Kramers nodal lines and disorder-driven 2D Kramers–Weyl fermions in transition metal dichalcogenides monolayers

Research on the sophisticated relationship between band topology and crystal symmetries in chiral and achiral bulk crystals has led to the discovery of Kramers–Weyl points (KWPs) and Kramers nodal lines (KNLs), which host exotic Fermi surfaces and non-trivial surface states spanning the full Brillouin zone. Extending such topological features to two-dimensional (2D) materials and studying their interplay with lattice disorder are then of great fundamental and practical importance. In this work, we realize the diverse topological properties of pristine and disordered monolayers of transition metal dichalcogenides (TMD). We demonstrate that pristine 1H-TMDs host topological edge states arising from KNLs. The origin of these topological states is the non-trivial Berry curvature at the touching points of the Fermi surface pockets formed by the KNLs. We show using tight-binding analysis that the lattice disorder creates complex asymmetric electron hopping between the nearest neighbors, and can be used to control the monolayer crystal symmetries to realize KNLs and 2D KWPs. The KNLs persist when the lattice disorder is confined to the transition metal layer; however, their number and shape are significantly modified, and their edge states shift to the Fermi level. When disorder is introduced into the chalcogen layers, the symmetries protecting KNLs are broken, and KWPs with 2D dispersion form at the time-reversal invariant momentum (TRIM) points. Furthermore, the lattice disorder increases the number of TRIM points, enhancing the robustness of the KWPs edge states. These 2D KWPs are enclosed by non-trivial Fermi surfaces and carry a finite chiral charge protected by time-reversal symmetry and Kramers degeneracy. Our findings unveil hidden topological properties in TMD monolayers and propose lattice disorder as a route for realizing KNLs and 2D KWPs edge states. The proposed lattice disorder ideas can be extended to other 2D materials, offering new directions for realizing exotic quantum phenomena in monolayer systems.