Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems

We study the geometric response of three-dimensional non-Hermitian crystalline systems with nontrivial point-gap topology. For fourfold rotation symmetry, we show that in presence disclination lines a total Frank angle which is an integer multiple $2\pi$, there can be one-dimensional topology along direction lines. This results disclination-induced skin effects. By doubling Hamiltonian to Hermitian chiral topological insulator, modes are zero effective surface Dirac fermion(s) pseudomagnetic flux induced by disclinations. Furthermore, find our have field theoretic description, and corresponding actions (e.g., Euclidean Wen-Zee action) enrich theory systems.