We report the electronic structure of the kagome compound ${\mathrm{LuNb}}_6{\mathrm{Sn}}_6$ using high-field torque magnetometry and first-principles calculations. This compound hosts a kagome lattice of Nb atoms and undergoes a charge density wave (CDW) transition below 70 K, accompanied by the formation of a $\sqrt{3}\times \sqrt{3}\times 3$ superlattice modulation [B. R. Ortiz et al., J. Am. Chem. Soc. 147, 5279 (2025)]. Torque measurements up to 41 T reveal pronounced de Haas-van Alphen (dHvA) oscillations for magnetic fields applied along both polar (ac-plane) and azimuthal (ab-plane) directions. The frequency spectra exhibit multiple branches, with the highest frequency reaching nearly 2500 T when the field is applied along the $c$ direction. To map the Fermi surface topology, we performed angle-dependent measurements with the magnetic field rotated in both polar and azimuthal directions. The frequencies vary systematically with polar angle while remaining nearly unchanged with azimuthal angle, indicating a quasi-two-dimensional Fermi surface. To further understand the experimental results, we carried out density functional theory calculations of the electronic structure and Fermi surface for both the pristine and CDW phases. While the dHvA frequencies calculated for the pristine structure fail to reproduce the experimental spectrum, those obtained for the CDW phase are in good agreement with the measured frequencies. These results establish a direct link between the observed quantum oscillations and the reconstructed Fermi surface of ${\mathrm{LuNb}}_6{\mathrm{Sn}}_6$ and provide important insights into the electronic structure of this and related kagome materials.

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• Charge density waves
• Electronic structure
• Fermi surface
• Magnetotransport
• Kagome lattice
• Density functional calculations
• Torque magnetometry
• de Haas-van Alphen effect