## 3. 4. 2013. Colloquium: Igor Herbut

Wednesday 3 April 2013 at 12PM

Zvonko Marić Room

IPB Colloquium

Igor Herbut

Simon Fraser University, Vancouver, Canada and

Max Planck Institute for the Physics of Complex Systems, Dresden, Germany

**Masses, Clifford algebras, and the quantum state of topological defects in graphene**

Abstract:

I will discuss the low-energy Dirac quasiparticles in the electronic systems such as graphene in the presence of topological defects of the ``preffered" order parameters. These orders appear as possible mass terms in the Dirac equation, in graphene there are 36 of them, and their topological defects have been known to carry non-trivial quantum numbers such as fractionalized charge since the seminal 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. In contrast to superconductor vortices in metals and alloys, for example, vortices, superconducting or insulating, in Dirac materials are thus never in the normal (metallic) state in their core, but unavoidably carry with them some other, emergent, competing local order.

The determination of the quantum state of the topological defect in Dirac systems turns out to be an interesting problem in the (real) representation theory of Clifford algebras; with the particularly interesting Clifford algebra C(2,5) playing a fundamental role in graphene. Physical examples of this new (collective) degree of freedom in Dirac-like systems, which also includes less obvious examples such as graphene bilayers and d-wave superconductors will be given.