Electron transport in disordered graphene Alexander D. Mirlin Institut fuer Nanotechnologie, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany and Institut fuer Theorie der Kondensierten Materie,Universitaet Karlsruhe, 76128 Karlsruhe, Germany Recently, Novoselov {\it et al}\ \ have succeeded in fabrication of monolayer graphite (graphene) samples [1]. This technological breakthrough was followed by  transport measurements [2] that have shown that graphene is a conductor with remarkable electronic properties. These discoveries have triggered an outbreak of research activity in the field of graphene physics, both on the experimental and the theoretical side. Charge carriers in graphene have a relativistic (massless Dirac) spectrum, which makes the transport properties of this material highly interesting from the point of view of both fundamental physics and potential applications. In this talk, I will first give a brief overview of the experimental results on transport properties of graphene samples. These include, in particular, a linear dependence of the conductivity on the electron concentration, the minimal conductivity at the neutrality point close to $4 e^2/h$ and remarkably independent on temperature, and unconventional quantum Hall effect. I will then present recent theoretical advances [3,4] on electron transport in disordered graphene. Our results show that transport properties of the system depend strongly on the character of disorder. Away from half filling, the concentration dependence of conductivity is linear in the case of strong scatterers, in line with recent experimental observations, and logarithmic for weak scatterers. At half filling the conductivity for the most generic disorder is strongly affected by localization effects. This is not the case, however, for two broad classes of disorder: (i) the randomness that preserves one of the chiral symmetries of the clean Hamiltonian (i.e. dislocations, ripples, strong point-like scatterers) and (ii) long-range disorder that does not mix the two valleys (i.e. Coulomb scatterers, ripples). We show that in these cases the system is at the quantum critical point and the conductivity is $\sim e^2/h$. [1] K.S.Novoselov et al., Science {\bf 306}, 666 (2004). [2] K.S. Novoselov et al., Nature {\bf 438}, 197 (2005); Y.B. Zhang et al., Nature {\bf 438}, 201 (2005). [3] P.M. Ostrovsky, I.V. Gornyi, and A.D. Mirlin, Phys. Rev. B 74, 235443 (2006). [4] P.M. Ostrovsky, I.V. Gornyi, and A.D. Mirlin, {\it Quantum criticality and minimal conductivity in graphene with  long-range disorder}, cond-mat/0702115. * also at Petersburg Nuclear Physics Institute, 188350 St. Petersburg, Russia