  Despite decades of research in spatially confined superconducting systems to
understand the modification of superconductivity from reduced length scales,
the investigation of the quantum confinement effect on high-temperature
superconductors remains an outstanding challenge. Here, we report scanning
tunneling spectroscopy measurements on laterally confined FeSe monolayers on
SrTiO3 substrates, which are formed by epitaxially growing FeSe films with a
coverage less than one unit cell. Comparing to the uniform regions of FeSe
monolayers, the peninsula regions at the monolayer boundary exhibit reduced
Fermi energy and undiminished superconductivity, leading to a putative
crossover from a Bardeen-Cooper-Schrieffer state to a Bose-Einstein condensate
state. In isolated FeSe monolayer islands, superconductivity is shown to exist
in samples of smaller volume in contrast to conventional superconductors, while
the validity of Anderson's criterion remains fulfilled. Our work reveals
lateral quantum confinement effects in unconventional superconductors, to
enrich the understanding of high-temperature superconductivity in
low-dimensional systems.
