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

Mesoscale and Nanoscale Physics;Optics;Quantum Physics