Superconductor-Insulator Quantum Phase Transition in Disordered FeSe Thin Films

The evolution of two-dimensional electronic transport with increasing disorder in epitaxial FeSe thin films is studied. Disorder is generated by reducing the film thickness. The extreme sensitivity of the films to disorder results in a superconductor-insulator transition. The finite-size scaling analysis in the critical regime based on the Bose-glass model strongly supports the idea of a continuous quantum phase transition. The obtained value for the critical-exponent product of approximately $7/3$ suggests that the transition is governed by quantum percolation. Finite-size scaling with the same critical-exponent product is also substantiated when the superconductor-insulator transition is tuned with an applied magnetic field.

Figure 1

(a) Variation of the resistivity ${\rho }_0$ at $T=0$ (left-hand scale) and the residual resistivity ratio RRR (right-hand scale) with the film thickness $t$ on a log scale. The dashed lines are guides to the eye. The bars indicate the spread of the data in the saturation region above 300 nm. (b) Dependence of the resistive midpoint $T_c$ on $t$. The bars represent the 10%-to-90% transition widths. The dashed line is a Cooper-law fit to the data points below 300 nm.

Figure 2

Temperature dependence of the sheet resistance $R_s$ per Fe-Se sheet with the mean film thickness $t$ as a parameter. The curves are labeled from bottom to top by $a$ to $l$ corresponding to $t=1300$, 800, 263, 95, 80, 64, 29, 20, 19, 10, 2, and 1 nm, respectively. The inset shows $R_s(B,T)$ with an applied magnetic field $B$ perpendicular to the plane of a 30 nm thick film as the tuning parameter. The values of $B$ are 0, 1, 3, 5, 7, 8.5, 8.9, 9.3, 9.8, 10.5, 11, 12, 13, and 14 T (from bottom to top).

Figure 3

Finite-size scaling analysis at nonzero temperatures of the negative film-thickness derivative of the sheet resistance $R_s$ per Fe-Se sheet, $-\partial R_s/\partial t$, evaluated at the critical thickness $t_c$ for $T<10\mathrm{K}$ on a log-log scale. The solid line up to 6.5 K is a linear least-square fit. Its slope gives an exponent product $z\nu =2.33\pm 0.03$. The inset shows the thickness dependence of $R_s$ for temperatures of 2, 4, 6, and 8 K. The plot serves to determine the critical thickness $t_c=19.5\mathrm{nm}$ (vertical arrow) and the critical resistance $R_c=19.8\mathrm{k}\Omega$ (horizontal arrow). Below $t_c$, $R_s$ decreases with increasing temperature (insulating regime). Above $t_c$, $R_s$ increases with increasing temperature (metallic regime).

Figure 4

$R_s(B,T)$ (cf. inset of Fig. 2) normalized to the critical value $R_c$ versus the magnetic-field scaling variable $|B-B_c|/T^{1/z\nu }$ ($B_c=8.92\mathrm{T}$, $z\nu =2.33$) for 9 temperatures between 1.2 and 2 K, and 29 values of the magnetic field from 0 to 14 T. The lower and upper branches take into account the change in sign of $B-B_c$ and are identified with $B<B_c$ and $B>B_c$, respectively. The intersection point of the isotherms between 1.2 and 2 K in steps of 0.1 K in the inset reveals the critical values of $B_c=8.92\mathrm{T}$ (vertical arrow) and $R_c=10.4\mathrm{k}\Omega$ (horizontal arrow)