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1. Emergent charge order near the doping-induced Mott-insulating quantum phase transition in Sr3Ru2O7

   https://doi.org/10.1038/s42005-019-0138-4  

   Leshen, Justin; Kavai, Mariam; Giannakis, Ioannis; Kaneko, Yoshio; Tokura, Yoshi; Mukherjee, Shantanu; Lee, Wei-Cheng; Aynajian, Pegor (March 2019, Communications Physics)

   Abstract Search for novel electronically ordered states of matter emerging near quantum phase transitions is an intriguing frontier of condensed matter physics. In ruthenates, the interplay between Coulomb correlations among the 4delectronic states and their spin-orbit interactions, lead to complex forms of electronic phenomena. Here we investigate the double layered Sr₃(Ru_1−xMn_x)₂O₇and its doping-induced quantum phase transition from a metal to an antiferromagnetic Mott insulator. Using spectroscopic imaging with the scanning tunneling microscope, we visualize the evolution of the electronic states in real- and momentum-space. We find a partial-gap at the Fermi energy that develops with doping to form a weak Mott insulating state. Near the quantum phase transition, we discover a spatial electronic reorganization into a commensurate checkerboard charge order. These findings bear a resemblance to the universal charge order in the pseudogap phase of cuprates and demonstrate the ubiquity of charge order that emanates from doped Mott insulators. 

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2. 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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3. Doping evolution of the Mott–Hubbard landscape in infinite-layer nickelates

   https://doi.org/10.1073/pnas.2007683118  

   Goodge, Berit H.; Li, Danfeng; Lee, Kyuho; Osada, Motoki; Wang, Bai Yang; Sawatzky, George A.; Hwang, Harold Y.; Kourkoutis, Lena F. (January 2021, Proceedings of the National Academy of Sciences)

   null (Ed.)

   The recent observation of superconductivity in N d 0.8 S r 0.2 N i O 2 has raised fundamental questions about the hierarchy of the underlying electronic structure. Calculations suggest that this system falls in the Mott–Hubbard regime, rather than the charge-transfer configuration of other nickel oxides and the superconducting cuprates. Here, we use state-of-the-art, locally resolved electron energy-loss spectroscopy to directly probe the Mott–Hubbard character of N d 1 − x S r x N i O 2 . Upon doping, we observe emergent hybridization reminiscent of the Zhang–Rice singlet via the oxygen-projected states, modification of the Nd 5d states, and the systematic evolution of Ni 3d hybridization and filling. These experimental data provide direct evidence for the multiband electronic structure of the superconducting infinite-layer nickelates, particularly via the effects of hole doping on not only the oxygen but also nickel and rare-earth bands. 

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4. Anomalous quantum criticality in the electron-doped cuprates

   https://doi.org/10.1073/pnas.1817653116  

   Mandal, P. R.; Sarkar, Tarapada; Greene, Richard L. (March 2019, Proceedings of the National Academy of Sciences)

   In the physics of condensed matter, quantum critical phenomena and unconventional superconductivity are two major themes. In electron-doped cuprates, the low critical field (H_C2) allows one to study the putative quantum critical point (QCP) at low temperature and to understand its connection to the long-standing problem of the origin of the high-T_Csuperconductivity. Here we present measurements of the low-temperature normal-state thermopower (S) of the electron-doped cuprate superconductor La_2−xCe_xCuO₄(LCCO) fromx= 0.11–0.19. We observe quantum critical $\mathit{S}/\mathit{T}$versus $\mathbf{l}\mathbf{n}\left(\mathbf{1}/\mathit{T}\right)$behavior over an unexpectedly wide doping rangex= 0.15–0.17 above the QCP (x= 0.14), with a slope that scales monotonically with the superconducting transition temperature (T_Cwith H = 0). The presence of quantum criticality over a wide doping range provides a window on the criticality. The thermopower behavior also suggests that the critical fluctuations are linked withT_C. Above the superconductivity dome, atx= 0.19, a conventional Fermi-liquid $\mathit{S}\propto \mathit{T}$behavior is found for $\mathit{T}\le$40 K. 

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5. Spin-orbital Jahn-Teller bipolarons

   https://doi.org/10.1038/s41467-024-46621-0  

   Celiberti, Lorenzo; Fiore_Mosca, Dario; Allodi, Giuseppe; Pourovskii, Leonid V; Tassetti, Anna; Forino, Paola Caterina; Cong, Rong; Garcia, Erick; Tran, Phuong M; De_Renzi, Roberto; et al (December 2024, Nature Communications)

   Abstract Polarons and spin-orbit (SO) coupling are distinct quantum effects that play a critical role in charge transport and spin-orbitronics. Polarons originate from strong electron-phonon interaction and are ubiquitous in polarizable materials featuring electron localization, in particular 3d transition metal oxides (TMOs). On the other hand, the relativistic coupling between the spin and orbital angular momentum is notable in lattices with heavy atoms and develops in 5d TMOs, where electrons are spatially delocalized. Here we combine ab initio calculations and magnetic measurements to show that these two seemingly mutually exclusive interactions are entangled in the electron-doped SO-coupled Mott insulator Ba₂Na_1−xCa_xOsO₆(0 < x < 1), unveiling the formation ofspin-orbital bipolarons. Polaron charge trapping, favoured by the Jahn-Teller lattice activity, converts the Os 5d¹spin-orbital J_eff = 3/2 levels, characteristic of the parent compound Ba₂NaOsO₆(BNOO), into a bipolaron 5d²J_eff = 2 manifold, leading to the coexistence of different J-effective states in a single-phase material. The gradual increase of bipolarons with increasing doping creates robust in-gap states that prevents the transition to a metal phase even at ultrahigh doping, thus preserving the Mott gap across the entire doping range from d¹BNOO to d²Ba₂CaOsO₆(BCOO). 

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