Prediction of monoclinic single-layer Janus ${\mathrm{Ga}}_2\mathrm{Te}X$ ( $X$ = S and Se): Strong in-plane anisotropy

By using density functional theory (DFT) based first-principles calculations, electronic, vibrational, piezoelectric, and optical properties of monoclinic Janus single-layer ${\mathrm{Ga}}_2\mathrm{Te}X$ ($X$ = S or Se) are investigated. The dynamical, mechanical, and thermal stability of the proposed Janus single layers are verified by means of phonon bands, stiffness tensor, and quantum molecular dynamics simulations. The calculated vibrational spectrum reveals the either pure or coupled optical phonon branches arising from Ga-Te and Ga-$X$ atoms. In addition to the in-plane anisotropy, single-layer Janus ${\mathrm{Ga}}_2\mathrm{Te}X$ exhibits additional out-of-plane asymmetry, which leads to important consequences for its electronic and optical properties. Electronic band dispersions indicate the direct band-gap semiconducting nature of the constructed Janus structures with energy band gaps falling into visible spectrum. Moreover, while orientation-dependent linear-elastic properties of Janus single layers indicate their strong anisotropy, the calculated in-plane stiffness values reveal the ultrasoft nature of the structures. In addition, predicted piezoelectric coefficients show that while there is a strong in-plane anisotropy between piezoelectric constants along armchair (AC) and zigzag (ZZ) directions, there exists a tiny polarization along the out-of-plane direction as a result of the formation of Janus structure. The optical response to electromagnetic radiation has been also analyzed through density functional theory by considering the independent-particle approximation. Finally, the optical spectra of Janus ${\mathrm{Ga}}_2\mathrm{Te}X$ structures is investigated and it showed a shift from the ultraviolet region to the visible region. The fact that the spectrum is between these regions will allow it to be used in solar energy and many nanoelectronics applications. The predicted monoclinic single-layer Janus ${\mathrm{Ga}}_2\mathrm{Te}X$ are relevant for promising applications in optoelectronics, optical dichroism, and anisotropic nanoelasticity.

Figure 1

For the Janus single layers of ${\mathrm{Ga}}_2\mathrm{TeSe}$ and ${\mathrm{Ga}}_2\mathrm{TeS}$; (a) top and side views and the corresponding charge distribution on the individual atoms. [(b), (c)] The phonon band dispersions for ${\mathrm{Ga}}_2\mathrm{TeSe}$ and ${\mathrm{Ga}}_2\mathrm{TeS}$, respectively. The primitive unit cell is denoted by the red lines by representing the lattice vectors, $a$ and $b$. The blue regions represent the zero charge regime while the yellow regions stand for the charge of 6.4 $e$/Å${}^3$. The green region represents the charge amount of 1.9 $e$/Å${}^3$ while the maximum charge region, red region, shows the 6.9 $e$/Å${}^3$.

Figure 2

(a) Raman spectra of Janus single layers ${\mathrm{Ga}}_2\mathrm{TeSe}$ and ${\mathrm{Ga}}_2\mathrm{TeS}$. (b) The atomic vibrations in some of the prominent Raman active modes.

Figure 3

Orientation-dependent linear-elastic constants for ${\mathrm{Ga}}_2\mathrm{Te}X$, (a) in-plane stiffness and (b) Poisson ratio. The two main orientations, namely $x$ (AC) and $y$ (ZZ), are shown on the crystal structure. The blue and green curves stand for single layers ${\mathrm{Ga}}_2\mathrm{Tes}$ and ${\mathrm{Ga}}_2\mathrm{TeSe}$, respectively.

Figure 4

The atom-dependent projected electronic band structures for (a) ${\mathrm{Ga}}_2\mathrm{TeS}$ and (b) ${\mathrm{Ga}}_2\mathrm{TeSe}$ in the scheme of DFT-PBE.

Figure 5

The electronic band structure of ${\mathrm{Ga}}_2\mathrm{Te}X$ in the framework of DFT-SOC and HSE06.

Figure 6

For single layers of ${\mathrm{Ga}}_2\mathrm{TeS}$ (left panel) and ${\mathrm{Ga}}_2\mathrm{TeSe}$ (right panel); [(a), (b)] imaginary part of the dielectric function, [(c), (d)] absorption, [(e), (f)] reflectivity, and [(g), (h)] directional optical conductivity.

Figure 7

The variation of the imaginary part of the dielectric function of with photon energy for in-plane polarization for ${\mathrm{Ga}}_2\mathrm{Te}X$ calculated within PBE and HSE06 functionals.