4 research outputs found
Electron-electron interaction and charging effects in graphene quantum dots
We analyze charging effects in graphene quantum dots. Using a simple model,
we show that, when the Fermi level is far from the neutrality point, charging
effects lead to a shift in the electrostatic potential and the dot shows
standard Coulomb blockade features. Near the neutrality point, surface states
are partially occupied and the Coulomb interaction leads to a strongly
correlated ground state which can be approximated by either a Wigner crystal or
a Laughlin like wave function. The existence of strong correlations modify the
transport properties which show non equilibrium effects, similar to those
predicted for tunneling into other strongly correlated systems.Comment: Extended version accepted for publication at Phys. Rev.
Dynamical polarization of graphene at finite doping
The polarization of graphene is calculated exactly within the random phase
approximation for arbitrary frequency, wave vector, and doping. At finite
doping, the static susceptibility saturates to a constant value for low
momenta. At it has a discontinuity only in the second derivative.
In the presence of a charged impurity this results in Friedel oscillations
which decay with the same power law as the Thomas Fermi contribution, the
latter being always dominant. The spin density oscillations in the presence of
a magnetic impurity are also calculated. The dynamical polarization for low
and arbitrary is employed to calculate the dispersion relation and
the decay rate of plasmons and acoustic phonons as a function of doping. The
low screening of graphene, combined with the absence of a gap, leads to a
significant stiffening of the longitudinal acoustic lattice vibrations.Comment: 17 pages, 6 figures, 1 tabl
Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
Investigations of emergent symmetry breaking phenomena occurring in small
finite-size systems are reviewed, with a focus on the strongly correlated
regime of electrons in two-dimensional semicoductor quantum dots and trapped
ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize
universal aspects and similarities of symmetry breaking found in these systems,
as well as in more traditional fields like nuclear physics and quantum
chemistry, which are characterized by very different interparticle forces. A
unified description of strongly correlated phenomena in finite systems of
repelling particles (whether fermions or bosons) is presented through the
development of a two-step method of symmetry breaking at the unrestricted
Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock
projection techniques. Quantitative and qualitative aspects of the two-step
method are treated and validated by exact diagonalization calculations.
Strongly-correlated phenomena emerging from symmetry breaking include: (I)
Chemical bonding, dissociation, and entanglement (at zero and finite magnetic
fields) in quantum dot molecules and in pinned electron molecular dimers formed
within a single anisotropic quantum dot. (II) Electron crystallization, with
particle localization on the vertices of concentric polygonal rings, and
formation of rotating electron molecules (REMs) in circular quantum dots. (III)
At high magnetic fields, the REMs are described by parameter-free analytic wave
functions, which are an alternative to the Laughlin and composite-fermion
approaches. (IV) Crystalline phases of strongly repelling bosons. In rotating
traps and in analogy with the REMs, such repelling bosons form rotating boson
molecules (RBMs).Comment: Review article published in Reports on Progress in Physics. REVTEX4.
95 pages with 37 color figures. To download a copy with high-quality figures,
go to publication #82 in http://www.prism.gatech.edu/~ph274cy