  The magnetotransport behaviour inside the nematic phase of bulk FeSe reveals
unusual multiband effects that cannot be reconciled with a simple two-band
approximation proposed by surface-sensitive spectroscopic probes. In order to
understand the role played by the multiband electronic structure and the degree
of two-dimensionality we have investigated the electronic properties of
exfoliated flakes of FeSe by reducing their thickness. Based on
magnetotransport and Hall resistivity measurements, we assess the mobility
spectrum that suggests an unusual asymmetry between the mobilities of the
electrons and holes with the electron carriers becoming localized inside the
nematic phase. Quantum oscillations in magnetic fields up to 38 T indicate the
presence of a hole-like quasiparticle with a lighter effective mass and a
quantum scattering time three times shorter, as compared with bulk FeSe. The
observed localization of negative charge carriers by reducing dimensionality
can be driven by orbitally-dependent correlation effects, enhanced interband
spin-fluctuations or a Lifshitz-like transition which affect mainly the
electron bands. The electronic localization leads to a fragile two-dimensional
superconductivity in thin flakes of FeSe, in contrast to the two-dimensional
high-Tc induced with electron doping via dosing or using a suitable interface.
