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Graphene deconstructed
Antonio H. Castro Neto
Evora, November 2008
Disclaimer
AHCN, P. Guinea, N. Peres, K. Novoselov,
A. Geim, Rev. Mod. Phys. (2008)
Disclaimer
Graphene is
discovered
Andre Geim
Kostya
Novoselov
AHCN, P. Guinea, N. Peres, K. Novoselov,
A. Geim, Rev. Mod. Phys. (2008)
Disclaimer
Graphene is
discovered
IQHE measuredAndre Geim
Kostya
Novoselov
Philip Kim
AHCN, P. Guinea, N. Peres, K. Novoselov,
A. Geim, Rev. Mod. Phys. (2008)
A brief history of graphene
5 µm
5 µm
Plus some nanotechnology…
2µm
!optical image
Plus some nanotechnology…
2µm
!optical image
!SEM image
Plus some nanotechnology…
2µm
!optical image
!SEM image
!design
Plus some nanotechnology…
2µm
!optical image
!SEM image
!design
!contacts and mesa
Plus some nanotechnology…
2µm
!!!"#$%
"#
&'!()*+,(+-
./,01#+2
!optical image
!SEM image
!design
!contacts and mesa
Some electronic properties of graphene
Some electronic properties of graphene
B
A
Unit cell
t ~ 2.7 eV
Some electronic properties of graphene
B
A
Unit cell Nearest neighbors
Some electronic properties of graphene
B
t’ ~ 0.1 eV
A
A
Next Nearest neighbors
In momentum space
In momentum space
In momentum space
Dirac Cone
In momentum space
Dirac Cone
“Ultra relativistic” Solid
State at low speed of light
In momentum space
“Ultra relativistic” Solid
State at low speed of light
In momentum space
Semi-Metal
“Ultra relativistic” Solid
State at low speed of light
Novoselov et al, Science 306, 666 (2004)
Novoselov et al, Science 306, 666 (2004)
Novoselov et al, Science 306, 666 (2004)
10
Graphene-Based Chemical Sensorsresponse to various gases
in concentration 1ppm
10
Graphene-Based Chemical Sensorsresponse to various gases
in concentration 1ppmcontinuous doping
by donors and acceptors
10
Graphene-Based Chemical Sensors
! straightforward 1 ppb resolution
response to various gases in concentration 1ppm
continuous doping by donors and acceptors
! graphene can be doped in concentrations >1012
cm-2
11
Single-Molecule Detection
step-like changes in Hall conductivitynear zero concentration
0 200 400 600
time (s)
0
10
20
30
!R
xy ("
)
adsorption
desorption
1e
1e
x1 x50
11
Single-Molecule Detection
step-like changes in Hall conductivitynear zero concentration
0 200 400 600
time (s)
0
10
20
30
!R
xy ("
)
adsorption
desorption
1e
1e
-4 -2 0 2 40
200
400
600
0
200
400
600
num
ber
of ste
ps
!Rxy (")
annealed
desorption adsorption
-1e+1e
x1 x50
11
Single-Molecule Detection
step-like changes in Hall conductivitynear zero concentration
0 200 400 600
time (s)
0
10
20
30
!R
xy ("
)
adsorption
desorption
1e
1e
extremely electronically quiet: few unstable defects highly conductive even in the limit of no carriers
4-probe measurements on single-crystal with low-R contactsall the volume exposed to environment
-4 -2 0 2 40
200
400
600
0
200
400
600
num
ber
of ste
ps
!Rxy (")
annealed
desorption adsorption
-1e+1e
x1 x50
Outline
•Coulomb impurity in graphene Vitor M. Pereira, Johan Nilsson, AHCN Phys.Rev.Lett. 99, 166802 (2007); Vitor M. Pereira, Valeri Kotov, AHCN
Phys. Rev. B 78, 085101 (2008).
•Anderson impurity in graphene Bruno Uchoa, Valeri Kotov, Nuno Peres, AHCN Phys. Rev. Lett. 101, 026805 (2008); Bruno Uchoa, Chiung-Yuan Lin, Nuno Peres, AHCN
Phys.Rev.B 77, 035420 (2008)!.
Johan Nilsson
Bruno Uchoa
Vitor Pereira
Valeri Kotov
Nuno Peres
E
N(E)
Anderson’s Impurity Model
T>TK
Non-interacting: U=0
Non-interacting: U=0
Energy
V=0
Non-interacting: U=0
Energy
Non-interacting: U=0
Energy
Non-interacting: U=0
Broadening
EnergyEnergy
Mean-Field
Mean-Field
The impurity moment can be switched on and off!
U = 1 eV
n_down
V=1eV, e0=0.2 eV
n_up
U = 40 meV
U = 0.1 eV
Conclusions
• Impurities in graphene behave in an unusual
way when compared to normal metals and
semiconductors.
• Control of the magnetic moment formation
using electric fields.
• Atoms that are not magnetic in ordinary
metal hosts (like hydrogen) can become
magnetic in graphene.
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