The phenomenon that best supports the theory that matter has a wave nature is the diffraction of electrons.

Here's why:

* Diffraction is a wave phenomenon where waves bend around obstacles or spread out through openings. It's a characteristic behavior of waves, not particles.

* Electrons were initially thought to be particles. However, experiments like the Davisson-Germer experiment showed that electrons can diffract when passed through a crystal lattice. This diffraction pattern is characteristic of waves, not particles.

This evidence strongly suggests that matter, including electrons, can exhibit wave-like properties. This concept is fundamental to quantum mechanics, which describes the behavior of matter at the atomic and subatomic level.