  Pursuing the confinement of linearly dispersive relativistic fermions is of
interest in both fundamental physics and potential applications. Here, we
report strong STM evidence for the equally spaced, strikingly sharp, and
densely distributed quantum well states (QWSs) near Fermi energy in Pb(111)
nanoislands, van-der-Waals epitaxially grown on graphitized 6H-SiC(0001). The
observations can be explained as the quantized energies of confined linearly
dispersive [111] electrons, which essentially 'simulate' the out-of-plane
relativistic quasiparticles. The equally spaced QWSs with an origin of confined
relativistic electrons are supported by phenomenological simulations and
Fabry-Perot fittings based on the relativistic fermions. First-principles
calculations further reveal that the spin-orbit coupling strengthens the
relativistic nature of electrons near Fermi energy. Our finding uncovers the
unique equally spaced quantum states in electronic systems beyond Landau
levels, and may inspire future studies on confined relativistic quasiparticles
in flourishing topological materials and applications in structurally simpler
quantum cascade laser.
