Coulomb interaction in graphene
Coulomb interaction in graphene
Coulomb interaction in graphene
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H =% †p,iFull Hamiltonian: <strong>Coulomb</strong>" + 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• Is the <strong>Coulomb</strong> <strong><strong>in</strong>teraction</strong> important?Dimensionless<strong><strong>in</strong>teraction</strong> strength!" = e2vh<strong>Coulomb</strong> <strong><strong>in</strong>teraction</strong>F<strong>in</strong>estructureconstant!n(r) =N# †i=1" QED= e2ch = 1137" i(r)" i(r)• Effective f<strong>in</strong>e structure constant!" = 300" ! QED# 2.2• Broken relativistic <strong>in</strong>variance:Interactions: photons at velocity c!Fermions: velocity v(Not small!)Next: Dimensional analysis
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