437 research outputs found
Electronic shells of Dirac fermions in graphene quantum rings in a magnetic field
We present results of tight binding calculations demonstrating existence of
degenerate electronic shells of Dirac Fermions in narrow, charge neutral
graphene quantum rings. We predict removal of degeneracy with finite magnetic
field. We show, using a combination of tight binding and configuration
interaction methods, that by filling a graphene ring with additional electrons
this carbon based structure with half-filled shell acquires a finite magnetic
moment.Comment: 10 pages, 4 figure
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
Graphene-Dielectric Composite Metamaterials: Evolution from Elliptic to Hyperbolic Wavevector Dispersion and The Transverse Epsilon-Near-Zero Condition
We investigated a multilayer graphene-dielectric composite material,
comprising graphene sheets separated by subwavelength-thick dielectric spacer,
and found it to exhibit hyperbolic isofrequency wavevector dispersion at far-
and mid-infrared frequencies allowing propagation of waves that would be
otherwise evanescent in a dielectric. Electrostatic biasing was considered for
tunable and controllable transition from hyperbolic to elliptic dispersion. We
explored the validity and limitation of the effective medium approximation
(EMA) for modeling wave propagation and cutoff of the propagating spatial
spectrum due to the Brillouin zone edge. We found that EMA is capable of
predicting the transition of the isofrequency dispersion diagram under certain
conditions. The graphene-based composite material allows propagation of
backward waves under the hyperbolic dispersion regime and of forward waves
under the elliptic regime. Transition from hyperbolic to elliptic dispersion
regimes is governed by the transverse epsilon-near-zero (TENZ) condition, which
implies a flatter and wider propagating spectrum with higher attenuation, when
compared to the hyperbolic regime. We also investigate the tunable transparency
of the multilayer at that condition in contrast to other materials exhibiting
ENZ phenomena.Comment: to be published in Journal of Nanophotonic
Symmetry operators and separation of variables in the -dimensional Dirac equation with external electromagnetic field
We obtain and analyze equations determining first-order differential symmetry
operators with matrix coefficients for the Dirac equation with an external
electromagnetic potential in a -dimensional Riemann (curved) spacetime.
Nonequivalent complete sets of mutually commuting symmetry operators are
classified in a -dimensional Minkowski (flat) space. For each of the
sets we carry out a complete separation of variables in the Dirac equation and
find a corresponding electromagnetic potential permitting separation of
variables.Comment: 24 pages, version accepted for publication in Int. J. Geom. Methods
Mod. Phy
Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations
In a parallel discrete-event simulation (PDES) scheme, tasks are distributed
among processing elements (PEs), whose progress is controlled by a
synchronization scheme. For lattice systems with short-range interactions, the
progress of the conservative PDES scheme is governed by the Kardar-Parisi-Zhang
equation from the theory of non-equilibrium surface growth. Although the
simulated (virtual) times of the PEs progress at a nonzero rate, their standard
deviation (spread) diverges with the number of PEs, hindering efficient data
collection. We show that weak random interactions among the PEs can make this
spread nondivergent. The PEs then progress at a nonzero, near-uniform rate
without requiring global synchronizations
Going through Rough Times: from Non-Equilibrium Surface Growth to Algorithmic Scalability
Efficient and faithful parallel simulation of large asynchronous systems is a
challenging computational problem. It requires using the concept of local
simulated times and a synchronization scheme. We study the scalability of
massively parallel algorithms for discrete-event simulations which employ
conservative synchronization to enforce causality. We do this by looking at the
simulated time horizon as a complex evolving system, and we identify its
universal characteristics. We find that the time horizon for the conservative
parallel discrete-event simulation scheme exhibits Kardar-Parisi-Zhang-like
kinetic roughening. This implies that the algorithm is asymptotically scalable
in the sense that the average progress rate of the simulation approaches a
non-zero constant. It also implies, however, that there are diverging memory
requirements associated with such schemes.Comment: to appear in the Proceedings of the MRS, Fall 200
Localization in an Inhomogeneous Quantum Wire
We study interaction-induced localization of electrons in an inhomogeneous
quasi-one-dimensional system--a wire with two regions, one at low density and
the other high. Quantum Monte Carlo techniques are used to treat the strong
Coulomb interactions in the low density region, where localization of electrons
occurs. The nature of the transition from high to low density depends on the
density gradient--if it is steep, a barrier develops between the two regions,
causing Coulomb blockade effects. Ferromagnetic spin polarization does not
appear for any parameters studied. The picture emerging here is in good
agreement with measurements of tunneling between two wires.Comment: 4 pages; 2 new figures, substantial revisions and clarification
Magnetism and correlations in fractionally filled degenerate shells of graphene quantum dots
When an electron is confined to a triangular atomic thick layer of graphene
[1-5] with zig-zag edges, its energy spectrum collapses to a shell of
degenerate states at the Fermi level (Dirac point) [6-9]. The degeneracy is
proportional to the edge size and can be made macroscopic. This opens up the
possibility to design a strongly correlated electronic system as a function of
fractional filling of the zero-energy shell, in analogy to the fractional
quantum Hall effect in a quasi-two-dimensional electron gas[10], but without
the need for a high magnetic field. In this work we show that electronic
correlations, beyond the Hubbard model[6,7] and mean-field density functional
theory (DFT) [7,8] play a crucial role in determining the nature of the ground
state and the excitation spectrum of triangular graphene quantum dots as a
function of dot size and filling fraction of the shell of zero-energy states.
The interactions are treated by a combination of DFT, tight-binding,
Hartree-Fock and configuration interaction methods (TB-HF-CI) and include all
scattering and exchange terms within second nearest neighbors as well as
interaction with metallic gate. We show that a half filled charge neutral shell
leads to full spin polarization of the island but this magnetic moment is
completely destroyed by the addition of a single electron, in analogy to the
effect of skyrmions on the quantum Hall ferromagnet [11-14] and spin
depolarization in electrostatically defined semiconductor quantum dots[15-18].
The depolarization of the ground state is predicted to result in blocking of
current through a graphene quantum dot due to spin blockade (SB) [18].Comment: v2: minor corrections, new forma
Spin-spin correlations of magnetic impurities in graphene
We study the interaction between two magnetic adatom impurities in graphene
using the Anderson model. The two-impurity Anderson Hamiltonian is solved
numerically by using the quantum Monte Carlo technique. We find that the
inter-impurity spin susceptibility is strongly enhanced at low temperatures,
significantly diverging from the well-known Ruderman-Kittel-Kasuya-Yoshida
(RKKY) result which decays as .Comment: 4 pages, 4 figure
Incipient Wigner Localization in Circular Quantum Dots
We study the development of electron-electron correlations in circular
quantum dots as the density is decreased. We consider a wide range of both
electron number, N<=20, and electron gas parameter, r_s<18, using the diffusion
quantum Monte Carlo technique. Features associated with correlation appear to
develop very differently in quantum dots than in bulk. The main reason is that
translational symmetry is necessarily broken in a dot, leading to density
modulation and inhomogeneity. Electron-electron interactions act to enhance
this modulation ultimately leading to localization. This process appears to be
completely smooth and occurs over a wide range of density. Thus there is a
broad regime of ``incipient'' Wigner crystallization in these quantum dots. Our
specific conclusions are: (i) The density develops sharp rings while the pair
density shows both radial and angular inhomogeneity. (ii) The spin of the
ground state is consistent with Hund's (first) rule throughout our entire range
of r_s for all 4<N<20. (iii) The addition energy curve first becomes smoother
as interactions strengthen -- the mesoscopic fluctuations are damped by
correlation -- and then starts to show features characteristic of the classical
addition energy. (iv) Localization effects are stronger for a smaller number of
electrons. (v) Finally, the gap to certain spin excitations becomes small at
the strong interaction (large r_s) side of our regime.Comment: 14 pages, 12 figure
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