Interlayer vibrational modes in few-quintuple-layerBi2Te3andBi2Se3two-dimensional crystals: Raman spectroscopy and first-principles studies

Layered materials, such as graphite/graphene, boron nitride, transition metal dichalcogenides, represent materials in which reduced size, dimensionality, and symmetry play critical roles in their physical properties. Here, we report on a comprehensive investigation of the phonon properties in the topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ and ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ two-dimensional (2D) crystals, with the combination of Raman spectroscopy, first-principles calculations, and group theory analysis. Low frequency $(l30\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1})$ interlayer vibrational modes are revealed in few-quintuple-layer (QL) $\mathrm{B}{\mathrm{i}}_{2}\mathrm{T}{\mathrm{e}}_{3}\text{/}\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$ 2D crystals, which are absent in the bulk crystal as a result of different symmetries. The experimentally observed interlayer shear and breathing mode frequencies both show blueshifts, with decreasing thickness in few-QL ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ (down to 2QL) and ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ (down to 1QL), in agreement with first-principles calculations and a linear chain model, from which the interlayer coupling force constants can be estimated. Besides, an intense ultralow $(l12\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1})$ frequency peak is observed in 2--4QL ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, which is tentatively attributed to a substrate-induced interface mode supported by a linear chain model analysis. The high frequency Raman peaks exhibit frequency shifts and broadening from 3D to 2D as a result of the phonon confinement effect. Our studies shed light on a general understanding of the influence of dimensionality and crystal symmetry on the phonon properties in layered materials.