Showcasing RRI

I shall discuss the non-Hermitian Su-Schrieffer-Heeger model as a prototypical example of one-dimensional lattice models with several sublattice sites for unveiling intriguing insulating and metallic phases with no Hermitian counterparts. These phases are characterized by composite cyclic loops of multiple complex-energy bands encircling single or multiple exceptional points on the parametric space of real and imaginary energy. The topology of these composite loops is similar to the well-known topological objects like Möbius strips and Penrose triangles and can be quantified by a nonadiabatic cyclic geometric phase which includes contributions only from the participating bands. I shall further introduce a particular boundary condition to recover the bulk-boundary correspondence in such non-Hermitian models, which is otherwise absent.