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Intrinsic Superconductivity in graphene ?
Electron-phonon mechanisms (Raman scattering)
Pure Coulomb mechanisms
“Dynamics and Relaxation in Complex Quantum and Classical Systemsand Nanostructures” – Max Planck Institute, Dresden, September 2006
Antonio H. Castro Neto
cond-mat/0608543 cond-mat/0608515cond-mat/0607343Phys. Rev. B 73, 245426 (2006)cond-mat/0604106Phys. Rev. B 73, 241403 (2006)Phys. Rev. B 73, 195411 (2006)Phys. Rev. B 73, 214418 (2006)Phys. Rev. B 73, 125411 (2006)Phys. Rev. Lett. 96, 036801 (2006)Phys. Rev. B 72, 174406 (2005)Annals of Physics 321, 1559 (2006).
Collaborators:Francisco Guinea (ICMM, Spain)Johan Nilsson (BU, USA)Vitor Pereira (Univ. Porto, Portugal)Nuno Peres (Univ. Minho, Portugal)Bruno Uchoa (BU, USA)Joao L. dos Santos (Univ. Porto, Portugal)
1 µm
0Å 9Å 13Å
Novoselov et al, Science 306, 666 (2004)
A Personal NoteFree non-relativistic electrons in a box
Paul Drude Arnold Sommerfeld
=
mpH2
2
=Ignorance is dumped here !
NO LATTICE
FelixBloch
NO INTERACTIONS
LevLandau
Novoselov et al, Science 306, 666 (2004)
Free relativisitic electronsin a box
PaulDirac
Ignorance is dumped here !
DISORDER INTERACTIONS
⎟⎟⎠
⎞⎜⎜⎝
⎛=
− 00
)(
)(
pi
pi
ee
vpHϕ
ϕ
A
Metal is traced out
What would be the effective theory forsuperconductivity in graphene ?
s-wavep+ip wave
BALS −== ⊗⊗=Ψ ψψψ 10
Mean field phenomenology
AHCN, Phys. Rev. Lett. 86, 4382 (2001)B.Uchoa, AHCN, G. Cabrera, Phys.Rev.B 69, 144512 (2004)B.Uchoa, G. Cabrera, AHCN, Phys.Rev.B 71, 184509 (2005)
Dirac Fermion pairing
The quantum theory is critical
Phase diagram
E
first order
s-wave phase
Electron-phonon coupling
222
2
0
22
/)(
1)(
)(
WE
avEEN
WEN
ENxdldt
F
F
FFg
FD
F
∝∝
∝
⎟⎠⎞
⎜⎝⎛=
ωλ
Weak coupling
QK K’
Metal coated grapheneA proposal
The idea: start with the non-interacting problem
A
2 Band superconductivity in grapheneAnd add Coulomb interactions
plane distance d
All interactions are repulsive !
Graphene Effective Interaction (RPA)
The interaction can be strongly attractive close to the zeros of the dielectric function
where electrons resonate with plasmons !
plasmon
2 Band superconductivity in grapheneDielectric function
where 2D Coulomb interaction
1
2
2DEG acoustic plasmon
screened acoustic plasmon
2DEG plasmon
screened acoustic plasmon
The screened mode will exist if it is not overdamped by the electronic particle-hole continuum:
for a pocket of a few eV.
If x is the fraction of electrons per metallic atom that migrates to graphene in the compound,
this condition is equivalent to
CmAn
Superconductivity is favored for a sufficiently diluted coverage of the metal (large n) !
Fullerenes
C60 is an insulator but
C60K3 is a superconductor (18 K)Hebard et al., Nature 352, 223 (1991)
but C60K4 is an insulator indicating that superconductivity happens with metal dilution
C60buckyball
Carbon Superconductivity
C2Li (1.9 K)
C6Yb (6.5 K)
Intercalated Graphite
C8K (0.5 K) C6Ca (11.5 K)
Graphite intercalated compounds (GIC ) Graphite
NFEB
Yb
Czanyi et al., Nat. Phys. 1, 42 (2005)
Graphite intercalated compounds (GIC )Graphite
NFEB
Yb
3D NFEB
C6Yb
Graphite intercalated compounds (GIC )
3D NFEB
C6Ca
Fermi surface
NFEB
Mazin et al., cond-mat/0606404
Graphite intercalated compounds (GIC )
NFEB FS?SC?
No No YesNo No Yes
Graphite intercalated compounds (GIC )
2 band model model superconductivity?
Czanyi et al., Nat. Phys. 1, 42 (2005)
Conclusions
We showed that superconductivity is possiblein graphene using a purely electronic mechanism
A reliable estimation of Tc requires the inclusion of retardation in the interaction (strong coupling theory)
Graphene has has a new superconducting phase with p+ip wave pairing in the singlet channel.
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