Anisotropic exciton states and excitonic absorption spectra in a freestanding monolayer black phosphorus

Abstract

The anisotropic exciton states and excitonic absorption spectra in a freestanding monolayer black phosphorus (BP) are theoretically investigated by a variationally optimized diagonalization method based on a two-dimensional (2D) nonorthogonal Laguerre basis. The exciton Hamiltonian works in the anisotropic form of the kinetic term, which has an advantage of a fully analytical expression for the matrix elements of the Hamiltonian. The energy of 1 s state is in good agreement with the reported result based on the Numerov approach. The exciton states are elongated along the x direction, while their radial nodes occur in the y direction, which leads to anomalous anisotropy in some excited states. The excitonic absorption spectra of monolayer BP possess highly anisotropic features and more peaks. The large anisotropy of the effective masses leads to the mixture of exciton states with different quantum numbers n and l , which results in highly nonhydrogenic and anisotropic features. These unusual excitonic and optical properties demonstrate the potential applications of monolayer BP in optoelectronics. Compared with my proposed diagonalization method, the variational method presented in the literatures is not a good approximation. My proposed variationally optimized diagonalization method based on a 2D nonorthogonal Laguerre basis is proven to be efficient and reliable in calculating highly accurate exciton states of anisotropic 2D materials . • A fully analytical expression of the matrix elements of the Hamiltonian is obtained. • The energy of 1 s state is in good agreement with the reported result based on the Numerov approach. • The states are elongated along the x direction while radial nodes occur in the y direction. • The excitonic absorption spectra possess highly anisotropic features and more peaks. • A 2D nonorthogonal Laguerre basis is efficient and reliable in calculating exciton states of anisotropic materials.