2023 Volume 78 Issue 1 Pages 4-12
X-ray Compton scattering is a powerful technique to measure the electron momentum distribution in the full Brillouin zone and thus the full shape of the Fermi surface. Here, we review a historical overview about Compton scattering, explain why it detects the electron momentum distribution, provide several examples of Fermi surface measurements, make a comparison with other techniques such as quantum oscillation and angle-resolved photoemission spectroscopy, and introduce a recent progress to reveal the shape of the Fermi surface in high-temperature cuprate superconductors and also other progresses.