Chemistry Reference
In-Depth Information
The presence of a gate voltage leads to a Fermi surface and consequently
J
c
(
q, T
)
→
0as
T →
0. For a given experimental coupling
J<J
c
(0) and
temperature
T
, one can tune the gate voltage to enter a Kondo phase. The
T
∗
(
temperature
q
) below which the system enters the Kondo phase for a
q, T
∗
)=
physical coupling
J
can be obtained using
J
c
(
J
which yields
k
B
T
∗
=Λexp
(1
/q
2
])
− J
c
(0)
/J
)
/
(2
q
ln[1
(18)
T
∗
35K.
30
We stress that
For a typical
J
2eV and voltage
eV
0
.
5eV,
even with overestimated
J
c
, physically reasonable
J
leads to experimentally
T
∗
for a wide range of experimentally tunable gate voltages.
Next, we discuss the possible ground state in the Kondo phase. In the
absence of the gate voltage a finite
achievable
J
c
implies that the ground state will
be non-Fermi liquid as also noted in Ref. 18 for flux phase systems. In
view of the large
J
c
estimated above, it might be hard to realize such a
state in undoped graphene. However, in the presence of the gate voltage, if
the impurity atom generates a spin half moment and the Kondo coupling
is independent of the valley(flavor) index, we shall have a realization of
two-channel Kondo effect in graphene owing to the valley degeneracy of
the Dirac electrons. This would again lead to overscreening and thus a
non Fermi-liquid like ground state.
17
The study of details of such a ground
state necessitates an analysis beyond our large
mean-field theory. To our
knowledge, such an analysis has not been undertaken for Kondo systems
with angular momentum mixing. In this work, we shall be content with
pointing out the possibility of such a multichannel Kondo effect in graphene
and leave a more detailed analysis as an open problem for future work.
The role of the scattering of graphene electrons from the impurity needs
to be analyzed in details for the above assertion of two channel Kondo
phenomenon. At first glance it seems that it would be impossible to achieve
this phenomenon in graphene since large momenta scattering from point-
like impurities will necessarily lead to channel mixing. However, it has been
recently shown that when the impurity resides at the center of the graphene
this does not happen.
25
To understand this phenomenon qualitatively, let
us consider an impurity at the center of the graphene hexagon with short-
range potential. Then the contribution to the scattering amplitude of this
electrons from this impurity is given by
N
S ∼
r
V
ψ
†
G
(
r
r
ψ
G
(
r
(
)
)
), where
V
(
r
) is a short range potential and
ψ
(
r
) denotes the wavefunction of the
graphene electrons, and the sum over
can be thought as sum over graphene
lattice point due to the short spread of the
p
z
r
orbital wavefunctions in the
graphene plane.
25
Thus the major contribution to the scattering comes
