21 Gennaio, 2013 17:00

Seminario Matematico e Fisico di Milano

QUANTUM NUMBERS OF TOPOLOGICAL DEFECTS AND REAL CLIFFORD ALGEBRAS IN DIRAC SYSTEMS

IGOR HERBUT, Simon Fraser University

Università di Milano, Dipartimento di Matematica

I will discuss the emergent Dirac quasiparticles in the lattice systems of electrons, exemplified by graphene, in the presence of topological defects of the allowed superconducting and insulating, order parameters. These orders appear as possible mass terms in the Dirac equation, and their topological defects have been known to carry non-trivial quantum numbers such as charge and spin since the work of Jackiw and Rebby in 1976.
In the talk I will discuss their additional internal degree of freedom: irrespectively of the nature of orders that support the defect, an extra
mass-order-parameter spontaneously emerges in the defect's core. The determination of the quantum state of the topological defect turns out to be an interesting problem in the representation theory of (real) Clifford algebras; with the Clifford algebra C(2,5) playing a fundamental role in graphene, for example. Ultimately, the particle-hole symmetry restricts the defects to always carry the quantum numbers of a single effective isospin-1/2, quite independently of the values of their electric charge or true spin. Examples of this new degree of freedom in graphene and on surfaces of topological insulators will be given.