Strain engineering of the lattice vibration modes in monolayer black phosphorus

Abstract

Strain engineering can be served as an efficient tool for tuning physical properties of two‐dimentional (2D) materials. However, the quantifying strain and characterizing its spatially inhomogeneous distribution are always challenging. Here, we report the strain‐induced lattice vibration mode variations in monolayer black phosphorus (BP) and clarify the underlying mechanism resorting to the bond relaxation theory based on the combination of mass‐spring model and Lagrangian dynamics. We reveal that the Ag2 and B2g modes exhibit blue (red) shifts while the Ag1 mode shows a red (blue) shift through applying an armchair (zigzag) strain, which can be ascribed to the orientation‐dependent lattice vibration mode variations resulting from the different responses of force constants. Moreover, it is found that a negative Poisson's ratio along the out‐of‐plane direction emerges when the strain is applied in the zigzag direction. Our results offer intriguing insights into the underlying physics of vibration mode variations in strained BP‐like 2D layered materials.

Polarization-resolved and helicity-resolved Raman spectra of monolayer XP3 (X = Ge and In)

“…2), suggesting the dynamic stability, which agrees with the theoretical results obtained by other groups. 16,21,25 The highest frequency of the phonon for GeP 3 (InP 3 ) is 448 cm À1 (452 cm À1 ), which is comparable to black phosphorene 51,52 and can be attributed to the apparent mechanical robustness of the covalent P-P bonds.…”

Anisotropic Single-Layer Tilted α-Bi: Identification of Uniaxial Strain via Raman Spectrum

“…Similar anisotropic behavior in the vibrational spectrum was observed for BP. 54 It was reported that three Raman-active modes (A g 2 , B 2g , and A g 2 ) of BP display red shift for A g 2 mode and blue shift for B 2g and A g 2 in the armchair direction under compressive strain. Conversely, A g 2 shifts blue, and B 2g and A g 2 modes shift red in tension.…”

Intrinsic negative Poisson’s ratio of the monolayer semiconductor β- TeO2

“…However, little is known about the mechanical responses of 2D β-TeO 2 . Given that mechanical deformation also affects the lattice vibrational modes, Raman spectroscopy, as a non-destructive characterization technique, can extract valuable information about the strain state of a material, aiding the study of NPR in 2D materials [17,18].…”