Phase engineering of monolayer transition-metal dichalcogenide
through coupled electron doping and lattice deformation
Supplementary Material
S1. The energy of 1T-MX2 in comparison with other MX2 allotropes
The energies of four phases of MX2 (2H, 1T, 1T’ and 1T’’) as functions of lattice
distortion a / a0 and electron doping density q are shown in Fig. S1. For each MX2
system, it is clear that the 1T phase always exhibit highest energy among the four
MX2 phases, thus being essentially an “unstable” phase compared to the other three.
Fig. S1. Energy profiles of four phases (2H, 1T, 1T’ and 1T’’) of (a) MoS2 (b) MoSe2 (c)
WS2 (d) WSe2 as functions of the lattice deformation ∆𝒂/𝒂𝟎 and electron doping density q
(in the unit of q0=1.14×1015 cm-2).
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S2. Equilibrium lattice constant a0
In the main text we denotes a0 as the ground state lattice constant of the 2H
phase at q = 0. We also examined the equilibrium lattice constants for different MX2
phases (at q = 0) obtained from DFT structure minimization, shown in Table SI.
We
see that in an approximate sense a0 can also be regarded as the equilibrium lattice
constant for other phases.
The values listed in Table SI are also in agreement with
the ones predicted by the parabolic fitting of the curves in Fig. 3 (see main text).
Table SI: The values of equilibrium lattice parameter a0 of different MX2 (M= Mo or W; X=S
or Se) phases.
MX2 System
MoS2
MoSe2
WS2
WSe2
Equilibrium lattice constant at q = 0 (Å)
2H
1T
1T’
1T’’
3.18
3.19
3.17
3.17
3.31
3.28
3.32
3.32
3.18
3.21
3.20
3.16
3.31
3.31
3.30
3.30
S3. Phonon dispersion spectrum of 1T-MX2
The phonon dispersion spectrums of the 1T-MX2 phases (at a / a0  0 and q =
0) are presented in Fig. S2. The real-space force constants were obtained with the
density-functional perturbation theory (DFPT)1 using a 4 × 4 × 1 supercell. An
energy convergence criterion of 10-8 eV was used to guarantee accuracy.
The
package PHONOPY2 was used to conduct phonon calculations.
Imaginary frequencies are observed in Fig. S2, indicating the instability of 1T
phase, consistent with what was reported in previous studies3. The imaginary
frequencies remain to exist when the 1T-MX2 is subjected to lattice deformation and
2
electronic modification.
Fig. S2 Phonon dispersion spectrums of the 1T phase for (a) MoS2, (b) MoSe2, (c) WS2
and (d) WSe2, the branches of imaginary frequencies are indicated by red dashed lines.
S4. Construction of the 2D diagram of energetically preferred phases
With a / a0 and q treated as state variables, we can compute the energy surface
for each individual MX2 system. In the above calculations, a 41×31 point grid was
used in sampling the range of q (i.e., from 0 to 1.0) and a / a0 (i.e., from 0 to 0.15),
followed by linear interpolation to obtain a smooth energy surface (see Fig. S3a). By
projecting the 3D energy surfaces to the 2D space of a / a0 and q, the diagram of
energetically preferred phases is obtained (Fig. S3b).
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Fig. S3 (a) The computed energy surfaces of different phases of MoS2 and (b) the
correspondent 2D diagram of energetically preferred phases, with the lattice deformation and
electron doping density as the state variables. q is in the unit of q0=1.14×1015 cm-2.
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3
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