Bulk-Boundary Correspondence for Non-Hermitian Hamiltonians via Green Functions.

Genuinely non-Hermitian topological phases can be realized in open systems with sufficiently strong gain and loss; in such phases, the Hamiltonian cannot be deformed into a gapped Hermitian Hamiltonian without energy bands touching each other. Comparing Green functions for periodic and open boundary conditions we find that, in general, there is no correspondence between topological invariants computed for periodic boundary conditions, and boundary eigenstates observed for open boundary conditions. Instead, we find that the non-Hermitian winding number in one dimension signals a topological phase transition in the bulk: It implies spatial growth of the bulk Green function.

Voigt Exceptional Points in an Anisotropic ZnO-Based Planar Microcavity: Square-Root Topology, Polarization Vortices, and Circularity.

Voigt points represent propagation directions in anisotropic crystals along which optical modes degenerate, leading to a single circularly polarized eigenmode. They are a particular class of exceptional points. Here, we report the fabrication and characterization of a dielectric, anisotropic optical microcavity based on nonpolar ZnO that implements a non-Hermitian system and mimics the behavior of Voigt points in natural crystals. We prove the exceptional-point nature by monitoring the complex-square-root topology of the mode eigenenergies (real and imaginary parts) around the Voigt points. Polarization state analysis shows that these artificially engineered Voigt points behave as vortex cores for the linear polarization and sustain chiral modes. Our findings apply to any planar microcavity with broken cylindrical symmetry and, thus, pave the way for exploiting exceptional points in widespread optoelectronic devices such as vertical cavity surface emitting lasers and resonant cavity light emitting diodes.