  Forcing systems though fast non-equilibrium phase transitions offers the
opportunity to study new states of quantum matter that self-assemble in their
wake. Here we study the quantum interference effects of correlated electrons
confined in monolayer quantum nanostructures, created by femtosecond
laser-induced quench through a first-order polytype structural transition in a
layered transition-metal dichalcogenide material. Scanning tunnelling
microscopy of the electrons confined within equilateral triangles, whose
dimensions are a few crystal unit cells on the side, reveals that the
trajectories are strongly modified from free-electron states both by electronic
correlations and confinement. Comparison of experiments with theoretical
predictions of strongly correlated electron behaviour reveals that the
confining geometry destabilizes the Wigner/Mott crystal ground state, resulting
in mixed itinerant and correlation-localized states intertwined on a length
scale of 1 nm. Occasionally, itinerant-electron states appear to follow quantum
interferences which are suggestive of classical trajectories (quantum scars).
The work opens the path toward understanding the quantum transport of electrons
confined in atomic-scale monolayer structures based on
correlated-electron-materials.
