1. Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene
- Author
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Roberto Soldati, Paola Giacconi, C. G. Beneventano, Eve Mariel Santangelo, C.G. Beneventano, P. Giacconi, E.M. Santangelo, and R. Soldati
- Subjects
High Energy Physics - Theory ,Statistics and Probability ,Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Condensed matter physics ,Field (physics) ,Minimal conductivity ,Dirac (software) ,Chern–Simons theory ,FOS: Physical sciences ,General Physics and Astronomy ,Física ,Statistical and Nonlinear Physics ,Mathematical Physics (math-ph) ,Magnetic field ,High Energy Physics - Theory (hep-th) ,Geometric phase ,Modeling and Simulation ,Electric field ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Gauge theory ,Quantum field theory ,Graphene ,Mathematical Physics - Abstract
We study 1-loop effects for massless Dirac fields in two spatial dimensions, coupled to homogeneous electromagnetic backgrounds, both at zero and at finite temperature and density. In the case of a purely magnetic field, we analyze the relationship between the invariance of the theory under large gauge transformations, the appearance of Chern-Simons terms and of different Berry's phases. In the case of a purely electric background field, we show that the effective Lagrangian is independent of the chemical potential and of the temperature. More interesting: we show that the minimal conductivity, as predicted by the quantum field theory, is the right multiple of the conductivity quantum and is, thus, consistent with the value measured for graphene, with no extra factor of pi in the denominator., Comment: 27 pages, no figures. Minor misprints corrected. Final version, to appear in J. Phys. A: Math. Gen
- Published
- 2009