Manifestations of topological effects in graphene
Abstract
Graphene is a monoatomic layer of graphite with Carbon atoms arranged in a two dimensional honeycomb lattice configuration. It has been known for more than sixty years that the electronic structure of graphene can be modelled by twodimensional massless relativistic fermions. This property gives rise to numerous applications, both in applied sciences and in theoretical physics. Electronic circuits made out of graphene could take advantage of its high electron mobility that is witnessed even at room temperature. In the theoretical domain the Diraclike behavior of graphene can simulate high energy effects, such as the relativistic Klein paradox. Even more surprisingly, topological effects can be encoded in graphene such as the generation of vortices, charge fractionalization and the emergence of anyons. The impact of the topological effects on graphene's electronic properties can be elegantly described by the AtiyahSinger index theorem. Here we present a pedagogical encounter of this theorem and review its various applications to graphene. A direct consequence of the index theorem is charge fractionalization that is usually known from the fractional quantum Hall effect. The charge fractionalization gives rise to the exciting possibility of realizing graphene based anyons that unlike bosons or fermions exhibit fractional statistics. Besides being of theoretical interest, anyons are a strong candidate for performing error free quantum information processing.
 Publication:

Contemporary Physics
 Pub Date:
 March 2009
 DOI:
 10.1080/00107510802650507
 arXiv:
 arXiv:0812.1116
 Bibcode:
 2009ConPh..50..375P
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 20 pages, 15 figures, invited article, to appear in Contemporary Physics