\prime }\sim -0.2$, we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders. 

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5. Density matrix renormalization group based downfolding of the three-band Hubbard model: Importance of density-assisted hopping

   https://doi.org/10.1103/PhysRevB.108.L161111  

   Jiang, Shengtao; Scalapino, Douglas J; White, Steven R (October 2023, Physical Review B)

   Typical Wannier-function downfolding starts with a mean-field or density functional set of bands to construct the Wannier functions. Here we carry out a controlled approach, using DMRG-computed natural orbital bands, to downfold the three-band Hubbard model to an effective single band model. A sharp drop-off in the natural orbital occupancy at the edge of the first band provides a clear justification for a single-band model. Constructing Wannier functions from the first band, we compute all possible two-particle terms and retain those with significant magnitude. The resulting single-band model includes two-site density-assisted hopping terms with tn∼0.6t. These terms lead to a reduction of the ratio U/teff, and are important in capturing the doping-asymmetric carrier mobility, as well as in enhancing the pairing in a single-band model for the hole-doped cuprates. 

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