The discovery of Kramers nodal line metals (KNLMs) and Kramers Weyl semimetals (KWSs) has significantly expanded the range of metallic topological materials to all noncentrosymmetric crystals. However, a key characteristic of this topology—the presence of topologically protected surface states in KNLMs—remains unclear. In this work, by constructing a $C_{1v}$ symmetric KNLM model with curved Kramers nodal lines (KNLs), we show that the Fermi-arc-like surface states (FALSSs), with a ${\mathbb{Z}}_2$ topological origin, can appear on the boundary surfaces parallel to the mirror plane. These states connect two surface momenta, corresponding to the projections of two touching points on the Fermi surfaces. Notably, upon gradually breaking achiral symmetries such as mirror and roto-inversion, the KNLM phase evolves into a KWS phase, allowing the FALSSs to evolve continuously into the Fermi arc states of the KWS. Conditions for the emergence of FALSSs in KNLMs with straight KNLs are also analyzed. Through bulk-boundary correspondence, we clarify the topological nature of KNLMs.

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• Surface states
• Topological materials
• Nodal-line semimetals
• Weyl semimetal
• Discrete symmetries in condensed matter
• Tight-binding model
• k dot p method