Origin of a shallow electron pocket: $β$-band in Co$_{1/3}$TaS$_2$ studied by angle-resolved photoemission spectroscopy

We investigate the electronic structure and Fermi surface of Co$_{1/3}$TaS$_2$ using angle-resolved photoemission spectroscopy (ARPES) combined with theoretical modeling beyond standard density functional theory (DFT+U). A shallow electron pocket, the so-called $β$ feature, is observed at the Fermi level near the corner of the superlattice Brillouin zone, representing the first experimental observation of this feature in an intercalated TaS$2$ compound. Similar pockets have been reported in $X{1/3}$NbS$2$ ($X$ = Co, Cr, Ni), where their surface versus bulk origin remains actively debated. Because conventional DFT+U does not capture this feature, we employ cluster perturbation theory (CPT) to incorporate an explicit treatment of strong electron correlations ($U$) on the Co sites. CPT successfully reproduces the $β$ feature, demonstrating its origin from correlation-driven bulk states rather than surface effects. To further substantiate this conclusion, we studied a reduced Co-content sample, Co${0.22}$TaS$_2$, where the reduced charge transfer modifies the Co-derived states near the Fermi level. Its electronic structure remains largely similar to that of pristine 2H-TaS$_2$, showing only a minor overall energy shift and lacking the $β$ feature, consistent with disrupted long-range Co ordering and modified orbital character near the Fermi level. We demonstrate that the $β$ feature arises from strong local correlations on the Co sites and requires long-range crystallographic order among intercalated Co atoms to maintain coherence. These results highlight the importance of strong electronic correlations in magnetically intercalated transition-metal dichalcogenides and provide a microscopic understanding of features not captured by conventional DFT+U.

💡 Research Summary

In this work the authors investigate the low‑energy electronic structure of the magnetically intercalated transition‑metal dichalcogenide Co₁⁄₃TaS₂ by combining high‑resolution angle‑resolved photoemission spectroscopy (ARPES) with advanced many‑body calculations that go beyond the static mean‑field treatment of DFT + U. ARPES measurements performed at 20 K (well below the antiferromagnetic transition at T_N ≈ 37 K) reveal the familiar double‑cylindrical Fermi‑surface sheets of the host 2H‑TaS₂ (α₁, α₂ around Γ and γ₁, γ₂ around K) together with an additional triangular electron pocket centred at the K point of the superlattice Brillouin zone. This pocket, referred to as the β feature, is a shallow electron‑like band that lies essentially at the Fermi level. Its intensity is essentially unchanged when the temperature is raised above T_N or when the photon energy is varied, indicating that it is not a surface resonance but a bulk electronic state.

Standard DFT + U calculations, even when the on‑site Hubbard interaction on Co (U ≈ 5.8 eV, obtained from linear‑response constrained DFT) is included, reproduce the main Ta‑derived bands but completely miss the β band. To capture the missing physics the authors construct a Wannier‑function representation of the DFT + U band structure and embed it in a cluster‑perturbation theory (CPT) framework. Each cluster contains four Wannier sites (three Ta‑derived interstitial orbitals forming a triangle and one Co‑centered orbital). The Hubbard U is applied explicitly to the Co orbital, and the cluster Hamiltonian is solved exactly; inter‑cluster hopping is treated perturbatively, yielding a momentum‑resolved Green’s function that can be unfolded to the extended Brillouin zone for direct comparison with ARPES.

CPT reproduces the β pocket with remarkable fidelity: a narrow, resonance‑like band appears at K, matching the experimental dispersion and spectral weight. The calculation shows that strong local correlations on the Co sites renormalize the Co‑Ta hybridization, pulling Co‑derived states toward the Fermi level and creating the shallow electron pocket. This mechanism is consistent with earlier slave‑boson and DMFT studies but provides a more exact treatment of spatial correlations.

To test the role of long‑range Co ordering, the authors also study an under‑doped crystal with only 22 % Co (Co₀․₂₂TaS₂). This sample shows a non‑metallic resistivity, a ferromagnetic‑like transition near 25 K, and, most importantly, the complete absence of the β pocket in ARPES. Its band structure closely resembles that of pristine 2H‑TaS₂, apart from a modest overall energy shift. The disappearance of the β feature in the Co‑deficient material demonstrates that coherent Co‑derived bands require the √3 × √3 superlattice order; disorder in the intercalant lattice destroys the momentum‑coherent hybridization necessary for the correlation‑driven pocket.

Overall, the paper establishes three essential ingredients for the β band: (i) a well‑ordered √3 × √3 Co superlattice, (ii) strong on‑site Coulomb repulsion on the Co 3d orbitals, and (iii) enhanced Co‑Ta hybridization that is amplified by the correlations. The work highlights that features missed by conventional DFT + U can be recovered by explicitly treating local many‑body effects, and it provides a clear microscopic picture of how intercalant‑derived states shape the low‑energy electronic structure of magnetic TMDs. The combined ARPES‑CPT methodology offers a powerful route to resolve surface versus bulk controversies in other intercalated dichalcogenides and underscores the pivotal role of electronic correlations in designing spintronic materials based on layered compounds.