Flat Topological Nodal Lines in Heavy-Fermion Compound CeCoGe$_3$

The interplay between strong electronic correlations, unconventional superconductivity, and symmetry-protected topology provides a fertile ground for discovering exotic quantum states. In this work, we investigate the correlated electronic structure and topological properties of the heavy fermion material CeCoGe$3$ using density functional theory combined with dynamical mean-field theory calculations. Our results reveal a crossover from high temperature incoherent states to low temperature coherent heavy quasiparticles, accompanied by a mass enhancement of $m^*/m{\text{DFT}}\sim 52.6$ at $T=25$ K. The interplay between electronic correlation, spin-orbit coupling and the noncentrosymmetric $I4mm$ crystal symmetry stabilize flat topological nodal lines within 10 meV of the Fermi level, which could contribute a significant density of states. The proximity of topological nodal lines to the Fermi surface suggests a potential role in mediating pressure induced unconventional superconductivity. Our work establishes CeCoGe$_3$ as a prototype topological nodal line Kondo semimetal. The coexistence of strong correlation, non-trivial band topology and superconductivity indicate CeCoGe$_3$ as a potential candidate for realizing topological superconductivity.

💡 Research Summary

In this work the authors combine density‑functional theory (DFT) with dynamical mean‑field theory (DMFT) to explore the correlated electronic structure and topological properties of the non‑centrosymmetric heavy‑fermion compound CeCoGe₃ (space group I4mm). Conventional DFT shows that Ce‑4f, Ce‑5d, Co‑3d and Ge‑4p orbitals all contribute near the Fermi level, but it fails to capture the strong on‑site Coulomb interaction of the Ce‑4f electrons. By performing temperature‑dependent DFT+DMFT calculations the authors follow the evolution from a high‑temperature incoherent regime (T = 500 K) to a low‑temperature coherent Kondo regime (T = 25 K). The imaginary part of the Matsubara self‑energy drops from ≈2.29 eV at 500 K to ≈0.125 eV at 25 K, signalling the onset of Kondo coherence around 50 K, consistent with ARPES observations. The quasiparticle weight Z≈0.019 yields an effective mass enhancement m*/m_DFT≈52.6, in line with specific‑heat (γ = 111 mJ K⁻² mol⁻¹) and de Haas‑van Alphen measurements (m* ≈ 30 m_e).

At low temperature the Ce‑4f₅/₂ manifold forms extremely flat bands within 10 meV of the Fermi energy. These flat 4f bands intersect the dispersive Co‑3d/Ge‑4p conduction bands, producing band crossings that are protected by the combination of strong spin‑orbit coupling and the crystal’s non‑centrosymmetric symmetry. Two families of nodal lines are identified: (i) essential Weyl nodal lines along the high‑symmetry paths Γ–Z and X–P, enforced by the anticommutation of a two‑fold rotation C₂z with vertical mirror operations; (ii) accidental nodal lines lying on the four vertical mirror planes (Mx, My, M₁₁₀, M₁̅₁₀), arising from the crossing of bands with opposite mirror eigenvalues (±i). Both types carry a non‑trivial Z‑topological invariant (|ξ| = 1), confirming their topological protection.

The authors construct an effective quasiparticle Hamiltonian H_QP = √Z