Heavy boron doping in superconducting carbon materials

Yuki Sakai, James R. Chelikowsky, and Marvin L. Cohen

Phys. Rev. Materials 4, 054801 – Published 4 May 2020

Abstract

We examine physical properties of heavily boron-doped $s p^{3}$ -hybridized carbon allotropes: cubic diamond, hexagonal diamond, and body centered tetragonal $C_{4}$ . The structural similarity between cubic diamond and hexagonal diamond leads to similar responses to substitutional boron doping. On the other hand, body centered tetragonal $C_{4}$ exhibits distinct structural and electronic properties because of its characteristic structure. Our study also shows that the superconducting transition temperatures up to 60 K are possible in heavily doped carbon materials despite their various atomistic structures.

Received 12 February 2020
Accepted 14 April 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.054801

Physics Subject Headings (PhySH)

Superconductivity

Diamond

First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuki Sakai¹, James R. Chelikowsky^1,2,3, and Marvin L. Cohen^4,5

¹Center for Computational Materials, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
²McKetta Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA
³Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
⁴Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
⁵Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

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Vol. 4, Iss. 5 — May 2020

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Images

Figure 1
Crystal structures of (a) cubic diamond, (b) hexagonal diamond, and (c) body centered tetragonal (bct) $C_{4}$ . The top and bottom panels of (b) and (c) represent the top and side views of the structures, respectively. Carbon atoms are illustrated with gray spheres. The size of the cell is equivalent to the initial undoped supercell used in this work. The number of atoms is 64 in (a) and (c), while (b) contains 72 atoms.
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Figure 2
Distorted crystals structure of 25% boron-doped carbon allotropes. The structure of cubic diamond, (a) with and (b) without boron pairing, hexagonal diamond (c) with and (d) without boron pairing, and bct $C_{4}$ (e) with and (f) without boron pairing. (a),(c),(e) The highest-energy structure among each set; (b),(d),(f) the lowest-energy structures. Gray and orange spheres represent carbon and boron atoms, respectively. (g) Charge density color plot taken at a plane right above the topmost atoms of (e). (h) Similar plot, but for (f). Here a black-brown-white color scale is used.
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Figure 3
Partial electronic DOS (PDOS) in states/eV/atom of (a),(b) cubic diamond, (c),(d) hexagonal diamond, and (e),(f) bct $C_{4}$ . (a),(c),(e) The PDOS for the structures with boron pairing; (b),(d),(f) those without boron pairing. The boron concentration is 25% and the PDOS is the average over all atoms from each atomic species. Blue solid and red dashed lines represent the partial DOS of carbon and boron atoms, respectively. The vertical dashed line shows the position of the Fermi energy.
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Figure 4
Superconducting transition temperature ( $T_{c}$ in K, bottom panels), logarithmic average of phonon frequency ( $ω_{\log}$ in ${cm}^{- 1}$ , center panels), and electron-phonon coupling constant ( $λ$ , top panels) for three boron-doped carbon materials as a function of electronic DOS at the Fermi energy [ $N (E_{F})$ in states/eV/atom]. Left, center, and right columns show the results for cubic diamond, hexagonal diamond, and bct $C_{4}$ , respectively. Blue squares and green circles represent the data for 12.5% and 25% boron-doped cases with boron pairing, respectively. Red triangles represent the results for 25% doping without boron paring.
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Figure 5
Eliashberg spectral function (top panel) and phonon density of states (bottom panel) of 25% boron-doped cubic diamond (blue dash-dotted lines), hexagonal diamond (black dashed lines), bct $C_{4}$ (red solid lines). Here we select the structure with the highest $T_{c}$ for each material. The finite phonon DOS around the zero frequency is an artifact because of the unconverged acoustic phonon modes at the $Γ$ point.
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