Electron-phonon coupling superconductivity in two-dimensional orthorhombic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:msub><mml:mi mathvariant="normal">B</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mi>Mg</mml:mi><mml:mo>,</mml:mo><mml:mi>Ca</mml:mi><mml:mo>,</mml:mo><mml:mi>Ti</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">Y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> and hexagonal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:msub><mml:mi mathvariant="normal">B</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mi>Mg</mml:mi><mml:mo>,</mml:mo><mml:mi>Ca</mml:mi><mml:mo>,</mml:mo><mml:mi>Sc</mml:mi><mml:mo>,</mml:mo><mml:mi>Ti</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>

Abstract

Combining crystal structure search and first-principles calculations, we report a series of two-dimensional (2D) metal borides including orthorhombic (ort-)$M{\mathrm{B}}_{6}$ $(M=\mathrm{Mg},\mathrm{Ca},\mathrm{Ti},\mathrm{Y})$ and hexagonal (hex-)$M{\mathrm{B}}_{6}$ $(M=\mathrm{Mg},\mathrm{Ca},\mathrm{Sc},\mathrm{Ti})$. Then, we investigate their geometrical structures, bonding properties, electronic structures, mechanical properties, phonon dispersions, thermal stability, dynamic stability, charge density wave (CDW) phase transition, electron-phonon coupling (EPC), superconducting properties, and so on. Our ab initio molecular dynamics simulation results show that these $M{\mathrm{B}}_{6}$ can maintain their original configurations up to about 1000 or 700 K (only for hex-${\mathrm{MgB}}_{6}$), indicating their excellent thermal stability. All their elastic constants satisfy the Born mechanically stable criteria and no imaginary frequencies are observed in their phonon dispersions. Interestingly, there may exist a CDW phase transition for ort-${\mathrm{TiB}}_{6}$ from type-I to type-II $2\ifmmode\times\else\texttimes\fi{}1$ supercell structure and for ort-${\mathrm{YB}}_{6}$ from type-I to type-III $2\ifmmode\times\else\texttimes\fi{}1$ supercell structure. Besides, these 2D $M{\mathrm{B}}_{6}$ are all predicted to be intrinsic phonon-mediated superconductors. By analytically solving the McMillan-Allen-Dynes formula derived from the microscopic theory of Bardeen, Cooper, and Schrieffer, we obtain the superconducting transition temperature (${T}_{\mathrm{c}}$) for these materials, which are in the range of 1.4--22.6 K. Among our studied $M{\mathrm{B}}_{6}$, the highest ${T}_{\mathrm{c}}$ (22.6 K) appears in hex-${\mathrm{CaB}}_{6}$, whose EPC constant $(\ensuremath{\lambda})$ is 0.87. By applying tensile/compressive strains on ort-/hex-${\mathrm{CaB}}_{6}$, we find that the compressive strain can obviously soften the acoustic-phonon branch and enhance the EPC as well as ${T}_{\mathrm{c}}$. The ${T}_{\mathrm{c}}$ of the hex-${\mathrm{CaB}}_{6}$ can be increased from 22.6 to 28.4 K under compressive strain of 3%. These findings enrich the database of 2D superconductors and should stimulate experimental synthesizing and characterizing of 2D superconducting metal borides.

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