SLIDE 1 Intrinsic Superconductivity in graphene ?
Electron-phonon mechanisms (Raman scattering) Pure Coulomb mechanisms
“Dynamics and Relaxation in Complex Quantum and Classical Systems and Nanostructures” – Max Planck Institute, Dresden, September 2006
Antonio H. Castro Neto
SLIDE 2 cond-mat/0608543 cond-mat/0608515 cond-mat/0607343
- Phys. Rev. B 73, 245426 (2006)
cond-mat/0604106
- Phys. 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)
SLIDE 3
SLIDE 4 A Personal Note
Free non-relativistic electrons in a box
Paul Drude Arnold Sommerfeld
=
m p H 2
2
=
Ignorance is dumped here !
NO LATTICE
Felix Bloch
NO INTERACTIONS
Lev Landau
SLIDE 5 Novoselov et al, Science 306, 666 (2004) Free relativisitic electrons in a box
Paul Dirac Ignorance is dumped here ! DISORDER INTERACTIONS
⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =
− ) ( ) ( p i p i
e e vp H
ϕ ϕ
SLIDE 6
A Metal is traced out
What would be the effective theory for superconductivity in graphene ?
s-wave
p+ip wave
B A L S − = =
⊗ ⊗ = Ψ ψ ψ ψ
1
SLIDE 7
Mean field phenomenology
SLIDE 8 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
SLIDE 9
The quantum theory is critical
SLIDE 10
Phase diagram
E
first order
s-wave phase
SLIDE 11 Electron-phonon coupling
2 2 2 2 2 2
/ ) ( 1 ) ( ) ( W E a v E E N W E N E N x dl dt
F F F F g F D F
∝ ∝ ∝ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ω λ
Weak coupling
SLIDE 12
Q K K’
SLIDE 13
Metal coated graphene
A proposal
SLIDE 14
The idea: start with the non-interacting problem
A
SLIDE 15
2 Band superconductivity in graphene
And add Coulomb interactions plane distance d
All interactions are repulsive !
SLIDE 16
Graphene Effective Interaction (RPA) The interaction can be strongly attractive close to the zeros of the dielectric function where electrons resonate with plasmons ! plasmon
SLIDE 17
2 Band superconductivity in graphene Dielectric function
where
2D Coulomb interaction
SLIDE 18
1 2 2DEG acoustic plasmon screened acoustic plasmon
SLIDE 19
2DEG plasmon
SLIDE 20
screened acoustic plasmon
SLIDE 21
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) !
SLIDE 22 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
SLIDE 23
C2Li (1.9 K) C6Yb (6.5 K)
Intercalated Graphite
C8K (0.5 K) C6Ca (11.5 K)
SLIDE 24 Graphite intercalated compounds (GIC )
Graphite NFEB Yb
Czanyi et al., Nat. Phys. 1, 42 (2005)
SLIDE 25
Graphite intercalated compounds (GIC )
Graphite NFEB Yb 3D NFEB C6Yb
SLIDE 26 Graphite intercalated compounds (GIC )
3D NFEB
C6Ca Fermi surface
NFEB
Mazin et al., cond-mat/0606404
SLIDE 27
Graphite intercalated compounds (GIC )
NFEB FS? SC? No No Yes No No Yes
SLIDE 28 Graphite intercalated compounds (GIC )
2 band model model superconductivity?
Czanyi et al.,
SLIDE 29 Conclusions We showed that superconductivity is possible in graphene using a purely electronic mechanism A reliable estimation of Tc requires the inclusion
- f retardation in the interaction (strong coupling
theory) Graphene has has a new superconducting phase with p+ip wave pairing in the singlet channel.
