Terahertz magnetoconductivity of excitons and electrons in quantum cascade structures

We examined the quasiparticles formed by the photoexcitation of $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ terahertz quantum cascade structures using terahertz time-domain spectroscopy. At low temperature and excitation density the measured conductivity was excitonic, with a $1s\text{−}2p$ transition energy indicative of three-dimensional excitons correlated across the quantum well barriers. Free electrons increasingly dominated the conductive response at higher lattice temperatures and excitation densities. Under an external magnetic field transitions from the $1s$ level into $2p$ states with different magnetic quantum number were observed, while at high excitation densities the electron cyclotron resonance became more prominent.

Figure 1

(Color online) Time-resolved photoexcited conductivity $\mid \sigma \mid$ of the $2.0\mathrm{THz}$ quantum cascade structure vs pump-probe delay time, averaged over the bandwidth of the terahertz pulse and at zero magnetic field. Data are shown obtained on photoexciting the cascade structure at $1.8\mathrm{K}$ (top points), the substrate at $1.8\mathrm{K}$ (middle), and the substrate at $300\mathrm{K}$ (bottom). The experimental geometry is shown in the inset, as described in the text.

Figure 2

(Color online) Spectral dependence of the photoexcited conductivity $\sigma \left(\omega \right)$ at various pump fluences at $T=1.8\mathrm{K}$. Points and shaded areas show (a) $\mathrm{Re}\left[\sigma \right]$ and (b) $\mathrm{Im}\left[\sigma \right]$ at pump fluences (from bottom to top) of 0.14, 0.50, 2.5, 3.7, and $6.2\times {10}^{11}{\mathrm{cm}}^{-2}$ photons per pulse. Solid lines are fits using the conductivity model described in the text. (c) $\mathrm{Re}\left[\sigma \right]$ as a function of photon frequency and pump fluence (black equals high conductivity). (d) Extracted exciton density $N_x$ (squares) and electron density $N_e$ (circles) from fits to $\sigma \left(\omega \right)$ at various pump fluences, at $T=1.8\mathrm{K}$ (filled markers) and $T=20\mathrm{K}$ (unfilled markers).

Figure 3

(Color online) Magnetic field $B$ dependence of the photoexcited conductivity $\sigma \left(\omega \right)$ at $1.8\mathrm{K}$ and sample angles of (a)–(c) 30° and (d) 45°. (a) and (b) plot the real and imaginary parts of the measured $\sigma \left(\omega \right)$ at $B=0$, 1.75, 2.75, and $3.75\mathrm{T}$ (from bottom to top). (c) At an electron density $N_e=7\times {10}^{15}{\mathrm{cm}}^{-3}$ the real part of $\sigma (\omega ,B)$ peaks around the dotted lines (guides to the eye), described in the text. (d) At a higher electron density of $N_e=1.2\times {10}^{16}{\mathrm{cm}}^{-3}$ the electron cyclotron resonance is more prominent, indicated by the dotted line.