Correlations and impurities in topological insulators

• Applicant: Professor Dr. Christoph Karrasch
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2011 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 193069739

Topological insulators are fundamentally different from ordinary insulating materials in that they feature an insulating gap in the bulk but exhibit robust metallic surface states. The latter can be attributed to topological properties of the bulk wave functions and can be observed experimentally. Most theoretical approaches to describe topological insulators ignore the Coulomb interactions between electrons. Adding such terms to the tight-binding model of graphene with spin-orbit couplings -- which is a paradigm in the field as it describes the most simple realization of topological order -- yields a two-band Hubbard model. Hubbard models, however, are well-know to exhibit a variety of strongly-correlated phases ranging from magnetic types of order to Mott insulating behavior. The honeycomb geometry was addressed in a few works, but a complete picture of how the different (conventional) kinds of order evolve out of the topological phase (persisting in absence of Coulomb interactions) is yet missing. As the first part of this proposal, I want to study this problem using a framework which provides an unbiased approach to the various instabilities of the Hubbard model -- the functional renormalization group.The low-energy physics of a normal metal is drastically modified by the addition of even a few magnetic impurities. A single spin degree of freedom can be screened completely by the conduction electrons by virtue of the Kondo effect. The surface of topological insulators represents a helical metal, but it is not obvious whether the Kondo effect persists. I want to study this problem of impurities on top of topological insulators using two complementary renormalization group frameworks - the functional and real-time renormalization group. Moreover, I want to investigate the real-time and steady state dynamics of a two-terminal transport geometry in a quantum dot setup.

• DFG Programme: Research Fellowships
• International Connection: USA
• Hosts: Professor Dr. Dung-Hai Lee; Professor Joel Moore, Ph.D.