ARPES
/ AR-pez /
Shine a strong enough light on a metal and it spits out electrons — the same effect Einstein explained over a century ago. Now imagine catching each escaping electron and carefully noting two things: how fast it was going, and the exact direction it flew out. ARPES is built on this idea, turning a flood of ejected electrons into a detailed portrait of how electrons live inside the material.
Its full name is angle-resolved photoemission spectroscopy. Ultraviolet or X-ray light knocks electrons out of a crystal's surface; from each electron's energy and its escape angle, one can reconstruct the energy and the momentum it had while still inside. Collecting millions of these gives a direct picture of the material's band structure — the allowed energies electrons may occupy and how those energies depend on direction of motion. It can even trace the exact boundary in momentum, the Fermi surface, that separates filled states from empty ones.
This matters because band structure is the hidden script behind whether a material is a metal, an insulator, or something stranger, and ARPES is almost the only tool that reads that script straight off, without guessing. The honest caveat is that escaping electrons travel only a few atomic layers before being absorbed, so ARPES sees mainly the surface; samples must be atomically clean, ultra-cold, and freshly cleaved in high vacuum to trust that the surface still reflects the bulk.
When physicists pointed ARPES at graphene, they saw electrons arranged in a sharp cone — a 'Dirac cone' — directly confirming that electrons there race along as if they had no mass, just as theory had predicted.
Graphene's Dirac cone seen by ARPES: the technique maps energy versus momentum directly.
ARPES measures occupied states only — the electrons that are actually there to be kicked out. It cannot directly see empty states above the Fermi level, which is why it pairs naturally with techniques that probe unoccupied bands.