Universality and Stability of the Edge States of Chiral-Symmetric Topological Semimetals and Surface States of the Luttinger Semimetal.

We theoretically demonstrate that the chiral structure of the nodes of nodal semimetals is responsible for the existence and universal local properties of the edge states in the vicinity of the nodes. We perform a general analysis of the edge states for an isolated node of a 2D semimetal, protected by chiral symmetry and characterized by the topological winding number N. We derive the asymptotic chiral-symmetric boundary conditions and find that there are N+1 universal classes of them.

Screening charged impurities and lifting the orbital degeneracy in graphene by populating Landau levels.

We report the observation of an isolated charged impurity in graphene and present direct evidence of the close connection between the screening properties of a 2D electron system and the influence of the impurity on its electronic environment. Using scanning tunneling microscopy and Landau level spectroscopy, we demonstrate that in the presence of a magnetic field the strength of the impurity can be tuned by controlling the occupation of Landau-level states with a gate voltage. At low occupation the impurity is screened, becoming essentially invisible.

Canted antiferromagnetic phase of the ν=0 quantum Hall state in bilayer graphene.

Motivated to understand the nature of the strongly insulating ν=0 quantum Hall state in bilayer graphene, we develop the theory of the state in the framework of quantum Hall ferromagnetism. The generic phase diagram, obtained in the presence of the isospin anisotropy, perpendicular electric field, and Zeeman effect, consists of the spin-polarized ferromagnetic (F), canted antiferromagnetic (CAF), and partially (PLP) and fully (FLP) layer-polarized phases. We address the edge transport properties of the phases.

Hall resistivity of granular metals.

We calculate the Hall conductivity sigma(xy) and resistivity rho(xy) of a granular system at large tunneling conductance g(T)>>1. We show that in the absence of Coulomb interaction the Hall resistivity depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula rho(xy)=H/(n*ec), where n* differs from the carrier density n inside the grains by a numerical coefficient determined by the shape of the grains. The Coulomb interaction gives rise to logarithmic in temperature T correction to rho(xy) in the range Gamma less or similar T less or similar min(g(T)E(c), E(Th)), where Gamma is the tunneling escape rate, E(c) is the charging energy, and E(Th) is the Thouless energy of the grain.