Terahertz response of confined electron-hole pair: crossover between strong and weak confinement

Abstract

We analyze theoretically THz response of an electron-hole pair confined in a semiconductor nanoparticle. We show that the interplay of particle confinement and electron-hole Coulomb interaction leads to significant renormalizations and energy shifts in THz linear conductivity of the nanocrystal. We develop and evaluate models in the strong and the weak confinement regime in order to correctly address the effect of Coulomb interaction. In the weak confinement regime, we find solutions of the problem in a form similar to the Wannier wavefunction whose spatial extent is reduced as a consequence of the confinement. The resulting states are scalable down to the strong confinement regime, enabling a theoretical description of the exciton response for arbitrarily sized nanoparticles.

Figures (3)

• Figure 1: Spectra (real part) of the normalized linear THz conductivity of a single e-h pair in a spherical nanoparticle in the ground state, employing different approximations: (a), (d) bare non-interacting electron-hole pairs; (b), (e) strong confinement model; and (c), (f) weak confinement model. First column displays dependency of the spectra on nanocrystal radius $A$ with $m_e=0.35M$ ($a_X=15$ nm), second column shows dependency of the spectra on electron effective mass, keeping $m_e+m_h=0.2m_0$ and setting crystal radius $A=30$ nm.
• Figure 2: The real part of calculated spectra of non-interacting electron-hole pairs (dashed lines) and result of strong-confinement model (solid lines) for various direct-gap nanoparticles (a) and indirect-gap nanoparticles (b). (c) Ratio of peak values of two resonances observed in Fig. \ref{['fig:spc']}(b) (solid lines) and the same ratio multiplied by $m_h/m_e$ (dashed lines). The exciton mass is $M=0.2m_0$ and the electron mass $m_e$ is a parameter.
• Figure 3: (a), (b), (c) comparison of observables evaluated using the strong (blue lines), weak (red line), dead layer (orange) and free exciton model (black line). Dotted and solid blue lines denote the model without and with Coulomb interaction included, using the minimal basis. Material parameters are those of bulk GaAs. The displayed observables are energy of the considered dipole transition (a), its dipole moment (b) and the oscillator strength (c). (d) correlation $|E_C|$ and binding energy $|u_0|$ compared to thermal energy $k_B T$. The dotted lines represent regimes in which the applicability of the given model can be questioned in favour of the other. In panel (d), both axes are in logarithmic scale.