Coulomb interaction in graphene

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• Kinetic energyLow-energy theory of graphene• Eigenvalues ! Energy bandsEk y!!a =1.42 Angstromk x• Two inequivalent nodes: Linear dispersionEmpty!• Near nodes:E(k) " ±v | k |v = 3ta /2VelocityFilled!!!i =1,...4Spin, node• Applies at low momenta:k
!Free fermions on the honeycomb lattice• “Relativistic” low-energy HamiltonianH = % †p,i" i(p)[vp# $]" i(p)Pauli matrices.• Condensed-matter phenomena:Photoemission, Infrared spectroscopyBostwick Nat. Phys 2007; Li Nat. Phys. 2008Novel Quantum Hall effect• “Relativistic” quantum field theory phenomena!Dirac fermions in B-fieldZhang et al Nature 2005Two-componentspinorObserve v " c /300 Novoselov Nature 2005Zitterbewegung Katsnelson 2006“jittery motion” of Dirac fermions - uncertainty principleSchwinger pair production Allor et al PRD 2008• What about Coulomb interaction?Unscreenedparticle-hole production in an electric field(No Fermi surface)Next: Full Hamiltonian
Page 2: Outline• Graphene: One-atom thick
Page 7 and 8: H =% †p,iDimensional analysis" +
Page 9 and 10: Prescription:2) Rescale momenta & f
Page 11 and 12: • Graphene: critical point at!Ren
Page 13 and 14: Recent compressibility dataJ. Marti
Page 15 and 16: Phase diagram: Crossover behaviorC
Page 17 and 18: Optical transparency of graphene•
Page 19 and 20: • Scaling: "(#,T,$) = "(#(b),T(b)
Page 21 and 22: Polarization approach"(#) = Lim q $
Page 23 and 24: Continuity:Ward Identity and conser
Page 25: Concluding remarks• Graphene: Dir

Coulomb interaction in graphene

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