Heesch Nodal Lines in Achiral Antiferromagnets

Previous work established that chiral antiferromagnetic crystals lacking time-reversal and parity-time (PT) symmetry host Heesch Weyl points, which are pinned at high-symmetry momenta when spin-orbit coupling is considered. In this work, we introduce Heesch nodal lines (HNLs), a novel class of symmetry-protected nodal lines emerging along high-symmetry lines in achiral antiferromagnets without T and PT symmetry. HNLs are protected by a combination of inadmissibility and achiral symmetries, and their origin in finite magnetic order fundamentally distinguishes them from Kramers nodal lines. Through a comprehensive group-theoretic analysis, we classify the magnetic little co-groups that enforce and pin HNLs. Guided by this framework and first-principles calculations, we identify both collinear antiferromagnets (e.g., MnTe and CrSb) and noncollinear antiferromagnets (e.g., Mn3GaN) as prime candidates for hosting these order-induced topological states. We also demonstrate that by gradually restoring achiral symmetries in chiral antiferromagnets that host Heesch Weyl points, HNLs annihilate these doubly degenerate points by connecting them. In addition, systems with HNLs generally exhibit high-order anomalous Hall responses, and we predict a large anomalous Hall effect arising from HNL splittings. Furthermore, the electrons near the Fermi surface are described by two-dimensional massless Dirac Hamiltonians with broken time-reversal symmetry. These can be tuned into a massive Dirac regime via strain or the Zeeman effect, thereby inducing chiral edge states consisting with other bulk conduction channels. Our work establishes a foundation for discovering exotic topological nodal-line metals in achiral antiferromagnets and significantly expands the landscape of magnetic topological materials.