Seminar on Disorder and strong electron correlations: "Metal- insulator transition in 2D random fermion systems of chiral symmetry classes"
Starts 8 Dec 2011 11:30
Ends 8 Dec 2011 20:00
Central European Time
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
We consider localization of Dirac fermions in graphene with strong scatterers and, more generally, metal-insulator transition in 2D disordered systems with chiral symmetry. A general approach is developed to describe a disordered sample with strong isolated scatterers. This approach provides a basis for an efficient numerical analysis of the charge transport and is applied to calculate the conductivity of undoped graphene with resonant impurities. In the case of smooth resonant scatterers, the symmetry class is identified as DIII and conductivity grows logarithmically with increasing impurity concentration. For vacancies (or strong on-site potential impurities, class BDI), conductivity saturates at a constant value that depends on the vacancy distribution among six sublattices. A general analysis of the metal-insulator transition in 2D system of a chiral symmetry class (AIII, BDI, and DIII) is based on the replica sigma-model formalism. Weak localization corrections to conductivity are absent in all orders of perturbation theory. We identify the non-perturbative contributions due to topological excitations. These excitations have the form of vortices; their dynamics leads to the metal-inculator transition analogous to the Berezinskii-Kosterlitz-Thouless transition in the 2D Coulomb gas. This vortex-driven mechanism becomes ineffective when the system possesses non-trivial topological properties (Wess-Zumino term in class AIII or Z_2 topological term in class CII). This, in particular, explains the lack of localization on the surface of a 3D topological insulator of class CII.
ICTP - Strada Costiera, 11
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