Coulomb interaction in graphene
Coulomb interaction in graphene
Coulomb interaction in graphene
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H =% †p,iDimensional analysis 2" + 1 i(p)[vp# $]" i(p)2e 2" d 2 rd 2 r' n(r)n(r')# r - r'!K<strong>in</strong>etic energy• Dirac fermion case!n– Gas of density :<strong>Coulomb</strong> <strong><strong>in</strong>teraction</strong>E <strong>Coulomb</strong>" n 3 / 2!E K<strong>in</strong>etic" n 3 / 2n(r) =N# †i=1" i(r)" i(r)Relative importance ofK<strong>in</strong>etic & <strong>Coulomb</strong><strong>in</strong>dependent of n!• Interactions are marg<strong>in</strong>al!!– No typical length scale!Perturbations break this symmetry– Applied chemical potential:" F# 1 E F– Applied Magnetic field:l B" 1 B• T = 0 Quantum critical po<strong>in</strong>t!!Next: RG analysis near QCP
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