[Seminar] "Topological Invariant for Magnon Hall Systems with Disorder" by Prof. Yutaka Akagi

Yutaka Akagi

Assistant Professor, The University of Tokyo

Apr. 2005 – Mar. 2009: Bachelor Degree in Physics, Department of Physics, Tokyo Institute of Technology

Apr. 2009 – Mar. 2014: Ph.D. in Engineering, Department of Applied Physics, The University of Tokyo (Motome group)

Apr. 2014 – Oct. 2015: Postdoctoral Scholar, Theory of Quantum Matter Unit, OIST

Nov. 2015 – present: Assistant Professor, Katsura group, Department of Physics, The University of Tokyo

Abstract of Talk

The highly successful studies on the topological phases for electrons have spread to bosonic systems showing novel phenomena such as magnon thermal Hall effect. As a definite difference from fermionic systems, bosonic systems have unique mathematical properties – non-Hermiticity. In addition, since topological invariants which characterize the topological phases are usually defined in terms of Bloch wave functions in translationally invariant systems, it is not obvious how to define such an invariant in disordered bosonic systems, where the Bloch momentum is no longer a good quantum number.

In this study, we define a topological invariant, corresponding to the Chern number, using the method of non-commutative geometry in the Bogoliubov-de Gennes type Hamiltonian which describes disordered magnon Hall systems. To demonstrate the validity of the definition, we study an artificial spin ice model in two dimensions numerically. In consequence, we find the method sufficient to determine the integer values of the invariant in the magnon Hall system with disorder.