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

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

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

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

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

Analytic Coulomb matrix elements in the lowest Landau level in disk geometry

Using Darling's theorem on products of generalized hypergeometric series an analytic expression is obtained for the Coulomb matrix elements in the lowest Landau level in the representation of angular momentum. The result is important in the studies of Fractional Quantum Hall effect (FQHE) in disk geometry. Matrix elements are expressed as simple finite sums of positive terms, eliminating the need to approximate these quantities with slowly-convergent series. As a by-product, an analytic representation for certain integals of products of Laguerre polynomials is obtained.Comment: Accepted to J. Math. Phys.; 3 pages revtex, no 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

Definitive observation of the dark triplet ground state of charged excitons in high magnetic fields

The ground state of negatively charged excitons (trions) in high magnetic fields is shown to be a dark triplet state, confirming long-standing theoretical predictions. Photoluminescence (PL), reflection, and PL excitation spectroscopy of CdTe quantum wells reveal that the dark triplet trion has lower energy than the singlet trion above 24 Tesla. The singlet-triplet crossover is "hidden" (i.e., the spectral lines themselves do not cross due to different Zeeman energies), but is confirmed by temperature-dependent PL above and below 24 T. The data also show two bright triplet states.Comment: 4 figure

Resonant Raman scattering off neutral quantum dots

Resonant inelastic (Raman) light scattering off neutral GaAs quantum dots which contain a mean number, N=42, of electron-hole pairs is computed. We find Raman amplitudes corresponding to strongly collective final states (charge-density excitations) of similar magnitude as the amplitudes related to weakly collective or single-particle excitations. As a function of the incident laser frequency or the magnetic field, they are rapidly varying amplitudes. It is argued that strong Raman peaks should come out in the spin-density channels, not related to valence-band mixing effects in the intermediate states.Comment: Accepted in Physical Review