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

Abstract

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.

4 pages, 1 figure

References in corpus (2)

• Electric Field Effect in Atomically Thin Carbon Films
• The structure of suspended graphene sheets

Cited by in corpus (10)

• Anderson Transitions
• Topological delocalization of two-dimensional massless Dirac fermions
• Theory of Anomalous Quantum Hall Effects in Graphene
• Collective cyclotron motion of the relativistic plasma in graphene
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• Anderson localization of electron states in graphene in different types of disorder
• Electronic transport in normal-conductor/graphene/normal-conductor junctions and conditions for insulating behavior at a finite charge-carrier density
• Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field
• Valley polarization effects on the localization in graphene Landau levels