Chemistry Reference
In-Depth Information
behavior of tunneling conductance.
10-13
In particular, it has been shown in
Refs. 11, 12 that the subgap tunneling conductance of graphene NIS junc-
tions, in contrast to its counterpart in conventional NIS junctions, is an
oscillatory function of the barrier strength of the applied barrier strength.
Similar unconventional oscillatory behavior was also observed in for critical
current
I
c
in graphene Josephson tunnel junctions.
13,14
An extremely interesting phenomenon in conventional metal systems
is the Kondo effect which occurs in the presence of dilute concentration
of localized quantum spins coupled to the spin-degenerate Fermi sea of
metal electrons.
15
The impurity spin-electron interaction then results in
perfect or partial screening of the impurity spin as one approaches zero
temperature. It also results in a sharp 'Kondo Resonance' in electron spec-
tral functions. Recent developments in quantum dots and nano devices
have given new ways in which various theoretical results in Kondo physics,
which are not easily testable otherwise, can be tested and confirmed exper-
imentally.
16
Most of the early studies in Kondo effect were carried on for
conventional metallic systems with constant density of states (DOS) at the
Fermi surface.
17
Some studies on Kondo effect in possible flux phases,
18
nodal quasiparticles in d-wave superconductors,
19
Luttinger liquids,
20
and
hexagonal Kondo lattice,
21
for which the DOS of the associated Fermions
vanishes as some power law at the Fermi surface, has also been undertaken.
Recently, there has been a interest in study of the physics of magnetic im-
purities in graphene.
23-27
The purpose of this article is to articulate a part
of this recent progress.
2. Analysis of the Kondo Model
The crucial requirement for occurrence of Kondo effect is that the em-
bedded impurities should retain their magnetic moment in the presence of
conduction of electrons of graphene. We will not quantitatively address the
problem of local moment formation in the presence of Dirac sea of elec-
trons; this has been recently addressed in Ref. 27. A shown in Ref. 27, the
large band width and small linearly vanishing density of states at the fermi
level in graphene should make survival of impurity magnetic moment easier
than in the conventional 3D metallic matrix. In fact, a detailed calculation
shows that Cobalt atoms may lead to an effective moment of
2when
placed at the center of the graphene hexagon.
27
In the rest of this article,
we shall therefore use the Kondo Hamiltonian
28
as our staring point.
or
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