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Electronic properties of FeSe can be tuned by various routes. Here, wepresent a comprehensive study on the evolution of the superconductivity andnematicity in FeSe with thickness from bulk single crystal down to bilayer($\sim$ 1.1 nm) through exfoliation. With decreasing flake thickness, both thestructural transition temperature $T_{\rm s}$ and the superconductingtransition temperature $T_{\rm c}^{\rm zero}$ are greatly suppressed. Themagnetic field ($B$) dependence of Hall resistance $R_{xy}$ at 15 K changesfrom $B$-nonlinear to $B$-linear behavior up to 9 T, as the thickness ($d$) isreduced to 13 nm. $T_{\rm c}$ is linearly dependent on the inverse of flakethickness (1/$d$) when $d\le$ 13 nm, and a clear drop of $T_{\rm c}$ appearswith thickness smaller than 27 nm. The $I$-$V$ characteristic curves inultrathin flakes reveal the signature of Berezinskii-Kosterlitz-Thouless (BKT)transition, indicating the presence of two-dimensional superconductivity.Anisotropic magnetoresistance measurements further support 2D superconductivityin few-layer FeSe. Increase of disorder scattering, anisotropic strains anddimensionality effect with reducing the thickness of FeSe flakes, might betaken into account for understanding these behaviors. Our study providessystematic insights into the evolution of the superconducting properties,structural transition and Hall resistance of a superconductor FeSe with flakesthickness and provides an effective way to find two-dimensionalsuperconductivity as well as other 2D novel phenomena.

Evolution of transport properties in FeSe thin flakes with thickness approaching the two-dimensional limit