Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals

We consider the impact of disorder on the spectrum of three-dimensional nodal-line semimetals. We show that the combination of disorder and a tilted spectrum naturally leads to a non-Hermitian self-energy contribution that can split a nodal line into a pair of exceptional lines. These exceptional lines form the boundary of an open and orientable bulk Fermi ribbon in reciprocal space on which the energy gap vanishes. We find that the orientation and shape of such a disorder-induced bulk Fermi ribbon is controlled by the tilt direction and the disorder properties, which can also be exploited to realize a twisted bulk Fermi ribbon with nontrivial winding number. Our results put forward a paradigm for the exploration of non-Hermitian topological phases of matter.

Figure 1

(a)–(d) The real part of the energy spectrum above (orange) and below (blue) the nodal-ring energy is presented as a function of $k_x$ and $k_y$ (with $k_z=0$), according to Eqs. (2), (7), (9), and (10), for a type-I nodal-line semimetal (NLSM) (a) without tilt and (b) with radial tilt, a type-II NLSM with (c) radial tilt and (d) axial tilt with first-order Born self-energy correction due to disorder. (e) The bulk Fermi ribbons of a disordered type-II NLSM with (left) axial tilt, (top) radial tilt, (bottom) axial and radial tilt, and (right) a twisting tilt vector with winding number equal to one. The nodal ring and exceptional lines are indicated in black, the bulk Fermi ribbon in red, and the tilt direction by the green arrows.

Figure 2

The spectrum of a disordered type-II nodal-line semimetal with strong axial tilt (along $k_z$), according to the self-energy correction of Eq. (10), evaluated close to the nodal ring with $k_z=0$. We have considered the following toy model parameters: $w_z/v=10, \gamma =100, v=1, Q=1, k_{\mathrm{C}}=0.5$.