Title: An introduction of higher-order topology

Speaker: Prof. Bitan Roy, Lehigh University, USA

Abstract: The bulk-boundary correspondence is the hallmark of topological phases of matter.Typically, a $d$-dimensional topological phase (insulating or gapless) supports robust metallic boundary modes on $d-1$ dimensional boundary, characterized by the codimension $d_c=1$. Recently, the bulk-boundary correspondence has been generalized to encompass boundary modes with $d_c=n>1$, such as corner and hinge states. The underlying bulk state is coined as "higher-order topological (HOT)" phase. In this talk, I will explain how one can construct HOT phases starting from conventional topological phases of matter by systematically breaking discrete crystalline symmetry. I will then highlight the possible realization of HOT insulators in amorphous materials (devoid of crystalline symmetry) and in a dynamic (Floquet) systems.