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The nesting condition requires only that the Fermi surfaces be identical in area and shape and not that the two layers have aligned honeycomb lattices and hence aligned Brillouin zones. Global wave vector mismatches can be removed by gauge transformations. When weak inter-valley electron-electron scattering processes are included only simultaneous momentum shifts of both valleys in a layer are allowed. In this case relative rotations of the two layers will have a small influence on details of the paired state. Relative rotations will also help to reduce the amplitude of bare interlayer tunneling process which weaken transport anomalies as discussed in Ref.. For misaligned layers, bare tunneling could possibly be weak enough to produce interesting transport anomalies even for vertical transport between epilayers similar to those discussed by PRLTAO 0031-9007 10.1103/PhysRevLett.100.125504
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The nesting condition requires only that the Fermi surfaces be identical in area and shape and not that the two layers have aligned honeycomb lattices and hence aligned Brillouin zones. Global wave vector mismatches can be removed by gauge transformations. When weak inter-valley electron-electron scattering processes are included only simultaneous momentum shifts of both valleys in a layer are allowed. In this case relative rotations of the two layers will have a small influence on details of the paired state. Relative rotations will also help to reduce the amplitude of bare interlayer tunneling process which weaken transport anomalies as discussed in Ref.. For misaligned layers, bare tunneling could possibly be weak enough to produce interesting transport anomalies even for vertical transport between epilayers similar to those discussed by J. Hass, F. Varchon, J. E. Millan-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.125504 100, 125504 (2008).
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In separate calculations not described here we found that coherence between the two remote bands has little effect for kF d>1 and that will act to raise the KT temperature for kF d<1.
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In parabolic band systems this procedure provides a good estimate of the critical temperature in both the weak-coupling BCS and the strong-coupling BEC limits. Note, however, that because graphene is a gapless semiconductor, it does not have a simple BEC strong-coupling limit.
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