Isotropic power-law decay indices of LDOS oscillations induced by line defects in monolayer black phosphorus

Due to its anisotropic crystal structure, the electronic, optical, and thermal properties of two-dimensional black phosphorus (BP) exhibit significant anisotropy. In this study, we investigate the oscillations of the local density of states (LDOS) near a line defect in monolayer BP. Utilizing the two-band effective $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonian, we numerically calculate the LDOS using the transfer matrix method and analytically derive the power-law decay indices of the LDOS oscillation patterns based on the stationary phase approximation. We find that the power-law decay indices of the LDOS oscillation patterns are always $\ensuremath{-}1/2$ irrespective of the orientation of the defects, indicating a remarkable isotropic behavior. While, the magnitude and period of the LDOS patterns are highly sensitive to the orientation of the line defect, which serves as a manifestation of the anisotropy inherent in BP. These results highlight a unique aspect of BP and are also applicable to commensurate multilayer BP, as they share a similar Hamiltonian to that of the monolayer.