  We probe theoretically the emergence of strong coupling in a system
consisting of a topological insulator (TI) and a III-V heterostructure using a
numerical approach based on the scattering matrix formalism. Specifically, we
investigate the interactions between terahertz excitations in a structure
composed of Bi$_{2}$Se$_{3}$ and GaAs materials. We find that the interaction
between the Bi$_{2}$Se$_{3}$ layer and AlGaAs/GaAs quantum wells with
intersubband transitions (ISBTs) in the terahertz frequency regime creates new
hybrid modes, namely Dirac plasmon-phonon-ISBT polaritons. The formation of
these hybrid modes results in anti-crossings (spectral mode splitting) whose
magnitude is an indication of the strength of the coupling. By varying the
structural parameters of the constituent materials, our numerical calculations
reveal that the magnitude of splitting depends strongly on the doping level and
the scattering rate in the AlGaAs/GaAs quantum wells, as well as on the
thickness of the GaAs spacer layer that separates the quantum-well structure
from the TI layer. Our results reveal the material and device parameters
required to obtain experimentally-observable signatures of strong coupling. Our
model includes the contribution of an extra two-dimensional hole gas (2DHG)
that is predicted to arise at the Bi$_{2}$Se$_{3}$/GaAs interface, based on
density functional theory (DFT) calculations that explicitly account for
details of the atomic terminations at the interface. The presence of this
massive 2DHG at the TI/III-V interface shifts the dispersion of the Dirac
plasmon-ISBT polaritons to higher frequencies. The damping rate at this
interface, in contrast, compensates the effect of the 2DHG. Finally, we observe
that the phonon resonances in the TI layer are crucial to the coupling between
the THz excitations in the TI and III-V materials.
