Topological quantum matter: From quantum Hall states to higher order topological phases

Dr. Vladimir Juričić

NORDITA, the Nordic Institute for Theoretical Physics, Stockholm

Topological states of matter, featuring exotic robust boundary states, are at the forefront of research in the modern condensed matter physics. In this talk, I will focus on the topological phases in the electronic systems, which are characterized by a topological invariant of the corresponding band structure. The emergent gapless edge or surface states are protected by the bulk topological invariant and arise as a consequence of the so-called bulk-boundary correspondence, which is a hallmark feature of a topological state.

I will first discuss the paradigmatic representatives of gapped topological states: The quantum Hall states, as well as two- and three-dimensional time reversal symmetric topological insulators, including the corresponding topological invariants and the bulk- boundary correspondence. Furthermore, it was established that crystalline symmetries, such as mirror and rotational symmetries, can give rise to yet different gapped topological phases, such topological crystalline insulators. Lattice symmetries play a prominent role also in the physics of gapless topological states, which I will illustrate in the case of certain magnetic lattices. More recently, the notion of topological states of matter has been extended to the so-called higher order topological states featuring gapless surface states at boundaries of co-dimension higher than one, such as hinges and corners. I will particularly discuss a general method for construction of these states within the Dirac Hamiltonian framework, the role of crystalline symmetries and realization of higher order topological insulators in non-crystalline settings.

Viernes 14 de junio, 16:00, Sala Luciano Laroze E-300