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Electronic structure of crystalline materials is their fundamentalcharacteristic which is the basis of almost all their physical and chemicalproperties. Angle-resolved photoemission spectroscopy (ARPES) is the mainexperimental tool to study all electronic structure aspects with resolution ink-space. However, its application to three-dimensional (3D) materials suffersfrom a fundamental problem of ill-defined surface-perpendicular wavevector kz.Here, we achieve sharp definition of kz to enable precise navigation in 3D kspace by pushing ARPES into the soft-X-ray photon energy range. Essential tobreak through the notorious problem of small photoexcitation cross-section wasan advanced photon flux performance of our instrumentation. We explore theelectronic structure of a transition metal dichalcogenide VSe2 which developscharge density waves (CDWs) possessing exotic 3D character. We experimentallyidentify nesting of its 3D Fermi surface (FS) as the precursor for these CDWs.Our study demonstrates an immense potential of soft-X-ray ARPES (SX-ARPES) toresolve various aspects of 3D electronic structure.

Three-Dimensional Fermiology by Soft-X-Ray ARPES: Origin of Charge Density Waves in VSe2