Excitons de subbandas em multicamadas de fósforo negro

Abstract

With the recent advances in two-dimensional (2D) materials fabrication techniques, the variety of these materials that became available for experimental studies has increased substantially over the past few years. The possibility of manipulating the number of layers in these materials also brings new perspectives to explore the physical properties of multilayer 2D materials. This is interesting because the physical properties of some 2D materials, such as the band alignment between layers, quasi-particle effective masses, and optical band gaps, can be tuned by the number of layers. One can explore such a multilayer semiconductor system in two ways: with a stack of layers of the same material, or combining layers of different materials. In this work, we consider the first case, where the material is black phosphorus (BP).

Motivated by recent experimental observations of light absorption in few-layer BP, we develop a theoretical model to explain the origin of a series of high-intensity peaks interspersed by pairs of low-intensity peaks, in the experimental absortion spectra of BP. The model consists in describing excitonic states in a few-layer of BP through the effective mass approximation, which deals with the electron and hole in-plane coordinates, along with a unidimensional tight-binding approximation that accounts for inter-layer couplings. This yields excitonics transitions between different combinations of the sub-bands created by the coupled BP layers, which leads to a series of high and low-intensity peaks that are related to the oscillator strength of the excitonic states involved. These high and low-intensity states are referred in the literature as bright and dark excitons states, respectively. The energy and oscillator strength of the sub-bands exciton states can be controlled through a perpendicular electric field and the number of layers. The results obtained by this model are consistent with what is observed in the experiment and, in addition, they help elucidating aspects that the experiment did not consider about subband excitonic states. Among them, are the hybridization between excitonic states and the dependency of diamagnetic shift with an electric field for different states.