Cu-doped Pb10_{10}(PO4_4)6_6O, and V doped SrTiO3_3 -- a tutorial on electron-crystal lattice coupling in insulating materials with transition metal dopants

We provide two pedagogical examples to understand the mechanisms at play in stabilizing an insulating state, and an impurity level in the bandgap in two insulators using DFT+U: Cu-doped Pb$_{10}$(PO$_4$)$_6$O and V-doped SrTiO$_3$ transition metal-doped insulators. We find both to be insulating, with isolated impurity (flat) bands, regardless of doping location. In both cases, the electron degeneracy and crystal lattice symmetry are broken, leading to an insulating state, and a magnetically and orbitally polarized impurity state within the gap, clearly separated from the valence and conduction bands. We also resolve previously noticed inconsistencies between DFT and experiment regarding doping site energetics, crystal structure, and transparency in Cu-doped phosphate lead apatite 'LK-99'. Doping one of each type of site in the same unit cell ($20 \%$ doping) also simply leads to two spin-polarized impurity bands in the material's gap. The local transition metal ion sites may behave like color centers (or f-centers), possibly giving color at low temperatures to what we predict to be a transparent, insulating material in the recently synthesized LK-99. Weak ferromagnetism may be possible due to the relatively delocalized unpaired spins in the valence band. Further work should take into account the possibility of further changes in stoichiometry, different doping locations, supercell effects, and quantification of magnetic exchange interactions

Trigonal Symmetry Breaking and its Electronic Effects in Two-Dimensional Dihalides and Trihalides

We study the consequences of the approximately trigonal ($D_{3d}$) point symmetry of the transition metal (M) site in two-dimensional van der Waals MX$_2$ dihalides and MX$_3$ trihalides. The trigonal symmetry leads to a 2-2-1 orbital splitting of the transition metal $d$ shell, which may be tuned by the interlayer distance, and changes in the ligand-ligand bond lengths. Orbital order coupled to various lower symmetry lattice modes may lift the remaining orbital degeneracies, and we explain how these may support unique electronic states using ZrI$_2$ and CuCl$_2$ as examples, and offer a brief overview of possible electronic configurations in this class of materials. By building and analysing Wannier models adapted to the appropriate symmetry we examine how the interplay among trigonal symmetry, electronic correlation effects, and $p$-$d$ orbital charge transfer leads to insulating, orbitally polarized magnetic and/or orbital-selective Mott states. Our work establishes a rigorous framework to understand, control, and tune the electronic states in low-dimensional correlated halides. Our analysis shows that trigonal symmetry and its breaking is a key feature of the 2D halides that needs to be accounted for in search of novel electronic states in materials ranging from CrI$_3$ to $\alpha$-RuCl$_3$

High-resolution spatial mapping of the temperature distribution of a Joule self-heated graphene nanoribbon

We investigate the temperature distributions of Joule self-heated graphene nanoribbons (GNRs) with a spatial resolution finer than 100 nm by scanning thermal microscopy (SThM). The SThM probe is calibrated using the Raman G mode Stokes/anti-Stokes intensity ratio as a function of electric power applied to the GNR devices. From a spatial map of the temperature distribution, heat dissipation and transport pathways are investigated. By combining SThM and scanning gate microscopy data from a defected GNR, we observe hot spot formation at well-defined, localized sites.Comment: 4 pages, 3 figures, accepted on App. Phys. Let

Database, Features, and Machine Learning Model to Identify Thermally Driven Metal-Insulator Transition Compounds

Metal-insulator transition (MIT) compounds are materials that may exhibit insulating or metallic behavior, depending on the physical conditions, and are of immense fundamental interest owing to their potential applications in emerging microelectronics. There is a dearth of thermally-driven MIT materials, however, which makes delineating these compounds from those that are exclusively insulating or metallic challenging. Here we report a material database comprising temperature-controlled MITs (and metals and insulators with similar chemical composition and stoichiometries to the MIT compounds) from high quality experimental literature, built through a combination of materials-domain knowledge and natural language processing. We featurize the dataset using compositional, structural, and energetic descriptors, including two MIT relevant energy scales, an estimated Hubbard interaction and the charge transfer energy, as well as the structure-bond-stress metric referred to as the global-instability index (GII). We then perform supervised classification, constructing three electronic-state classifiers: metal vs non-metal (M), insulator vs non-insulator (I), and MIT vs non-MIT (T). We identify two important descriptors that separate metals, insulators, and MIT materials in a 2D feature space: the average deviation of the covalent radius and the range of the Mendeleev number. We further elaborate on other important features (GII and Ewald energy), and examine how they affect classification of binary vanadium and titanium oxides. We discuss the relationship of these atomic features to the physical interactions underlying MITs in the rare-earth nickelate family. Last, we implement an online version of the classifiers, enabling quick probabilistic class predictions by uploading a crystallographic structure file