Electronic properties of gated triangular graphene quantum dots: Magnetism, correlations, and geometrical effects

We present a theory of electronic properties of gated triangular graphene quantum dots with zigzag edges as a function of size and carrier density. We focus on electronic correlations, spin and geometrical effects using a combination of atomistic tight-binding, Hartree-Fock and configuration interaction methods (TB+HF+CI) including long range Coulomb interactions. The single particle energy spectrum of triangular dots with zigzag edges exhibits a degenerate shell at the Fermi level with a degeneracy N_{edge} proportional to the edge size. We determine the effect of the electron-electron interactions on the ground state, the total spin and the excitation spectrum as a function of a shell filling and the degeneracy of the shell using TB+HF+CI for N_{edge} < 12 and approximate CI method for N_{edge}\geq 12. For a half-filled neutral shell we find spin polarized ground state for structures up to N=500 atoms in agreement with previous {\it ab initio} and mean-field calculations, and in agreement with Lieb's theorem for a Hubbard model on a bipartite lattice. Adding a single electron leads to the complete spin depolarization for N_{edge}\leq 9. For larger structures, the spin depolarization is shown to occur at different filling factors. Away from half-fillings excess electrons(holes) are shown to form Wigner-like spin polarized triangular molecules corresponding to large gaps in the excitation spectrum. The validity of conclusions is assessed by a comparison of results obtained from different levels of approximations. While for the charge neutral system all methods give qualitatively similar results, away from the charge neutrality an inclusion of all Coulomb scattering terms is necessary to produce results presented here.Comment: 13 pages, 13 figure

Magnetoexcitons And Correlated Electrons In Quantum Dots In A Magnetic Field

Magnetoexcitons interacting with strongly correlated electronic states in quantum dots in a strong magnetic field are studied. Exact calculations relate the absorption and emission of few-electron artificial atoms to magnetic-field-induced phase transitions between "magic" states. For large compact droplets, the coupling of magnetoexcitons to low-energy excitations (edge magnetorotons) leads to a strong enhancement of the oscillator strength at the Fermi level (Fermi edge singularity) both in absorption and in emission on acceptors. The condensation of edge magnetorotons signals the reconstruction of the droplet and is accompanied by different structures in the absorption spectrum.54161139711409Kastner, M., (1993) Phys. Today, 24 (1), p. 24Chakraborty, T., (1992) Comments Condens. Matter Phys., 16, p. 35Petroff, P.M., Denbaars, S.P., (1994) Superlatt. Microstruct., 15, p. 15Drexler, H., Leonard, D., Hansen, W., Kotthaus, J.P., Petroff, P.M., (1994) Phys. Rev. Lett., 73, p. 2252Wojs, A., Hawrylak, P., (1995) Phys. Rev. B, 51, p. 10880Ashoori, R.C., Stormer, H.L., Weiner, J.S., Pfeiffer, L.N., Baldwin, K.W., West, K.W., (1993) Phys. Rev. Lett., 71, p. 613Su, B., Goldman, V.J., Cunningham, J.E., (1992) Science, 255, p. 313Hawrylak, P., (1993) Phys. Rev. Lett., 71, p. 3347De Chamon, C., Wen, X.-G., (1994) Phys. Rev. B, 49, p. 8227Palacios, J.J., (1993) Europhys. Lett., 23, p. 495(1995) Phys. Rev. B, 51, p. 2363MacDonald, A.H., Eric Yang, S.R., Johnson, M.D., (1993) Aust. J. Phys., 46, p. 345Klein, O., (1995) Phys. Rev. Lett., 74, p. 785Kane, C.L., Fisher, M.P.A., Polchinski, J., (1994) Phys. Rev. Lett., 72, p. 4129Maksym, P.A., (1993) Physica B, 184, p. 385Maksym, P.A., Chakraborty, T., (1990) Phys. Rev. Lett., 65, p. 108(1992) Phys. Rev. B, 45, p. 1947Palacios, J.J., Martin-Moreno, L., Chiappe, G., Louis, E., Tejedor, C., (1994) Phys. Rev. B, 50, p. 5760(1995) Phys. Rev. Lett., 74, p. 5120Apalkov, V.M., Rashba, E.I., (1995) Solid State Commun., 93, p. 193Chen, X.M., Quinn, J.J., (1994) Phys. Rev. B, 50, p. 2354MacDonald, A.H., (1992) Phys. Rev. Lett., 68, p. 1939Buchmann, H., (1990) Phys. Rev. Lett., 65, p. 1056Turb-erfield, A.J., (1990) Phys. Rev. Lett., 65, p. 637Goldberg, B.B., (1990) Phys. Rev. Lett., 65, p. 641Hawrylak, P., (1991) Phys. Rev. B, 44, p. 3821Uneyama, T., Sham, L.J., (1990) Phys. Rev. Lett., 65, p. 1048Hawrylak, P., Pfannkuche, D., (1993) Phys. Rev. Lett., 70, p. 485Pfannkuche, D., (1994) Solid State Electron., 37, p. 1221Apalkov, V.M., Rashba, E.I., (1991) Pis'ma Zh. Éksp. Teor. Fiz., 53, p. 420(1991) JETP Lett., 53, p. 442Hawrylak, P., (1992) Phys. Rev. B, 45, p. 4237Hawrylak, P., Pulsford, N., Ploog, K., (1993) Phys. Rev. B, 46, p. 15593(1992) Solid State Commun., 81, p. 525Petrou, A., Smith, M.C., Perry, C.H., Worlock, J.M., Aggarwal, R.L., (1984) Solid State Commun., 52, p. 93Kukushkin, I.V., Klitzing, K.V., Ploog, K., Timofeev, V.B., (1990) Phys. Rev. B, 40, p. 7788Plaut, A.S., Lage, H., Grambow, P., Heitmann, D., Von Klitzing, K., Ploog, K., (1991) Phys. Rev. Lett., 67, p. 1642Buhmann, H., Joss, W., Von Klitzing, K., Kukushkin, I.V., Martinez, G., Plaut, A.S., Ploog, K., Timofeev, V.B., (1990) Phys. Rev. Lett., 65, p. 1056Buhmann, H., Joss, W., Von Klitzing, K., Kukushkin, I.V., Plaut, A.S., Martinez, G., Ploog, K., Timofeev, V.B., (1991) Phys. Rev. Lett., 66, p. 926Kukushkin, I.V., Pulsford, N.J., Von Klitzing, K., Ploog, K., Haug, R.J., Koch, S., Timofeev, V.B., (1992) Phys. Rev. B, 45, p. 4532Stone, M.D., Wyld, H.W., Schult, R.L., (1992) Phys. Rev. B, 45, p. 14156Stone, M.D., (1990) Int. J. Mod. Phys., 5, p. 503Kallin, C., Halperin, B.I., (1985) Phys. Rev. B, 31, p. 3635Wu, J.-W., Hawrylak, P., Quinn, J.J., (1985) Phys. Rev. B, 31, p. 6592Hawrylak, P., (1995) Phys. Rev. B, 51, p. 1770

Fermions out of Dipolar Bosons in the lowest Landau level

In the limit of very fast rotation atomic Bose-Einstein condensates may reside entirely in the lowest two-dimensional Landau level (LLL). For small enough filling factor of the LLL, one may have formation of fractional quantum Hall states. We investigate the case of bosons with dipolar interactions as may be realized with Chromium-52 atoms. We show that at filling factor equal to unity the ground state is a Moore-Read (a.k.a Pfaffian) paired state as is the case of bosons with purely s-wave scattering interactions. This Pfaffian state is destabilized when the interaction in the s-wave channel is small enough and the ground state is a stripe phase with unidimensional density modulation. For filling factor 1/3, we show that there is formation of a Fermi sea of ``composite fermions''. These composites are made of one boson bound with three vortices. This phase has a wide range of stability and the effective mass of the fermions depends essentially only of the scattering amplitude in momentum channels larger or equal to 2. The formation of such a Fermi sea opens up a new possible route to detection of the quantum Hall correlations.Comment: 12 pages, 5 figures, published versio

Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands

We investigate an interaction-driven transition between crystalline and liquid states of strongly correlated spinless fermions within topological flat bands at low density (with filling factors nu = 1/5, 1/7, 1/9). Using exact diagonalization for finite-size systems with periodic boundary conditions, we distinguish different phases, whose stability depends on the interaction range, controlled by the screening parameter of the Coulomb interaction. The crystalline phases are identified by a crystallization strength, calculated from the Fourier transforms of pair correlation density, while the fractional Chern insulator (FCI) phases are characterized using momentum counting rules, entanglement spectrum, and overlaps with corresponding fractional quantum Hall states. The type of the phase depends on a particular single-particle model and its topological properties. We show that for nu = 1/7 and 1/5 it is possible to tune between theWigner crystal and fractional Chern insulator phase in the kagome lattice model with the band carrying the Chern number C = 1. In contrast, in the C = 2 models, the Wigner crystallization was absent at nu = 1/5, and appeared at nu = 1/9, suggesting that C = 2 FCIs are more stable agains

Energy Spectra for Fractional Quantum Hall States

Fractional quantum Hall states (FQHS) with the filling factor nu = p/q of q < 21 are examined and their energies are calculated. The classical Coulomb energy is evaluated among many electrons; that energy is linearly dependent on 1/nu. The residual binding energies are also evaluated. The electron pair in nearest Landau-orbitals is more affected via Coulomb transition than an electron pair in non-nearest orbitals. Each nearest electron pair can transfer to some empty orbital pair, but it cannot transfer to the other empty orbital pair because of conservation of momentum. Counting the numbers of the allowed and forbidden transitions, the binding energies are evaluated for filling factors of 126 fraction numbers. Gathering the classical Coulomb energy and the pair transition energy, we obtain the spectrum of energy versus nu. This energy spectrum elucidates the precise confinement of Hall resistance at specific fractional filling factors.Comment: 5 pages, 3 figure

Ultrafast non-linear optical signal from a single quantum dot: exciton and biexciton effects

We present results on both the intensity and phase-dynamics of the transient non-linear optical response of a single quantum dot (SQD). The time evolution of the Four Wave Mixing (FWM) signal on a subpicosecond time scale is dominated by biexciton effects. In particular, for the cross-polarized excitation case a biexciton bound state is found. In this latter case, mean-field results are shown to give a poor description of the non-linear optical signal at small times. By properly treating exciton-exciton effects in a SQD, coherent oscillations in the FWM signal are clearly demonstrated. These oscillations, with a period corresponding to the inverse of the biexciton binding energy, are correlated with the phase dynamics of the system's polarization giving clear signatures of non-Markovian effects in the ultrafast regime.Comment: 10 pages, 3 figure

Charged exctions in the fractional quantum Hall regime

We study the photoluminescence spectrum of a low density ($\nu <1$) two-dimensional electron gas at high magnetic fields and low temperatures. We find that the spectrum in the fractional quantum Hall regime can be understood in terms of singlet and triplet charged-excitons. We show that these spectral lines are sensitive probes for the electrons compressibility. We identify the dark triplet charged-exciton and show that it is visible at the spectrum at $T<2$ K. We find that its binding energy scales like $e^{2}/l$, where $l$ is the magnetic length, and it crosses the singlet slightly above 15 T.Comment: 10 pages, 5 figure

Resonant Enhancement of Inelastic Light Scattering in the Fractional Quantum Hall Regime at ν=1/3\nu=1/3

Strong resonant enhancements of inelastic light scattering from the long wavelength inter-Landau level magnetoplasmon and the intra-Landau level spin wave excitations are seen for the fractional quantum Hall state at $\nu = 1/3$. The energies of the sharp peaks (FWHM $\lesssim 0.2meV$) in the profiles of resonant enhancement of inelastic light scattering intensities coincide with the energies of photoluminescence bands assigned to negatively charged exciton recombination. To interpret the observed enhancement profiles, we propose three-step light scattering mechanisms in which the intermediate resonant transitions are to states with charged excitonic excitations.Comment: 5 pages, 5 figure