Non-Hermitian Hopf-Link Exceptional Line Semimetals

We study a new class of non-Hermitian topological phases in three dimension, where the topological robust band degeneracies are Hopf-link exceptional lines. As a concrete example, we investigate the non-Hermitian band structure of nodal line semimetals under non-Hermitian perturbations, where the Fermi surfaces can transit from 1d nodal lines to 2d twisting surfaces with Hopf-link boundaries. The topological invariants of these linked exceptional line phases are also proposed. Due to non-Hermitian skin effect, We also find a huge difference between the band structure of periodic and open boundary conditions. After complexification of the momentum in the Bloch Hamiltonian, we find the correct bulk-boundary correspondence in non-Hermitian system. The possible experimental realizations are also discussed.