Magneto-optics of two-dimensional electron gases modified by strong Coulomb interactions in ZnSe quantum wells

The optical properties of two-dimensional electron gases in $\mathrm{Zn}\mathrm{Se}∕(\mathrm{Zn},\mathrm{Be})\mathrm{Se}$ and $\mathrm{Zn}\mathrm{Se}∕(\mathrm{Zn},\mathrm{Be},\mathrm{Mg})\mathrm{Se}$ modulation-doped quantum wells with electron densities up to $1.4\times {10}^{12}{\mathrm{cm}}^{-2}$ were studied by photoluminescence, photoluminescence excitation, and reflectivity in a temperature range between 1.6 and $70\mathrm{K}$ and in external magnetic fields up to $48\mathrm{T}$. In these structures, the Fermi energy of the two-dimensional electron gas falls in the range between the trion binding energy and the exciton binding energy. Optical spectra in this regime are shown to be strongly influenced by the Coulomb interaction between electrons and photoexcited holes. In high magnetic fields, when the filling factor of the two-dimensional electron gas becomes smaller than 2, a change from Landau-level-like spectra to exciton-like spectra occurs. We attempt to provide a phenomenological description of the evolution of optical spectra for quantum wells with strong Coulomb interactions.

Figure 1

(Color online) Photoluminescence (PL), photoluminescence excitation (PLE), and reflectivity (R) spectra of two $67\text{−}\mathrm{\AA }$-thick $\mathrm{Zn}\mathrm{Se}∕{\mathrm{Zn}}_{0.82}{\mathrm{Be}}_{0.08}{\mathrm{Mg}}_{0.10}\mathrm{Se}$ QWs, with different electron densities: (a) reference QW $1R$ with $n_e=3\times {10}^{10}{\mathrm{cm}}^{-2}$, (b) doped QW $1D$ with $n_e=5\times {10}^{11}{\mathrm{cm}}^{-2}$. $B=0\mathrm{T}$, and $T=1.6\mathrm{K}$. Scheme shows a sketch of samples type 1.

Figure 2

(Color online) Photoluminescence (PL), photoluminescence excitation (PLE), and reflectivity (R) spectra of two $100\text{−}\mathrm{\AA }$-thick $\mathrm{Zn}\mathrm{Se}∕{\mathrm{Zn}}_{0.94}{\mathrm{Be}}_{0.06}\mathrm{Se}$ QWs, with different electron densities: (a) reference QW $2R$ with $n_e=8\times {10}^{10}{\mathrm{cm}}^{-2}$, (b) doped QW $2D$ with $n_e=1.4\times {10}^{12}{\mathrm{cm}}^{-2}$. $B=0\mathrm{T}$, and $T=1.6\mathrm{K}$. Scheme shows a sketch of samples type 2.

Figure 3

(Color online) (a) PL spectra of the $2D$ sample with $n_e=1.4\times {10}^{12}{\mathrm{cm}}^{-2}$ at different temperatures (solid lines). Circles represent a fitting of the high energy side of the spectra by a Fermi distribution using the electron temperature as a parameter. Arrows indicate indirect transition from Fermi level (FL) and from the bottom of conduction band (CB) $\mathrm{FL}-{\epsilon }_F$ to the top of valence band (VB). (b) A scheme of these transitions in the band-to-band model. Panel (c) shows the results of the fitting vs sample bath temperature.

Figure 4

(Color online) Temperature broadening of resonances in reflectivity spectra for undoped and doped ZnSe-based QWs. Squares represent data of the exciton broadening in sample $1R$. Circles represent data for the ${\omega }_1$ resonance in $1D$. Lines are guide to the eye. The energy distribution of electrons in vicinity of the Fermi energy is shown schematically in the inset.

Figure 5

(Color online) PL spectra from a doped $67\text{−}\mathrm{\AA }$-thick $\mathrm{Zn}\mathrm{Se}∕{\mathrm{Zn}}_{0.82}{\mathrm{Be}}_{0.08}{\mathrm{Mg}}_{0.10}\mathrm{Se}$ QW sample $1D$ with $n_e=5\times {10}^{11}{\mathrm{cm}}^{-2}$ for magnetic fields varied from $0\text{to}46\mathrm{T}$ and $T=1.6\mathrm{K}$. (a) in ${\sigma }^{-}$ polarization. (b) in ${\sigma }^{+}$ polarization.

Figure 6

(Color online) (a) Energy of PL maxima of a doped $67\text{−}\mathrm{\AA }$-thick $\mathrm{Zn}\mathrm{Se}∕{\mathrm{Zn}}_{0.82}{\mathrm{Be}}_{0.08}{\mathrm{Mg}}_{0.10}\mathrm{Se}$ QW $1D$ with $n_e=5\times {10}^{11}{\mathrm{cm}}^{-2}$ vs magnetic field detected in ${\sigma }^{+}$ (open symbols) and ${\sigma }^{-}$ (closed symbols) polarizations. Exciton $\left(X\right)$ and trion $\left(T\right)$ quadratic diamagnetic shifts for $1R$ sample are shown by lines. Landau level fan chart is shown for off-diagonal transitions with in-plane electron and hole effective masses of $m_e=0.15m_0$ and of $m_h=0.46m_0$, respectively. Vertical lines indicate magnetic fields of integer filling factors. The fundamental emission edge (FEE) at $2.808\mathrm{eV}$ corresponds to the low energy side of the luminescence band at $B=0$. (b) Same for a doped $100\text{−}\mathrm{\AA }$-thick $\mathrm{Zn}\mathrm{Se}∕{\mathrm{Zn}}_{0.94}{\mathrm{Be}}_{0.06}\mathrm{Se}$ QW $2D$ with $n_e=1.4\times {10}^{12}{\mathrm{cm}}^{-2}$ and the corresponding reference sample $2R$. Squares represent the energy of the transitions of electrons at the Fermi level (FL). The fundamental emission edge (FEE) is located at $E_{\mathrm{FEE}}=2.797\mathrm{eV}$. It is equal to the low energy side of the luminescence band $\mathrm{FL}-{\epsilon }_F$ at $B=0$ (see also Fig. 3). $T=1.6\mathrm{K}$.

Figure 7

(Color online) PL spectra from a doped $100\text{−}\mathrm{\AA }$-thick $\mathrm{Zn}\mathrm{Se}∕{\mathrm{Zn}}_{0.94}{\mathrm{Be}}_{0.06}\mathrm{Se}$ QW $2D$ with $n_e=1.4\times {10}^{12}{\mathrm{cm}}^{-2}$ for magnetic fields varied from $0\text{to}46\mathrm{T}$ and $T=1.6\mathrm{K}$. (a) in ${\sigma }^{-}$ polarization. (b) in ${\sigma }^{+}$ polarization.

Figure 8

(Color online) Summary of nonmonotonic behavior of the magneto-optical properties of a doped $67\text{−}\mathrm{\AA }$-thick $\mathrm{Zn}\mathrm{Se}∕{\mathrm{Zn}}_{0.82}{\mathrm{Be}}_{0.08}{\mathrm{Mg}}_{0.10}\mathrm{Se}$ QW $1D$ with $n_e=5\times {10}^{11}{\mathrm{cm}}^{-2}$: (a) polarization degree and linewidth of PL band; (b) PL intensity for two circular polarizations; (c) integrated emission intensity over both polarizations and energy shift of PL maxima detected in ${\sigma }^{-}$ polarization. Dotted lines indicate locations of integer filling factors.

Figure 9

(Color online) Summary of nonmonotonic behavior of the magneto-optical properties of a doped $100\text{−}\mathrm{\AA }$-thick $\mathrm{Zn}\mathrm{Se}∕{\mathrm{Zn}}_{0.94}{\mathrm{Be}}_{0.06}\mathrm{Se}$ QW $2D$ with $n_e=1.4\times {10}^{12}{\mathrm{cm}}^{-2}$: (a) Polarization degree and linewidth of luminescence band; (b) PL intensity for two circular polarization; (c) integrated emission intensity over both polarizations, and energy shift of PL maxima detected in polarization. Dotted lines indicate locations of integer filling factors.

Figure 10

(Color online) Reflectivity spectra of a doped $67\text{−}\mathrm{\AA }$-thick $\mathrm{Zn}\mathrm{Se}∕{\mathrm{Zn}}_{0.82}{\mathrm{Be}}_{0.08}{\mathrm{Mg}}_{0.10}\mathrm{Se}$ QW $1D$ with $n_e=5\times {10}^{11}{\mathrm{cm}}^{-2}$ in a magnetic field range from $0\text{to}45\mathrm{T}$ at $T=1.6\mathrm{K}$. (a) ${\sigma }^{-}$ polarization. (b) ${\sigma }^{+}$ polarization.

Figure 11

(Color online) Energies of reflectivity lines vs magnetic field detected in ${\sigma }^{+}$ (open symbols) and ${\sigma }^{-}$ (closed symbols) polarizations for a doped $67\text{−}\mathrm{\AA }$-thick $\mathrm{Zn}\mathrm{Se}∕{\mathrm{Zn}}_{0.82}{\mathrm{Be}}_{0.08}{\mathrm{Mg}}_{0.10}\mathrm{Se}$ QW $1D$ with $n_e=5\times {10}^{11}{\mathrm{cm}}^{-2}$. Intensities of resonances are displayed by the size of the symbols. Solid lines represent the Landau level fan chart for diagonal transitions with in-plane electron and hole effective masses of $m_e=0.15m_0$ and of $m_h=0.46m_0$, respectively. Vertical lines indicate locations of integer filling factors. The energy of the renormalized band gap at $2.8065\mathrm{eV}$ obtained from the extrapolation to zero field corresponds well to the energy position $\hslash {\omega }_1-(1+m_e∕m_h){\epsilon }_F=2.8053\mathrm{eV}$. Dashed curves represent the quadratic diamagnetic shift of the trion and exciton as well as the energy of the combined TrCR and ExCR processes.

Figure 12

Energetic hierarchy summarized from experimental data, which are obtained for QWs containing a 2DEG of moderate density.