Three-dimensional electron realm in VSe2 by soft-x-ray photoelectron spectroscopy: origin of charge-density waves.

The resolution of angle-resolved photoelectron spectroscopy (ARPES) in three-dimensional (3D) momentum k is fundamentally limited by ill defined surface-perpendicular wave vector k(perpendicular to) associated with the finite photoelectron mean free path. Pushing ARPES into the soft-x-ray energy region sharpens the k(perpendicular to) definition, allowing accurate electronic structure investigations in 3D materials. We apply soft-x-ray ARPES to explore the 3D electron realm in a paradigm transition metal dichalcogenide VSe2. Essential to break through the dramatic loss of the valence band photoexcitation cross section at soft-x-ray energies is the advanced photon flux performance of our synchrotron instrumentation. By virtue of the sharp 3D momentum definition, the soft-x-ray ARPES experimental band structure and Fermi surface of VSe2 show a textbook clarity. We identify pronounced 3D warping of the Fermi surface and show that its concomitant nesting acts as the precursor for the exotic 3D charge-density waves in VSe2. Our results demonstrate the immense potential of soft-x-ray ARPES to explore details of 3D electronic structure.