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

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

Figure 1

(a) Optical image of few-layer flakes of FeSe cleaved onto thermally evaporated ${\mathrm{Al}}_2{\mathrm{O}}_3$ thin film (thickness $\sim 80$ nm). FeSe/${\mathrm{Al}}_2{\mathrm{O}}_3$ stack is supported on a PDMS substrate. Image was taken in transmission mode. Number of layers is labeled on selected flakes. Scale bar, $20\mu \mathrm{m}$. (b) Transmittance as a function of the number of layers. The transmittance (red dots) follows the Beer-Lambert law (blue line). (c) The thickness of a seven-layer FeSe is about 4 nm. The inset shows an optical image of a seven-layer FeSe device capped with a thin layer ($\sim 15$ nm) of $h$-BN. Scale bar, $10\mu \mathrm{m}$. (d) A schematic illustration of the FeSe thin flake device.

Figure 2

(a) Temperature dependence of the normalized resistance $R(T$)/$R$(200 K) for a bulk crystal and thin flakes with different thickness. The thinnest thickness is about 2.2 nm (4L). The arrows indicate the kink in the resistance curve, which corresponds to the structural transition ($T_{\mathrm{s}}$). (b) Temperature dependence of the normalized derivative of resistance, $dR$/$dT$, for the bulk crystal and thin flakes in (a). The arrows indicate the position of the structural transition, which is determined by the midpoint of the step-like anomaly of $dR$/$dT$. Note that the curves in (a) and (b) are shifted by 0.5 for clarity. (c) The details of normalized resistance $R(T$)/$R$(15 K) with temperature range from 2 to 15 K for watching the superconducting transition. The $T_{\mathrm{c}}^{\mathrm{onset}}$ is determined from the cross point of two red dash lines. $T_{\mathrm{c}}^{\mathrm{mid}}$ is defined as the temperature at which resistance reaches half the value of normal state. $T_{\mathrm{c}}^{\mathrm{zero}}$ is defined as the temperature at which resistance reaches zero. The same color is used for the same thickness in (a)–(c). (d) Temperature dependence of the resistance for bilayer and trilayer flakes.

Figure 3

[(a) and (b)] The evolution of the magnetic-filed dependent Hall resistance $R_{xy}$ with different thickness at $T=15$ K. (c) Thickness dependence of carrier density $n$ at 15 K. The error bars are defined as the standard deviations of measurements.

Figure 4

(a) Structural transition temperature and superconducting transition temperature as a function of thin flakes thickness $d$. (b) The $T_{\mathrm{c}}^{\mathrm{zero}}$ as a function of the inverse of the flakes thickness 1/$d$.

Figure 5

(a) The $V\text{−}I$ relationship at different temperatures in superconducting regime for hexalayer FeSe flake. The curves are plotted on logarithmic scale. The two black dashed lines refer to $V\sim I$ and $V\sim I^3$, respectively. (b) The variation of exponent $\alpha$ as a function of temperature, extracting from the power-law fittings in (a), showing that $T_{\mathrm{BKT}}=3.52$ K. (c) The $R\left(\mathrm{T}\right)$ curve plotted with the $\left[d\ln \right(R$)/${dT]}^{-2/3}$ scale. The dashed line shows the fitting to the Halperin-Nelson formula $R\left(\mathrm{T}\right)=R_0\exp [-b/{(T-T_{\mathrm{BKT}})}^{1/2}$] with $T_{\mathrm{BKT}}=3.59$ K.

Figure 6

[(a) and (b)] Temperature-dependent resistance under a constant out-of-plane and in-plane magnetic field. (c) Temperature-dependent $H_{\mathrm{c}2}$ with magnetic field applied along out-of-plane (red) and in-plane (black) directions. Dashed curves are theoretical curves obtained from the 2D Ginzburg-Landau equations.