Optics of 2-D Excitons in High Magnetic Fields

Excitons in solids consist of correlated electron-hole (e-h) pairs, which form “hydrogenic” internal states in addition to continua due to their center-of-mass motion and induce a rich variety of effects in optical spectra. They have varying Bohr radii (of order 5-50 nm) and binding energies (of order 1-100 meV), depending on, e.g., band parameters, external electric and magnetic fields, and many-body effects. Because of their large spatial extent, these “quasi-atoms” have very large oscillator strengths compared to real atoms. Transitions between these atom-like levels lie in the far-infrared and mid-infrared wavelength ranges, and hence, excitons (confined magneto-excitons in particular) in an intense THz or MIR laser field provide an ideal system in which to study strong light-matter phenomena in a regime inaccessible in atomic spectroscopy. Furthermore, a fascinating array of phenomena and exotic ground states are predicted for many-exciton systems due to the Boson nature of excitons. We are exploring new exciton physics in semiconductor quantum wells, especially in the simultaneous presence of a high DC magnetic field and an intense laser field.

Figure 1: Absorption spectra for InGaAs/GaAs multiple quantum wells at different magnetic fields. Solid lines are guides to the eye, indicating 1s hydrogenic exciton levels.

Figure 1 shows an example demonstrating the richness of exciton spectra in semiconductors. Here we performed an absorption spectroscopy study of InGaAs quantum wells in magnetic fields up to 30 T. We can see a smooth transition of the density of states from 2-D like staircase functions to 0-D like delta-functions as we increase the magnetic field in the Faraday configuration. Different excitonic levels show different field dependences, and when two levels meet, they show anti-crossing and crossing behaviors depending on the nature and symmetry of the states involved. We have attributed some of the observed mixing behaviors to the valence-band complexity and others to Coulomb interactions. The latter includes a previously unreported mixing of “bright” and “dark” exciton states.

Fig. 2. PL spectra excited by a Ti:sapphire amplifier at various excitation intensities in (a) undoped and (b) n-type modulation doped In 0.19­ Ga 0.81­­ As/ Al 0.41­ Ga 0.59­­ As quantum wells at 4.2 K and at 25 T. The top and bottom traces correspond to cw absorption spectra and PL pumped by He-Ne laser, respectively. In the doped sample, PL from Fermi-edge singularity dominates over band-edge emission in our doping density of 1.4 x 10 12 cm -2 .

In Fig. 2, we show the PL spectra at 25 T as a function of excitation intensities in both undoped (Fig. 2a) and doped (Fig. 2b) samples. For comparison, both CW PL using He-Ne laser excitation and absorption are also displayed. In Fig. 2(a), we observe the PL peak from 0-0 transition (1s magneto-exciton, ~1395 meV) split and develop into four distinct peaks above 8.3 GW/cm 2 . These four peaks evolve in a complicated manner as the intensity increases (showing both red- and blue-shifts depending on peak). In contrast, the 2s state (~1465 meV) remains a single peak and monotonically red shifts with increasing excitation intensity. We note that for the doped sample (Fig. 2b), however, the optically excited carriers recombine at non-zero wavevectors above the Fermi-edge (defined by the doping density), preventing a direct comparison with CW absorption data.Figure 3 displays the field-dependent traces for the undoped sample for two excitation intensities. In the low power limit (Fig. 3a), the 1s transition shows a slight red shift up to ~7 T, followed by the conventional diamagnetic blue shift. The inset shows the peak energy trace with increasing magnetic field. This red shift has not been observed in CW PL nor in absorption spectra to our knowledge and possibly indicates that the magnetic confinement enhances the exchange interaction and competes against Pauli exclusion up to certain point, depending on the carrier density. In Fig. 3 (b), the main peak splits into two even at low field and two additional transitions are pronounced above 20 T.

Fig. 3. PL spectra of the undoped sample versus magnetic field at two different excitation intensities, (a) 0.8 GW/cm 2 and (b) 33.3 GW/cm2 . The inset in Fig. 3(a) plots the peak position versus magnetic field.

References:

Y. D. Jho, F. V. Kyrychenko, J. Kono, X. Wei, S. A. Crooker, G. D. Sanders, D. H. Reitze, C. J. Stanton, and G. S. Solomon, “Dark-Bright Magneto-Exciton Mixing Induced by Coulomb Interaction in Strained Quantum Wells,” submitted. (abstractfull text)

F. V. Kyrychenko, Y . D. Jho, J. Kono, S. A. Crooker, G. D. Sanders, D. H. Reitze, C. J. Stanton, X. Wei, C. Kadow, and A. C. Gossard, “Interband Magnetoabsorption Study of the Shift of the Fermi Energy of a 2DEG with an In-plane Magnetic Field,” Physica E 22, 624 (2004). (full text)

Collaborators:

Scott A. Crooker, NHMFL, Los Alamos

David H. Reitze, University of Florida

Christopher J. Stanton, University of Florida