Nodal-Line Semimetals: Emerging Opportunities for Topological Electronics and Beyond

Abstract

Topological semimetals have emerged as an important class of quantum materials with novel electronic responses and unconventional transport phenomena. Among them, nodal-line semimetals are distinguished by band crossings that extend along one-dimensional lines in momentum space rather than occurring at discrete points, forming closed loops, chains, or extended lines. The stability of these nodal structures is governed by crystalline symmetries such as mirror, spin-rotation, and nonsymmorphic operations, which give rise to characteristic topological invariants and surface states, including drumhead-like bands. In this review, we present a comprehensive overview of the theoretical framework and experimental realization of nodal-line semimetals, with particular emphasis on symmetry protection and the consequences of symmetry breaking. We discuss the classification of nodal-line structures, their evolution into other topological phases, and their signatures in electronic structure measurements and transport phenomena. Special attention is given to insights obtained from angle-resolved photoemission spectroscopy and related probes. By bringing together symmetry analysis, band topology, and experimental observations, this review aims to clarify the relationship between topology, magnetism, and measurable electronic responses in nodal-line semimetals. These considerations highlight their potential as a versatile platform for next-generation topological electronic functionalities and emergent quantum phenomena beyond conventional paradigms.

Figures (12)

• Figure 1: Schematic overview of nodal-line semimetals showing a nodal-line band crossing. Symmetry analysis explains its protection, angle-resolved photoemission spectroscopy (ARPES) visualizes the nodal lines and drumhead states, transport measurements probe electronic signatures, and resonant inelastic X-ray scattering (RIXS) provides bulk-sensitive information on elementary excitations.
• Figure 2: ARPES investigation of nodal-line semimetals. (a) Schematic illustration of the ARPES setup. Incident photons ($h\nu$) excite photoelectrons from the sample surface, and the kinetic energy and emission angles ($\theta$, $\phi$) are analyzed to reconstruct the electronic band dispersion in momentum space. (b) Comparison between a Dirac point (DP), characterized by a linear band crossing at a discrete point, and a nodal-line (NL) semimetal, where the band crossing forms a continuous closed loop in momentum space. (c) Calculated three-dimensional bulk band structure in the first Brillouin zone showing linear band crossings forming a nodal loop. Energies are referenced to $E_F$. (d) ARPES data compared with theoretical calculations, evidencing symmetry-protected degeneracy and robustness against spin--orbit coupling in ZrAs$_{2}$. (e) ARPES dispersions of LaSbTe, CeSbTe, GdSbTe, LaBiTe, and GdBiTe demonstrating SOC-induced gap opening and tunability via strain and doping. Adapted from references. fu2019diracWadge21cai2025observation
• Figure 3: (a) Crystal structure of ZrSi$X$ ($X$ = S, Se, Te), highlighting the Si square-net layer responsible for the Dirac nodal-line states. (b–d) ARPES Fermi-surface maps of ZrSiS, ZrSiSe, and ZrSiTe, showing the characteristic diamond-shaped Fermi contours in the $k_x$–$k_y$ plane and their evolution with increasing spin–orbit coupling. Adapted from references. schoop2016dirachosen2017tunability
• Figure 4: Comparison of bulk nodal-line electronic structures in Zr$X_2$ compounds. (a) Crystal structure of Zr$X_2$ ($X$ = P, As) in the nonsymmorphic Pnma structure. (b) ARPES Fermi surface of ZrP$_2$ at $k_z \approx 0$ with corresponding DFT calculation. (c,d) Bulk band dispersions of ZrP$_2$ along high-symmetry directions, showing agreement between ARPES and projected DFT bands. (e) Fermi surface of ZrAs$_2$ measured by ARPES. (f) ARPES dispersion along $\bar{Y}-\bar{\Gamma}-\bar{Y}$ revealing nodal-line crossings (NL1 and NL5). (g) Corresponding DFT band structure including spin–orbit coupling, indicating small SOC-induced gaps at the nodal lines. Panels (b–d) adapted from reference bannies2021extremelyhossain2025superconductivity
• Figure 5: ARPES spectra of (a) Fermi-surface map and schematic illustration of magnetic nodal lines at $k_z=0$, showing the location of symmetry-protected band crossings in elemental Co. (b) Experimental Fermi-surface intensity map with high-symmetry points indicated, together with a representative band dispersion. (c–k) Momentum-resolved ARPES dispersions along selected cuts, revealing the evolution of the nodal-line crossings in energy–momentum space in YMn$_2$Ge$_2$. adapted fromclark2026manifoldyang2024topological