Tunable Octdong and Spindle-Torus Fermi Surfaces in Kramers Nodal Line Metals

Abstract

Abstract Kramers nodal lines are doubly degenerate band crossings in achiral non-centrosymmetric crystals, arising from spin-orbit coupling and connecting time-reversal invariant momenta. When intersecting the Fermi level, they generate exotic three-dimensional Fermi surfaces, in some cases described by two-dimensional massless Dirac fermions, enabling enhanced graphene-like physics such as quantized optical conductivity and large anomalous Hall effects. However, no experimental realization of such materials has been reported. Here, we identify Kramers nodal line metals beyond the case of Fermi surfaces enclosing a single time-reversal invariant momentum. Using angle-resolved photoemission spectroscopy and first-principles calculations, we show that 3R-TaS 2 and 3R-NbS 2 host open Octdong and Spindle-torus Fermi surfaces, respectively. We observe a filling-controlled transition between these configurations and evidence of size quantization in 3R-TaS 2 inclusions within 2H-TaS 2 . We further predict a strain- or pressure-driven transition to a conventional metal. Our results establish 3R transition-metal dichalcogenides as a tunable platform for Kramers nodal line physics.