Phonon dispersion of a two-dimensional boron sheet on Ag(111)

Two-dimensional (2D) atomically thin boron layers designated as borophene or boraphene, attract great interest as promising post-graphene 2D materials. The borophene layer phonon structure has not yet been clarified by experimentation in spite of its importance for application for possible superconduction and thermal technologies. For this work we measured, by experimentation, the phonon dispersion of an incommensurate three-domain ${\chi }_3$-borophene formed on Ag(111) using high-resolution electron energy loss spectroscopy. Measured phonons were analyzed using first-principles theoretical calculations. Because the phonon band of the substrate Ag(111) lies in a low-energy region, the borophene phonon is well separated from the substrate. For our calculations, a commensurate slab supercell model was adopted, the periodicity of which was Ag(111) $3\times 3$. The lattice parameter of the model was determined using experimentally obtained phonon data. The highest frequency phonon of an isolated borophene layer was fitted to the data as a function of the electronic charge in it. The best fitted lattice parameter was used in the supercell model. The model well reproduced the experimentally observed phonon dispersion. No marked anomaly was found in the phonon structure.

Figure 1

RHEED (a)–(c), LEED (d), and AES (lower panel) of (a) clean Ag(111) surface and (b)–(d) borophene covered Ag(111). Primary electron energies ($E_0$) are 15 keV for RHEED and 113.7 eV for LEED. The azimuthal orientations are $\left[1\overline{2}1\right]$ for (a) and (b), and $\left[\overline{1}01\right]$ for (c). The Ag(111) fundamental diffractions and those from borophene are represented, respectively, by black and red lines as a guide to the eyes. The LEED pattern has some pincushion distortion because of the planar screen.

Figure 2

Specular HREEL spectrum of the borophene on Ag(111). $E_0=10.0$ eV and ${\theta }_{\mathrm{in}}={\theta }_{\mathrm{out}}={75}^{\circ }$.

Figure 3

Typical series of off-specular HREEL spectra of the borophene on Ag(111) along the $\langle 11\overline{2}\rangle$ ($\overline{\mathrm{\Gamma }}\text{−}\overline{M}$) azimuth of the substrate.

Figure 4

Experimentally measured phonon dispersion of borophene on Ag(111). $E_0=6.0$ eV (purple diamonds), 10.0 eV (green squares), and 17.0 eV (blue circles). Red triangles represent the Raman spectroscopy data [30].

Figure 5

(a) Plan-view supercell structure model and (b) surface Brillouin zones. For the blue rhombus, vectors $\mathit{a}$ and $\mathit{b}$ represent the unit cell in the calculation. A red one (vectors $\mathit{c}$ and $\mathit{d}$) is the unit cell of ${\chi }_3$-borophene overlayer. Gray and green balls, respectively, represent Ag and B atoms.

Figure 6

Calculated lattice constant (red circles) and frequency of the highest energy at $\overline{\mathrm{\Gamma }}$ point (blue squares) of the free-standing ${\mathrm{B}}_{20}{\chi }_3$-borophene with respect to the excess electron charge.

Figure 7

Calculated phonon dispersion curves of (a) domain 1 (along and perpendicular to the vacancy row) and (b) domains 2 and 3 ($\pm {120}^{\circ }$ from the domain 1).

Figure 8

Calculated partial-density phonon dispersion (brown curves) of the borophene layer and the experimentally obtained data (green dots): (a) in-plane modes and (b) out-of-plane modes. Color darkness represents the phonon density.

Figure 9

Calculated electronic band structure of an isolated ${\chi }_3$-borophene. The projected density is represented with the color darkness of magenta (B $2p_{\mathrm{z}}$), cyan (B $2p_{\mathrm{xy}}$), and yellow (B $2s$). The energy scale is taken as $E_f$ (Fermi energy) = 0 eV.

Figure 10

Projected electronic band structure of the Ag(111)$3\times 3-{\chi }_3\mathrm{B}$ slab for the domain 1 [Fig. 7]. The color depth represents the projected density of the B $2p_{\mathrm{z}}$ (magenta), B $2p_{\mathrm{xy}}$ (cyan), and the subsurface layer Ag $s+p+d$ (yellow). The energy scale is taken as $E_f=0$ eV.