Raman vibrational spectra of bulk to monolayer $\mathrm{Re}{\mathrm{S}}_2$ with lower symmetry

The lattice structure and symmetry of two-dimensional (2D) layered materials are of key importance to their fundamental mechanical, thermal, electronic, and optical properties. Raman spectroscopy, as a convenient and nondestructive tool, however, has its limitations in identifying all symmetry allowing Raman modes and determining the corresponding crystal structure of 2D layered materials with high symmetry, such as graphene and $\mathrm{Mo}{\mathrm{S}}_2$. Due to the lower structural symmetry and extraordinary weak interlayer coupling of $\mathrm{Re}{\mathrm{S}}_2$, we successfully identify all 18 first-order Raman active modes for bulk and monolayer $\mathrm{Re}{\mathrm{S}}_2$. Without a van der Waals correction, our local density approximation (LDA) calculations successfully reproduce all the Raman modes. Our calculations also suggest no surface reconstruction effect and the absence of low frequency rigid-layer Raman modes below $100\mathrm{c}{\mathrm{m}}^{-1}$. Combining Raman spectroscopy and LDA thus provides a general approach for studying the vibrational and structural properties of 2D layered materials with lower symmetry.

Figure 1

(a) A typical microscopic image of monolayer (in the red circle) and multilayer $\mathrm{Re}{\mathrm{S}}_2$ flakes on a Si substrate with 300 nm thick $\mathrm{Si}{\mathrm{O}}_2$. (b) An AFM image of the monolayer $\mathrm{Re}{\mathrm{S}}_2$ flake in the red circle of (a). Inset: The height probe profile of monolayer $\mathrm{Re}{\mathrm{S}}_2$, showing a monolayer $\mathrm{Re}{\mathrm{S}}_2$ height of 0.742 nm. (c) The lattice structure of bulk $\mathrm{Re}{\mathrm{S}}_2$. Left: Perspective drawing of a primitive cell of bulk $\mathrm{Re}{\mathrm{S}}_2$ down the interlayer lattice vector $a$. The vectors $b$ and $c$ are in-plane lattice vectors. Right: Periodical lattice structure of bulk $\mathrm{Re}{\mathrm{S}}_2$. The parallelepiped is the primitive cell of bulk $\mathrm{Re}{\mathrm{S}}_2$.

Figure 2

(a) Raman spectrum of bulk $\mathrm{Re}{\mathrm{S}}_2$. The arrows mark the concrete positions of 18 Raman active modes of bulk $\mathrm{Re}{\mathrm{S}}_2$. (b) Raman spectra of few-layer $\mathrm{Re}{\mathrm{S}}_2$. The arrows mark the concrete positions of 18 Raman active modes of monolayer $\mathrm{Re}{\mathrm{S}}_2$.

Figure 3

Four $E_g$-like vibrational modes at 153.6, 163.4, 218.2, and $238.1\mathrm{c}{\mathrm{m}}^{-1}$ and two $A_g$-like vibrational modes at 136.8 and $144.5\mathrm{c}{\mathrm{m}}^{-1}$ for bulk $\mathrm{Re}{\mathrm{S}}_2$, from LDA theoretical calculations and analysis of the vibrational eigenvectors. The lengths of the arrows are proportional to the modular of the phonon eigenvectors, with length weights less than $15\%$ ignored.