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.