Accurate assignment of double resonant Raman bands in Janus MoSSe monolayer from first-principles calculations

doi:10.1016/j.jmst.2022.05.022

Abstract

Abstract:

Janus transition metal dichalcogenides (TMDs) structures, as a new type of two-dimensional layered materials, have drawn increasing research efforts mostly by the Raman characterization technique since their successful synthesis. First- and second-order resonant Raman spectra (RRS) have been reported by experiments. But, unlike much interest paid to the first-order RRS, there has been so far no much discussion dedicated to the second-order double resonant Raman (DRR) bands and band assignments of Janus TMDs, which nevertheless is indispensable but hampered by the difficulty of calculations. In this work, we calculate the DRR spectra of Janus MoSSe monolayer within the first-principles framework and succeed in achieving accurate assignments of the DRR bands. The assignments are in agreement with our group theoretical analysis. Moreover, taking advantage of its strain-sensitive feature, we calculate the DRR spectra under biaxial strain, and further verify the rationality of our assignments by analyzing strain-induced shift of the DRR bands. Our present study supplies an efficient strategy for quantitative understanding on the electron-phonon coupling in the Janus structures.

Key words: First-principles calculation, Double resonant Raman, Raman band assignments, Janus MoSSe monolayer

Yujia Pang, Jianqi Huang, Teng Yang, Zhidong Zhang. Accurate assignment of double resonant Raman bands in Janus MoSSe monolayer from first-principles calculations[J]. J. Mater. Sci. Technol., 2022, 131: 82-90.

Figures/Tables 7

Fig. 1. (a) Top view and side view of Janus MoSSe monolayer in hexagonal lattice with a primitive unit cell enclosed by the red dashed line. (b) The hexagonal first Brillouin zone (BZ) surrounded by solid black lines and the irreducible BZ denoted by the pink region. High-symmetry points and line segments along the edge of irreducible BZ are labeled with Greek letters at their corresponding positions. (c) Calculated electronic energy band structure and electronic density of states (DOS) with considering the spin-orbit coupling. (d) The phonon dispersion relation and phonon DOS. Little-point-groups (point group of the space group of wavevector) of the wavevectors Γ, K and M are listed in parenthesis with the irreducible representations given on each colored vibrational branch. (e) Visualization of Raman-active optical modes at Γ point.

Table 1. Group theoretical selection rules for two-phonon Raman activity at the Brillouin zone points of Γ, K(K′) and M in Janus MoSSe monolayer. The cell with underlined irreducible representations (Irreps) means including at least one of the two Raman-active Irreps of A1 and E within point group C3v in the reduction and thus corresponds to a Raman-active binary combination.

C_3v (Γ)	A₁	A₂	E	C₃ (K, K')	A	¹E	²E
A₁	A₁	A₂	E	A	A₁ (C_3v) A + ¹E (C₃)	A₂ (C_3v) ²E (C₃)	E (C_3v) ²E (C₃)
A₂	A₂	A₁	E	¹E	A₂ (C_3v) ²E (C₃)	E (C_3v) A + ¹E (C₃)	A₁ (C_3v) ²E (C₃)
E	E	E	A₁±A₂±E	²E	E (C_3v) ²E (C₃)	A₁ (C_3v) ²E (C₃)	A₂ (C_3v) A + ¹E (C₃)
C_s (M)	A' × A'		A' × A"	A" × A'		A" × A"
	A₁±E (C_3v) A' + A" (C_s)		A₂±E (C_3v) A' + A" (C_s)	A₂ ± E (C_3v) A' + A" (C_s)		A₁ ± E (C_3v) A' + A" (C_s)

Fig. 2. Calculated double resonant Raman (DRR) spectrum of Janus MoSSe monolayer under the laser excitation energies of 1.96 eV, with positions of the first-order Raman modes identified by thin blue bars. A total number of eleven DRR bands indicated by the green arrows are labeled with Pi (i = 1, 2, · · ·, 11) and the Raman shifts are presented in the bottom panel.

Fig. 3. Process of assigning P1 band. (a) The q-resolved Raman intensity distribution pattern of P1 band in the whole Brillouin zone. (b) The q-resolved Raman intensity distribution pattern of five major binary combinations. Each one shows the dominant q points associated with branches pair indicated by the binary combination. (c) Contribution percentages of Raman intensity of each binary combination with respect to that of P1 band. (d) The double resonant Raman spectra of five binary combinations with two peaks in each Raman curve corresponding to one subtraction mode and one combination mode. (e) Subtraction modes of ZO2-ZO1 and LO2-LO1 are assigned to the P1 band with ZO2-LO1 and TO2-LA removed for deviating from P1 band and ZO2-TO1 having a relatively minor contribution.

Table 2. Assignments of the eleven double resonant Raman bands in Janus MoSSe monolayer. For the bands with more than one assignment, the ratio between the contribution proportion of the assignments with respect to the Raman intensity of the band is given. If the band consists of only one assignment, the ratio is set to 1. Generally speaking, the Brillouin zone point in the parenthesis denotes that the corresponding assignment distribute over the area around the point, not exactly at the point.

Raman band	Raman shift (cm⁻¹)	Assignments	Ratio
P₁	136.7	ZO₂-ZO₁(Γ) LO₂-LO₁(Γ)	2.28
P₂	172.1	LO₂-LA(M) TO₂-LA(K)	1.80
P₃	238.3	2TA (M) LO₂-LA(Γ)	3.56
P₄	292.8	2ZA (K) 2TA (K)	1.79
P₅	349.5	2LA (M)	1
P₆	413.1	LA+LO₁(M)	1
P₇	452.9	2TO₁ (M) LA+ZO₁(M)	1.56
P₈	505.1	TO₁+ZO₁(M)	1
P₉	536.8	2ZO₁ (M)	1
P₁₀	618.2	ZO₁+LO₂(Γ)	1
P₁₁	687.3	2LO₂ (Γ)	1

Fig. 4. Assignments verification in terms of Raman selection rules for linearly polarized light. (a) Double resonant Raman spectra of Janus MoSSe monolayer between 100 and 150 cm?1 under parallel and cross configuration. (b) The q-resolved Raman intensity distribution pattern of $\text{P}_{1}^{\prime }$ band.

Fig. 5. Assignments verification in terms of Raman band shift induced by strain. (a) Calculated double resonant Raman spectra of Janus MoSSe monolayer under no strain and biaxial compressive (-3%) and tensile (+3%) strain. (b) The q-resolved Raman intensity distribution patterns of P1 band and (c) optical phonon dispersion relations and corresponding phonon DOS under various strains. The arrows with different colors mark the q points under various strains at which the ZO2-ZO1 is assigned to the P1 band.

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