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1. Perpendicular electric field drives Chern transitions and layer polarization changes in Hofstadter bands

   https://doi.org/10.1038/s41467-022-35421-z  

   Adak, Pratap Chandra; Sinha, Subhajit; Giri, Debasmita; Mukherjee, Dibya Kanti; Chandan; Sangani, L. D.; Layek, Surat; Mukherjee, Ayshi; Watanabe, Kenji; Taniguchi, Takashi; et al (December 2022, Nature Communications)

   Abstract Moiré superlattices engineer band properties and enable observation of fractal energy spectra of Hofstadter butterfly. Recently, correlated-electron physics hosted by flat bands in small-angle moiré systems has been at the foreground. However, the implications of moiré band topology within the single-particle framework are little explored experimentally. An outstanding problem is understanding the effect of band topology on Hofstadter physics, which does not require electron correlations. Our work experimentally studies Chern state switching in the Hofstadter regime using twisted double bilayer graphene (TDBG), which offers electric field tunable topological bands, unlike twisted bilayer graphene. Here we show that the nontrivial topology reflects in the Hofstadter spectra, in particular, by displaying a cascade of Hofstadter gaps that switch their Chern numbers sequentially while varying the perpendicular electric field. Our experiments together with theoretical calculations suggest a crucial role of charge polarization changing concomitantly with topological transitions in this system. Layer polarization is likely to play an important role in the topological states in few-layer twisted systems. Moreover, our work establishes TDBG as a novel Hofstadter platform with nontrivial magnetoelectric coupling. 

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2. Non-Fermi liquid to charge-transfer Mott insulator in flat bands of copper-doped lead apatite

   https://doi.org/10.1039/D4MH00971A  

   Kim, Sun-Woo; Haule, Kristjan; Pascut, Gheorghe Lucian; Monserrat, Bartomeu (November 2024, Materials Horizons)

   Copper-doped lead apatite, called LK-99, was initially claimed to be a room temperature superconductor driven by flat electron bands, but was later found to be a wide gap insulator. Despite the lack of room temperature superconductivity, there is growing evidence that LK-99 and related compounds host various strong electron correlation phenomena arising from their flat electron bands. Depending on the copper doping site and crystal structure, LK-99 can exhibit two distinct flat bands crossing the Fermi level in the non-interacting limit: either a single or two entangled flat bands. We explore potential correlated metallic and insulating phases in the flat bands of LK-99 compounds by constructing their correlation phase diagrams, and find both non-Fermi liquid and Mott insulating states. We demonstrate that LK-99 is a charge-transfer Mott insulator driven by strong electron correlations, regardless of the flat band type. We also find that the non-Fermi liquid state in the multi-flat band system exhibits strange metal behaviour, while the corresponding state in the single flat band system exhibits pseudogap behaviour. Our findings align with available experimental observations and provide crucial insights into the correlation phenomenology of LK-99 and related compounds that could arise independently of superconductivity. Overall, our research highlights that LK-99 and related compounds offer a compelling platform for investigating correlation physics in flat band systems. 

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3. Orbital Ingredients and Persistent Dirac Surface State for the Topological Band Structure in ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$

   https://doi.org/10.1103/PhysRevX.14.021043  

   Li, Y-F; Chen, S-D; García-Díez, M; Iraola, M I; Pfau, H; Zhu, Y-L; Mao, Z-Q; Chen, T; Yi, M; Dai, P-C; et al (June 2024, Physical Review X)

   ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$(FTS) occupies a special spot in modern condensed matter physics at the intersections of electron correlation, topology, and unconventional superconductivity. The bulk electronic structure of FTS is predicted to be topologically nontrivial due to the band inversion between the $d_{xz}$and $p_z$bands along $\mathrm{\Gamma }\text{−}Z$. However, there remain debates in both the authenticity of the Dirac surface states (DSSs) and the experimental deviations of band structure from the theoretical band inversion picture. Here we resolve these debates through a comprehensive angle-resolved photoemission spectroscopy investigation. We first observe a persistent DSS independent of $k_z$. Then, by comparing FTS with FeSe, which has no band inversion along $\mathrm{\Gamma }\text{−}Z$, we identify the spectral weight fingerprint of both the presence of the $p_z$band and the inversion between the $d_{xz}$and $p_z$bands. Furthermore, we propose a renormalization scheme for the band structure under the framework of a tight-binding model preserving crystal symmetry. Our results highlight the significant influence of correlation on modifying the band structure and make a strong case for the existence of topological band structure in this unconventional superconductor. Published by the American Physical Society2024 

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4. Catalog of topological phonon materials

   https://doi.org/10.1126/science.adf8458  

   Xu, Yuanfeng; Vergniory, M G; Ma, Da-Shuai; Mañes, Juan L; Song, Zhi-Da; Bernevig, B Andrei; Regnault, Nicolas; Elcoro, Luis (May 2024, Science)

   Phonons play a crucial role in many properties of solid-state systems, and it is expected that topological phonons may lead to rich and unconventional physics. On the basis of the existing phonon materials databases, we have compiled a catalog of topological phonon bands for more than 10,000 three-dimensional crystalline materials. Using topological quantum chemistry, we calculated the band representations, compatibility relations, and band topologies of each isolated set of phonon bands for the materials in the phonon databases. Additionally, we calculated the real-space invariants for all the topologically trivial bands and classified them as atomic or obstructed atomic bands. We have selected more than 1000 “ideal” nontrivial phonon materials to motivate future experiments. The datasets were used to build the Topological Phonon Database. 

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5. Flat bands, strange metals and the Kondo effect

   https://doi.org/10.1038/s41578-023-00644-z  

   Checkelsky, Joseph G; Bernevig, B Andrei; Coleman, Piers; Si, Qimiao; Paschen, Silke (February 2024, Nature Reviews Materials)

   Flat-band materials such as the kagome metals or moiré superlattices are of intense current interest. Flat bands can result from the electron motion on numerous (special) lattices and usually exhibit topological properties. Their reduced bandwidth proportionally enhances the effect of Coulomb interaction, even when the absolute magnitude of the latter is relatively small. Seemingly unrelated to these materials is the large family of strongly correlated electron systems, which include the heavy-fermion compounds, and cuprate and pnictide superconductors. In addition to itinerant electrons from large, strongly overlapping orbitals, they frequently contain electrons from more localized orbitals, which are subject to a large Coulomb interaction. The question then arises as to what commonality in the physical properties and microscopic physics, if any, exists between these two broad categories of materials. A rapidly increasing body of strikingly similar phenomena across the different platforms — from electronic localization–delocalization transitions to strange-metal behaviour and unconventional superconductivity — suggests that similar underlying principles could be at play. Indeed, it has recently been suggested that flat-band physics can be understood in terms of Kondo physics. Inversely, the concept of electronic topology from lattice symmetry, which is fundamental in flat-band systems, is enriching the field of strongly correlated electron systems, in which correlation-driven topological phases are increasingly being investigated. In this Perspective article, we elucidate this connection, survey the new opportunities for cross-fertilization across platforms and assess the prospect for new insights that may be gained into correlation physics and its intersection with electronic topology. 

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