On the effect of far impurities on the density of states of two-dimensional electron gas in a strong magnetic field

The effect of impurities situated at different distances from a two-dimensional electron gas on the density of states in a strong magnetic field is analyzed. Based on the exact result of Brezin, Gross, and Itzykson, we calculate the density of states in the whole energy range, assuming the Poisson distribution of impurities in the bulk. It is shown that in the case of small impurity concentration the density of states is qualitatively different from the model case when all impurities are located in the plane of the two-dimensional electron gas.Comment: 6 pages, 1 figure, submitted to JETP Letter

Effect of in-plane magnetic field on the photoluminescence spectrum of modulation-doped quantum wells and heterojunctions

The photoluminescence (PL) spectrum of modulation-doped GaAs/AlGaAs quantum wells (MDQW) and heterojunctions (HJ) is studied under a magnetic field ($B_{\|}$) applied parallel to the two-dimensional electron gas (2DEG) layer. The effect of $B_{\|}$ strongly depends on the electron-hole separation ($d_{eh}$), and we revealed remarkable $B_{\|}$-induced modifications of the PL spectra in both types of heterostructures. A model considering the direct optical transitions between the conduction and valence subband that are shifted in k-space under $B_{\|}$, accounts qualitatively for the observed spectral modifications. In the HJs, the PL intensity of the bulk excitons is strongly reduced relatively to that of the 2DEG with increasing $B_{\|}$. This means that the distance between the photoholes and the 2DEG decreases with increased $B_{\|}$, and that free holes are responsible for the hole-2DEG PL.Comment: 6pages, 5figure

Theory of Phonon Shakeup Effects on Photoluminescence from the Wigner Crystal in a Strong Magnetic Field

We develop a method to compute shakeup effects on photoluminescence from a strong magnetic field induced two-dimensional Wigner crystal. Only localized holes are considered. Our method treats the lattice electrons and the tunneling electron on an equal footing, and uses a quantum-mechanical calculation of the collective modes that does not depend in any way on a harmonic approximation. We find that shakeup produces a series of sidebands that may be identified with maxima in the collective mode density of states, and definitively distinguishes the crystal state from a liquid state in the absence of electron-hole interaction. In the presence of electron-hole interaction, sidebands also appear in the liquid state coming from short-range density fluctuations around the hole. However, the sidebands in the liquid state and the crystal state have different qualitative behaviors. We also find a shift in the main luminescence peak, that is associated with lattice relaxation in the vicinity of a vacancy. The relationship of the shakeup spectrum with previous mean-field calculations is discussed.Comment: 14 pages, uuencoded postscript file for entire paper, also available at (click phd14) http://rainbow.uchicago.edu/~ldz/paper/paper.htm

Harmonic Solid Theory of Photoluminescence in the High Field Two-Dimensional Wigner Crystal

Motivated by recent experiments on radiative recombination of two-dimensional electrons in acceptor doped GaAs-AlGaAs heterojunctions as well as the success of a harmonic solid model in describing tunneling between two-dimensional electron systems, we calculate within the harmonic approximation and the time dependent perturbation theory the line shape of the photoluminescence spectrum corresponding to the recombination of an electron with a hole bound to an acceptor atom. The recombination process is modeled as a sudden perturbation of the Hamiltonian for the in-plane degrees of freedom of the electron. We include in the perturbation, in addition to changes in the equilibrium positions of electrons, changes in the curvatures of the harmonically approximated potential. The computed spectra have line shapes similar to that seen in a recent experiment. The spectral width, however, is roughly a factor of 3 smaller than that seen in experiment if one assumes a perfect Wigner crystal for the initial state state of the system, whereas a simple random disorder model yields a width a factor of 3 too large. We speculate on the possible mechanisms that may lead to better quantitative agreement with experiment.Comment: 22 pages, RevTex, 8 figures. Submitted to the Physical Review

Goldstone Mode Relaxation in a Quantum Hall Ferromagnet due to Hyperfine Interaction with Nuclei

Spin relaxation in quantum Hall ferromagnet regimes is studied. As the initial non-equilibrium state, a coherent deviation of the spin system from the ${\vec B}$ direction is considered and the breakdown of this Goldstone-mode state due to hyperfine coupling to nuclei is analyzed. The relaxation occurring non-exponentially with time is studied in terms of annihilation processes in the "Goldstone condensate" formed by "zero spin excitons". The relaxation rate is calculated analytically even if the initial deviation is not small. This relaxation channel competes with the relaxation mechanisms due to spin-orbit coupling, and at strong magnetic fields it becomes dominating.Comment: 8 page

Temperature dependence of spin polarizations at higher Landau Levels

We report our results on temperature dependence of spin polarizations at $\nu=1$ in the lowest as well as in the next higher Landau level that compare well with recent experimental results. At $\nu=3$, except having a much smaller magnitude the behavior of spin polarization is not much influenced by higher Landau levels. In sharp contrast, for filling factor $\nu=\frac83$ we predict that unlike the case of $\nu=\frac23$ the system remains fully spin polarized even at vanishingly small Zeeman energies.Comment: 4 pages, REVTEX, and 3 .ps files, To be published in Physical Review Letter

Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials

We study a non-relativistic charged particle on the Euclidean plane R^2 subject to a perpendicular constant magnetic field and an R^2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the Hilbert space L^2(R^2) is restricted to the eigenspace of a single but arbitrary Landau level. For a wide class of Gaussian random potentials we rigorously prove that the associated restricted integrated density of states is absolutely continuous with respect to the Lebesgue measure. We construct explicit upper bounds on the resulting derivative, the restricted density of states. As a consequence, any given energy is seen to be almost surely not an eigenvalue of the restricted random Landau Hamiltonian.Comment: 16 pages, to appear in "Journal of Mathematical Physics