Non-Hermitian Hopf-link exceptional line semimetals

We study a new class of non-Hermitian topological phases in three dimensions in the absence of any symmetry, where the topological robust band degeneracies are Hopf-link exceptional lines. As a concrete example, we investigate the non-Hermitian band structures of nodal line semimetals under non-Hermitian perturbations, where the Fermi surfaces can transit from one-dimensional nodal lines to two-dimensional twisting surfaces with Hopf-link boundaries when the winding number defined along the nodal line is ±1 . The linking numbers of these linked exceptional line phases are also proposed, based on the integral of Chern-Simons form over the Brillouin zone.