High-Pressure Synthesis of Dirac Materials: Layered van der Waals Bonded ${\mathrm{BeN}}_{4}$ Polymorph

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High-Pressure Synthesis of Dirac Materials: Layered van der Waals Bonded ${BeN}_{4}$ Polymorph

Maxim Bykov, Timofey Fedotenko, Stella Chariton, Dominique Laniel, Konstantin Glazyrin, Michael Hanfland, Jesse S. Smith, Vitali B. Prakapenka, Mohammad F. Mahmood, Alexander F. Goncharov, Alena V. Ponomareva, Ferenc Tasnádi, Alexei I. Abrikosov, Talha Bin Masood, Ingrid Hotz, Alexander N. Rudenko, Mikhail I. Katsnelson, Natalia Dubrovinskaia, Leonid Dubrovinsky, and Igor A. Abrikosov

Phys. Rev. Lett. 126, 175501 – Published 26 April 2021

Abstract

High-pressure chemistry is known to inspire the creation of unexpected new classes of compounds with exceptional properties. Here, we employ the laser-heated diamond anvil cell technique for synthesis of a Dirac material ${BeN}_{4}$ . A triclinic phase of beryllium tetranitride $tr − {BeN}_{4}$ was synthesized from elements at $\sim 85 GPa$ . Upon decompression to ambient conditions, it transforms into a compound with atomic-thick ${BeN}_{4}$ layers interconnected via weak van der Waals bonds and consisting of polyacetylene-like nitrogen chains with conjugated $π$ systems and Be atoms in square-planar coordination. Theoretical calculations for a single ${BeN}_{4}$ layer show that its electronic lattice is described by a slightly distorted honeycomb structure reminiscent of the graphene lattice and the presence of Dirac points in the electronic band structure at the Fermi level. The ${BeN}_{4}$ layer, i.e., beryllonitrene, represents a qualitatively new class of 2D materials that can be built of a metal atom and polymeric nitrogen chains and host anisotropic Dirac fermions.

Received 30 November 2020
Revised 16 January 2021
Accepted 24 March 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.175501

Physics Subject Headings (PhySH)

Chemical bonding Crystal structure Dirac fermions Pressure effects

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Maxim Bykov ^1,2,*, Timofey Fedotenko³, Stella Chariton ⁴, Dominique Laniel ³, Konstantin Glazyrin ⁵, Michael Hanfland ⁶, Jesse S. Smith⁷, Vitali B. Prakapenka ⁴, Mohammad F. Mahmood², Alexander F. Goncharov¹, Alena V. Ponomareva ⁸, Ferenc Tasnádi⁹, Alexei I. Abrikosov¹⁰, Talha Bin Masood¹⁰, Ingrid Hotz¹⁰, Alexander N. Rudenko^12,11,13, Mikhail I. Katsnelson^12,13, Natalia Dubrovinskaia ^3,9, Leonid Dubrovinsky^14,†, and Igor A. Abrikosov^9,‡

¹The Earth and Planets Laboratory, Carnegie Institution for Science, Washington, D.C. 20015, USA
²College of Arts and Science, Howard University, Washington, D.C. 20059, USA
³Material Physics and Technology at Extreme Conditions, Laboratory of Crystallography, University of Bayreuth, 95440 Bayreuth, Germany
⁴Center for Advanced Radiation Sources, University of Chicago, Chicago, Illinois 60637, USA
⁵Photon Sciences, Deutsches Electronen Synchrotron (DESY), D-22607 Hamburg, Germany
⁶European Synchrotron Radiation Facility, 38043 Grenoble Cedex 9, France
⁷HPCAT, X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁸Materials Modeling and Development Laboratory, National University of Science and Technology “MISIS,” 119049 Moscow, Russia
⁹Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-58183 Linköping, Sweden
¹⁰Department of Science and Technology (ITN), Linköping University, SE-60174 Norrköping, Sweden
¹¹Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
¹²Radboud University, Institute for Molecules and Materials, 6525AJ Nijmegen, The Netherlands
¹³Department of Theoretical Physics and Applied Mathematics, Ural Federal University, 620002 Ekaterinburg, Russia
¹⁴Bayerisches Geoinstitut, University of Bayreuth, 95440 Bayreuth, Germany

^*Corresponding author. maks.byk@gmail.com
^†Corresponding author. leonid.dubrovinsky@uni-bayreuth.de
^‡Corresponding author. igor.abrikosov@liu.se

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Vol. 126, Iss. 17 — 30 April 2021

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Figure 1
Crystal structure of $tr − {BeN}_{4}$ at 84 GPa. (a) The view along the [100] direction; (b) coordination of a Be atom by one of the polymeric nitrogen chains. (c) ${BeN}_{6}$ octahedron with Be-N distances given in Å. (d) Coordination geometry of the nitrogen chain. (e) Scheme showing the transformation of $tr − {BeN}_{4}$ upon decompression. (f) Single layer of ${BeN}_{4}$ at ambient pressure. (g) Stacking sequence of polymeric nitrogen chains belonging to neighboring layers of $tr − {BeN}_{4}$ at ambient pressure; viewing direction is perpendicular to the layer. Beryllium and nitrogen atoms are represented as gray and blue spheres, respectively.
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Figure 2
Evolution of the crystal structure and the charge density of $tr − {BeN}_{4}$ upon decompression from the synthesis pressure to ambient. At the synthesis pressure, Be and N atoms form corrugated nets and the Be atoms (green) are octahedrally coordinated by six N atoms (blue) (left figure). Upon decompression, below about 50 GPa, the structure relaxes in such a way that the corrugated nets of Be and N atoms flatten, their increasing mutual separation reduces the coordination number of Be atoms to 4, thus turning the structure motif to layered (right figure). The gray planes between the layers indicate the position of the charge density slice and visualize the depletion of the charge density between two layers of $tr − {BeN}_{4}$ at zero pressure relative to that at synthesis pressure. Topological data analysis of the charge density (see Supplemental Material, Methods, Figs. S10–S11 [24]) confirms a stronger interaction within layers and weaker interaction between layers as the pressure is decreased. Experimental lattice parameters for $tr − {BeN}_{4}$ at 1 bar: $a = 3.275 (2)$ , $b = 4.212 (2)$ , $c = 3.704 (2) Å$ , $α = 103.43 (3)$ , $β = 105.61 (4)$ , $γ = 111.86 (4) °$ , $V = 42.4 Å^{3}$ . Optimized atomic positions: Be (0.5 0 0), N1 (0.1592 0.66170 0.5144), N2 (0.15840 0.6630 0.14780).
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Figure 3
Electronic structure of the beryllonitrene (a) Effective electronic lattice (green) superimposed onto the real-space crystal structure of single-layer ${BeN}_{4}$ (a) Green balls centered on the N-N bond correspond to the wave functions shown on the right side. Fourfold-coordinated gray balls depict Be atoms, dirty-blue threefold coordinated balls correspond to N atoms. Arrows denote two main interaction parameters defined in terms of a tight-binding Hamiltonian. (b) Electronic band structure and the density of states calculated using DFT (red) and the electronic lattice model (blue) shown in (a). The inset shows the Brillouin zone with the high-symmetry points, as well as the Fermi surface corresponding to the Fermi energy of $- 0.5 eV$ .
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High-Pressure Synthesis of Dirac Materials: Layered van der Waals Bonded BeN4 Polymorph

Phys. Rev. Lett. 126, 175501 – Published 26 April 2021

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High-Pressure Synthesis of Dirac Materials: Layered van der Waals Bonded ${BeN}_{4}$ Polymorph