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1. Transport of Topological Semimetals

   https://doi.org/10.1146/annurev-matsci-070218-010023  

   Hu, Jin; Xu, Su-Yang; Ni, Ni; Mao, Zhiqiang (July 2019, Annual Review of Materials Research)

   Three-dimensional (3D) topological semimetals represent a new class of topological matters. The study of this family of materials has been at the frontiers of condensed matter physics, and many breakthroughs have been made. Several topological semimetal phases, including Dirac semimetals (DSMs), Weyl semimetals (WSMs), nodal-line semimetals (NLSMs), and triple-point semimetals, have been theoretically predicted and experimentally demonstrated. The low-energy excitation around the Dirac/Weyl nodal points, nodal line, or triply degenerated nodal point can be viewed as emergent relativistic fermions. Experimental studies have shown that relativistic fermions can result in a rich variety of exotic transport properties, e.g., extremely large magnetoresistance, the chiral anomaly, and the intrinsic anomalous Hall effect. In this review, we first briefly introduce band structural characteristics of each topological semimetal phase, then review the current studies on quantum oscillations and exotic transport properties of various topological semimetals, and finally provide a perspective of this area. 

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2. Polymorphism of low dimensional boron nanomaterials driven by electrostatic gating: a computational discovery

   https://doi.org/10.1039/C9NR10774F  

   Jiao, Yalong; Ma, Fengxian; Gu, Jinxing; Chen, Zhongfang; Du, Aijun (May 2020, Nanoscale)

   null (Ed.)

   The successful synthesis of two-dimensional (2D) boron sheets typically relies on the utilization of a silver surface, which acts as a gated substrate compensating for the electron-deficiency of boron. However, how the structures of one-dimensional (1D) boron are affected by the gating effect remains unclear. By means of an unbiased global minimum structure search and density functional theory (DFT) computations, we discovered the coexistence of 2D boron sheets and 1D ribbons triggered by electrostatic gating. Specifically, at a low excess charge density level (<0.1 e per atom), 2D boron sheets dominate the low energy configurations. As the charge density increases (>0.3 e per atom), more 1D boron ribbons emerge, while the number of 2D layers is reduced. Additionally, a number of low-lying 1D boron ribbons were discovered, among which a flat borophene-like ribbon (FBR) was predicted to be stable and possess high mechanical strength. Moreover, the electride Ca 2 N was identified as an ideal substrate for the fabrication of the FBR because of its ability to supply a strong electrostatic field. This work bridges the gap between 2D and 1D boron structures, reveals the polymorphism of 1D boron ribbons under the electrostatic gating effect, and in general provides broad implications for future synthesis and applications of low-dimensional boron materials. 

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3. Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

   https://doi.org/10.1038/s41467-020-14443-5  

   Wieder, Benjamin J.; Wang, Zhijun; Cano, Jennifer; Dai, Xi; Schoop, Leslie M.; Bradlyn, Barry; Bernevig, B. Andrei (January 2020, Nature Communications)

   Abstract Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of ans–d-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- (α) and intermediate-temperature (α″) phases of Cd₃As₂, KMgBi, and rutile-structure ($$ \beta ^{\prime} $$ ${\beta }^{\prime }$-) PtO₂. 

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4. Superoctahedral two-dimensional metallic boron with peculiar magnetic properties

   https://doi.org/10.1039/C9CP03786A  

   Tkachenko, Nikolay V.; Steglenko, Dmitriy; Fedik, Nikita; Boldyreva, Natalia M.; Minyaev, Ruslan M.; Minkin, Vladimir I.; Boldyrev, Alexander I. (September 2019, Physical Chemistry Chemical Physics)

   Among the diversity of new materials, two-dimensional crystal structures have been attracting significant attention from the broad scientific community due to their promising applications in nanoscience. In this study we predict a novel two-dimensional ferromagnetic boron material, which has been exhaustively studied with DFT methods. The relaxed structure of the 2D-B 6 monolayer consists of slightly flattened octahedral units connected with 2c-2e B–B σ-bonds. The calculated phonon spectrum and ab initio molecular dynamics simulations reveal the thermal and dynamical stability of the designed material. The calculation of the mechanical properties indicate a relatively high Young's modulus of 149 N m −1 . Moreover, the electronic structure indicates the metallic nature of the 2D-B 6 sheets, whereas the magnetic moment per unit cell is found to be 1.59 μ B . The magnetism in the 2D-B 6 monolayer can be described by the presence of two unpaired delocalized bonding elements inside every distorted octahedron. Interestingly, the nature of the magnetism does not lie in the presence of half-occupied atomic orbitals, as was shown for previously studied magnetic materials based on boron. We hope that our predictions will provide promising new ideas for the further fabrication of boron-based two-dimensional magnetic materials. 

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5. Anomalous Crystalline-Electromagnetic Responses in Semimetals

   https://doi.org/10.1103/PhysRevX.14.041060  

   Hirsbrunner, Mark R; Dubinkin, Oleg; Burnell, F J; Hughes, Taylor L (December 2024, Physical Review X)

   We present a unifying framework that allows us to study the mixed crystalline-electromagnetic responses of topological semimetals in spatial dimensions up to $D=3$through dimensional augmentation and reduction procedures. We show how this framework illuminates relations between the previously known topological semimetals and use it to identify a new class of quadrupolar nodal line semimetals for which we construct a lattice tight-binding Hamiltonian. We further utilize this framework to quantify a variety of mixed crystalline-electromagnetic responses, including several that have not previously been explored in existing literature, and show that the corresponding coefficients are universally proportional to weighted momentum-energy multipole moments of the nodal points (or lines) of the semimetal. We introduce lattice gauge fields that couple to the crystal momentum and describe how tools including the gradient expansion procedure, dimensional reduction, compactification, and the Kubo formula can be used to systematically derive these responses and their coefficients. We further substantiate these findings through analytical physical arguments, microscopic calculations, and explicit numerical simulations employing tight-binding models. Published by the American Physical Society2024 

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