L. TRIFUNOVIC: Higher-order topological insulators and superconductors and beyond

         Not so long ago, the concept of higher-order topological insulators and superconductors was mentioned for the first time in print (see Viewpoint [1]). Since then, the concept of higher-order topology has been recognized to be key for the description of boundary phenomenology of topological crystalline insulators and superconductors.
         Although higher-order boundary phenomenology can exist without a topologically nontrivial bulk band structure, recent excitement stems from the observation that it can also be a consequence of (and protected by) nontrivial bulk topology if additional crystalline symmetries are present. In this picture, higher-order topological phases are not a new kind of topological phases, rather they are a new type of boundary manifestation of nontrivial bulk topology.

         I will introduce extrinsic and intrinsic higher-order boundary phenomenology and discuss both bulk and boundary topological classification. A new type of bulk-boundary correspondence that naturally includes a higher-order boundary phenomenology will be also discussed [2].

[1] https://physics.aps.org/articles/v10/132

[2] L. Trifunovic, P.W. Brouwer, Phys. Status Solidi B, 258, 2000090 (2021).