Size-dependent optical properties of shallow quantum dot excitons close to a dielectric-hyperbolic material interface

The resonance frequency shift and the radiative decay rate of single quantum dot excitions in close proximity to a dielectric-hyperbolic material interface are theoretically investigated. The previous nonlocal susceptibility model for a quantum-confined exciton in inhomogeneous surroundings has been substantially upgraded in a way to incorporate exciton's envelope functions with a non-zero orbital angular momentum and a dyadic Green function tensor for uniaxially anisotropic multilayer structures. Different eigenstates of spatially localized excitons are considered with a distance to the interface of half-infinite Tetradymites(Bi₂Se₃), a natural hyperbolic material in a visible-to-near infrared wavelength range. From numerically obtained self-energy corrections (SEC) of the exciton as a function of its spatial confinement, eigenfunction, and distance, where the real and imaginary parts correspond to the resonance frequency shift and the radiative decay rate of the exciton, respectively, both optical properties show a significant dependence on the spatial confinement of the exciton than expected. The SEC of very weakly confined (quasi free) two-dimensional excitons is almost immune to specific choice of the eigenfunction and to anisotropic properties of the hyperbolic material even at a close distance, while such conditions are decisive for the SEC of strongly confined excitons.