Quantum criticality and minimal conductivity in graphene with long-range disorder

Details Quantum criticality and minimal conductivity in graphene with long-range disorder Quantum criticality and minimal conductivity in graphene with long-range disorder

2007-02-05

arxiv.org/abs/cond-mat/0702115v1

Phys. Rev. Lett. 98, 256801 (2007)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.98.256801

We consider the conductivity $\sigma_{xx}$ of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class $\sigma$-model including a topological term with $\theta=\pi$. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of $e^2/h$. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and $\sigma_{xx}$ acquires the value characteristic for the quantum Hall transition.

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