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

Theory of Exciton Recombination from the Magnetically Induced Wigner Crystal

We study the theory of itinerant-hole photoluminescence of two-dimensional electron systems in the regime of the magnetically induced Wigner crystal. We show that the exciton recombination transition develops structure related to the presence of the Wigner crystal. The form of this structure depends strongly on the separation $d$ between the photo-excited hole and the plane of the two-dimensional electron gas. When $d$ is small compared to the magnetic length, additional peaks appear in the spectrum due to the recombination of exciton states with wavevectors equal to the reciprocal lattice vectors of the crystal. For $d$ larger than the magnetic length, the exciton becomes strongly confined to an interstitial site of the lattice, and the structure in the spectrum reflects the short-range correlations of the Wigner crystal. We derive expressions for the energies and the radiative lifetimes of the states contributing to photoluminescence, and discuss how the results of our analysis compare with experimental observations.Comment: 10 pages, no figures, uses Revtex and multicol.st

Exchange Instabilities in Semiconductor Double Quantum Well Systems

We consider various exchange-driven electronic instabilities in semiconductor double-layer systems in the absence of any external magnetic field. We establish that there is no exchange-driven bilayer to monolayer charge transfer instability in the double-layer systems. We show that, within the unrestricted Hartree-Fock approximation, the low density stable phase (even in the absence of any interlayer tunneling) is a quantum ``pseudospin rotated'' spontaneous interlayer phase coherent spin-polarized symmetric state rather than the classical Ising-like charge-transfer phase. The U(1) symmetry of the double quantum well system is broken spontaneously at this low density quantum phase transition, and the layer density develops quantum fluctuations even in the absence of any interlayer tunneling. The phase diagram for the double quantum well system is calculated in the carrier density--layer separation space, and the possibility of experimentally observing various quantum phases is discussed. The situation in the presence of an external electric field is investigated in some detail using the spin-polarized-local-density-approximation-based self-consistent technique and good agreement with existing experimental results is obtained.Comment: 24 pages, figures included. Also available at http://www-cmg.physics.umd.edu/~lzheng/preprint/ct.uu/ . Revised final version to appear in PR

Spontaneous coherence and the quantum Hall Effect in triple-layer electron systems

We investigate spontaneous interlayer phase coherence and the occurrence of the quantum Hall effect in triple-layer electron systems. Our work is based on a simple tight-binding model that greatly facilitates calculations and whose accuracy is verified by comparison with recent experiments. By calculating the ground state in an unrestricted Hartree-Fock approximation and the collective-mode spectrum in a time-dependent Hartree-Fock approximation, we construct a phase diagram delimiting regions in the parameter space of the model where the integer quantum Hall effect occurs in the absence of interlayer tunneling.Comment: To appear in Phys. Rev. B, 20 pages, 5 PostScript figures uuencoded with TeX fil

Spontaneous Interlayer Coherence in Double-Layer Quantum Hall Systems: Symmetry Breaking Interactions, In-Plane Fields and Phase Solitons

At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous inter-layer phase coherence. The system can be mapped to an equivalent system of pseudospin $1/2$ particles with pseudospin-dependent interactions and easy-plane magnetic order. In this paper we discuss how the presence of a weak interlayer tunneling term alters the properties of double-layer systems when the broken symmetry is present. We use the energy functional and equations of motion derived earlier to evaluate the zero-temperature response functions of the double-layer system and use our results to discuss analogies between this system and Josephson-coupled superconducting films. We also present a qualitative picture of the low-energy charged excitations of this system. We show that parallel fields induce a highly collective phase transition to an incommensurate state with broken translational symmetry.Comment: 26 pages, RevTex, 8 postscript figures (submitted to Phys. Rev. B