665 research outputs found
On the Ruderman-Kittel-Kasuya-Yosida interaction in graphene
The two dimensionality plus the linear band structure of graphene leads to
new behavior of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which is
the interaction between two magnetic moments mediated by the electrons of the
host crystal. We study this interaction from linear response theory. There are
two equivalent methods both of which may be used for the calculation of the
susceptibility, one involving the integral over a product of two Green's
functions and the second that involves the excitations between occupied and
unoccupied states, which was followed in the original work of Ruderman and
Kittel. Unlike the behavior of an
ordinary two-dimensional (2D) metal, in graphene falls off as ,
shows the -type of behavior, which contains
an interference term between the two Dirac cones, and it oscillates for certain
directions and not for others. Quite interestingly, irrespective of any
oscillations, the RKKY interaction in graphene is always ferromagnetic for
moments located on the same sublattice and antiferromagnetic for moments on the
opposite sublattices, a result that follows from particle-hole symmetry.Comment: 12 pages, 5 figures, submitted to AIP Conference Proceeding
RKKY Interaction in Graphene from Lattice Green's Function
We study the exchange interaction between two magnetic impurities in
graphene (the RKKY interaction) by directly computing the lattice Green's
function for the tight-binding band structure for the honeycomb lattice. The
method allows us to compute numerically for much larger distances than can
be handled by finite-lattice calculations as well as for small distances. %
avoids the use of a cutoff function often invoked in the literature to curtail
the diverging contributions from the linear bands and yields results that are
valid for all distances. In addition, we rederive the analytical long-distance
behavior of for linearly dispersive bands and find corrections to the
oscillatory factor that were previously missed in the literature. The main
features of the RKKY interaction in graphene are that unlike the behavior of an ordinary 2D metal in the
long-distance limit, in graphene falls off as , shows the -type oscillations with additional phase factors depending on the
direction, and exhibits a ferromagnetic interaction for moments on the same
sublattice and an antiferromagnetic interaction for moments on the opposite
sublattices as required by particle-hole symmetry. The computed with the
full band structure agrees with our analytical results in the long-distance
limit including the oscillatory factors with the additional phases.Comment: 8 pages, 11 figure
Analytical Expression for the RKKY Interaction in Doped Graphene
We obtain an analytical expression for the Ruderman-Kittel-Kasuya-Yosida
(RKKY) interaction in electron or hole doped graphene for linear Dirac
bands. The results agree very well with the numerical calculations for the full
tight-binding band structure in the regime where the linear band structure is
valid. The analytical result, expressed in terms of the Meijer G-function,
consists of a product of two oscillatory terms, one coming from the
interference between the two Dirac cones and the second coming from the finite
size of the Fermi surface. For large distances, the Meijer G-function behaves
as a sinusoidal term, leading to the result for moments located on the same sublattice. The
dependence, which is the same for the standard two-dimensional electron gas, is
universal irrespective of the sublattice location and the distance direction of
the two moments except when (undoped case), where it reverts to the
dependence. These results correct several inconsistencies found in the
literature.Comment: 5 pages, 5 figure
RKKY Interaction in Graphene from Lattice Green's Function
http://arxiv.org/abs/1008.4834We study the exchange interaction between two magnetic impurities in graphene (the RKKY interaction) by directly computing the lattice Green's function for the tight-binding band structure for the honeycomb lattice. The method allows us to compute numerically for much larger distances than can be handled by finite-lattice calculations as well as for small distances. % avoids the use of a cutoff function often invoked in the literature to curtail the diverging contributions from the linear bands and yields results that are valid for all distances. In addition, we rederive the analytical long-distance behavior of for linearly dispersive bands and find corrections to the oscillatory factor that were previously missed in the literature. The main features of the RKKY interaction in graphene are that unlike the behavior of an ordinary 2D metal in the long-distance limit, in graphene falls off as , shows the -type oscillations with additional phase factors depending on the direction, and exhibits a ferromagnetic interaction for moments on the same sublattice and an antiferromagnetic interaction for moments on the opposite sublattices as required by particle-hole symmetry. The computed with the full band structure agrees with our analytical results in the long-distance limit including the oscillatory factors with the additional phases.This work was supported by the U. S. Department of Energy through Grant No. DE-FG02-00ER45818
Electronic structure of the substitutional vacancy in graphene: Density-functional and Green's function studies
We study the electronic structure of graphene with a single substitutional
vacancy using a combination of the density-functional, tight-binding, and
impurity Green's function approaches. Density functional studies are performed
with the all-electron spin-polarized linear augmented plane wave (LAPW) method.
The three dangling bonds adjacent to the vacancy introduce
localized states (V) in the mid-gap region, which split due to the
crystal field and a Jahn-Teller distortion, while the states
introduce a sharp resonance state (V) in the band structure. For a planar
structure, symmetry strictly forbids hybridization between the and the
states, so that these bands are clearly identifiable in the calculated
band structure. As for the magnetic moment of the vacancy, the Hund's-rule
coupling aligns the spins of the four localized V, V, and the V electrons resulting
in a S=1 state, with a magnetic moment of , which is reduced by about
due to the anti-ferromagnetic spin-polarization of the band
itinerant states in the vicinity of the vacancy. This results in the net
magnetic moment of . Using the Lippmann-Schwinger equation, we
reproduce the well-known decay of the localized V wave function
with distance and in addition find an interference term coming from the two
Dirac points, previously unnoticed in the literature. The long-range nature of
the V wave function is a unique feature of the graphene vacancy and we
suggest that this may be one of the reasons for the widely varying relaxed
structures and magnetic moments reported from the supercell band calculations
in the literature.Comment: 24 pages, 15 figures. Accepted for publication in New Journal of
Physic
Electronic structure of the substitutional vacancy in graphene: density-functional and Greens function studies (vol 14, 083004, 2012)
Link to the corrected article: [https://vinar.vin.bg.ac.rs/handle/123456789/4991
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