Geometric response and disclination-induced skin effects in non-Hermitian systems

We study the geometric response of three-dimensional non-Hermitian crystalline systems with non-trivial point gap topology. For systems with four-fold rotation symmetry, we show that in presence of disclination lines with a total Frank angle which is an integer multiple of $2\pi$, there can be non-trivial, one-dimensional point gap topology along the direction of disclination lines. This results in disclination-induced non-Hermitian skin effects. We extend the recently proposed non-Hermitian field theory approach to describe this phenomenon as a Euclidean Wen-Zee term. Furthermore, by doubling a non-Hermitian Hamiltonian to a Hermitian 3D chiral topological insulator, we show that the disclination-induced skin modes are zero modes of the surface Dirac fermion(s) in the presence of a pseudo-magnetic flux induced by disclinations.