Author Affiliations
1Xi'an University of Posts and Telecommunications, Xi'an 710121, China2School of Electronic Engineering, Xi'an University of Posts and Telecommunications, Xi'an 710121, Chinashow less
Fig. 1. (Color online) The crystal structures of
(M = Zr and Hf) monolayers: (a) top view and (b) side view.
Fig. 2. (Color online)The phonon dispersion curves of
(M = Zr and Hf) monolayers with GGA.
Fig. 3. (Color online) (a) The fluctuations of temperature and total energy with the time obtained from MD simulation of
monolayer at 600 K. (b, c) The snapshot of
monolayer at the end of MD simulation at 600 K ((b): Top views, (c): Side views).
Fig. 4. (Color online) Band structures of
(M = Zr and Hf) monolayers without/with SOC (GGA/GGA+SOC).
Fig. 5. (Color online) Band structures of
monolayer with SOC (
from 0.90 to 1.10).
Fig. 6. (Color online) The band gaps of
(M = Zr and Hf) monolayers vs
with SOC.
Fig. 7. The larger version around CBM for
(M = Zr and Hf) monolayers with SOC at 1.04 strain.
Fig. 8. (Color online) In-plane spin textures calculated at the iso-energy surface of 1.5 eV above the Fermi level for
monolayer with red/blue colours being spin-up/spin-down states.
Fig. 9. (Color online) The calculated optical dielectric function of
(M = Zr and Hf) monolayers with real parts (Left) and imaginary parts (Right) along xx/yy and
directions.
Fig. 10. (Color online) The optical absorption coefficients of
(M = Zr and Hf) monolayers along xx/yyand zzdirections from 0 to 4 eV, and the visible light region (1.6–3.1 eV) is shown.
Parameter | Value |
---|
(Å)
| 3.110 (3.097) | | 403.92 (465.93) | (N/m)
| 110.58 (135.19) | | 146.67 (165.37) | (N/m)
| 373.65 (426.71) | | 0.274 (0.290) | Gap (eV) | 1.134 (1.336) | Gap-SOC (eV) | 1.115 (1.282) |
|
Table 1. For the
(
) monolayer, the lattice constants
; the physical quantities associated with elasticity (the elastic constants
, shear modulus
, Young's modulus
and Poisson's ratio
); the gaps without/with SOC.
| | | | |
---|
Zr | 2.950 | 1.006 | 0.094 | 0.018 | Hf | 2.251 | 0.680 | 0.068 | 0.011 | Mo | 5.116 | 1.494 | −0.087 | −0.014 | W | 3.790 | 1.050 | 0.073 | 0.011 |
|
Table 2. Piezoelectric Coefficients
(
C/m) and
(pm/V) of
-
(M = Zr and Hf) and
-
(M = Mo and W) monolayers.