Transport properties and anisotropy of Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ single crystals

Single crystals of Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ are successfully synthesized with superconducting transition temperatures ${\mathrm{T}}_c\approx$ 31 – 32.5 K. A clear humplike anomaly of resistivity was observed in the normal state in the temperature region ${\mathrm{T}}_{\mathit{an}}$ of 150 K–186 K, as found in a similar system, ${\mathrm{K}}_x$Fe${}_{2-y}$Se${}_2$. It is found that the Meissner screening volume and the superconducting transition temperatures are higher for the sample with higher ${\mathrm{T}}_{\mathit{an}}$, indicating that the hump of resistivity is strongly related to the superconductivity. The upper critical field has been determined with the magnetic field along the $\mathit{ab}$ plane and $c$ axis for two typical samples with different ${\mathrm{T}}_{\mathit{an}}$, yielding an anisotropy of $\Gamma \approx$ 3.5 when ${\mathrm{T}}_{\mathit{an}}$ $=$ 150 K, while $\Gamma \approx$ 4.8 when ${\mathrm{T}}_{\mathit{an}}$ $=$ 186 K. The angle-dependent resistivity measured below ${\mathrm{T}}_c$ allow a perfect scaling feature based on the anisotropic Ginzburg–Landau theory, leading to consistent values of the anisotropy. Comparing with the anisotropy determined for Ba${}_{0.6}$K${}_{0.4}$Fe${}_2$As${}_2$ and Ba(Fe${}_{0.92}$Co${}_{0.08}$)${}_2$As${}_2$ using the same method, we find that the present sample is more anisotropic and the Fermi surfaces with stronger two-dimensional characters are expected.

Figure 1

The XRD patterns of Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ crystals indicate that the (00$l$) ($l$ $=$ 2$n$) reflections dominate the pattern.

Figure 2

(a) Temperature dependence of resistivity for the Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ crystal at zero field up to 300 K. A hump of resistivity in the normal state at around 150 K for sample 1 and 186 K for sample 2 can be clearly seen. (b) Temperature dependence of dc magnetization for both zero-field-cooling and field-cooling processes at a magnetic field of $H$ $=$ 20 Oe.

Figure 3

The temperature dependence of resistivity for the Rb${}_{0.76}$Fe${}_{1.62}$Se${}_2$ single crystal (sample 1) at zero field and under magnetic fields of (a) $H//\mathit{ab}$ and(b)$H//c$ up to 9 T with increments of 2 T.

Figure 4

The temperature dependence of resistivity for the Rb${}_{0.8}$Fe${}_{1.68}$Se${}_2$ single crystal (sample 2) at zero field and under magnetic fields of (a) $H//\mathit{ab}$ and (b) $H//c$ up to 9 T with increments of 2 T.

Figure 5

The upper critical fields with the magnetic field parallel to the $c$ axis and within the $\mathit{ab}$ plane for the two Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ single crystals.

Figure 6

Scaling of the resistivity versus $\mathrm{H̃}=H\sqrt{\sin {}^2(\theta )+{\Gamma }^2\cos {}^2(\theta )}$ at 27 K, 28 K in different magnetic fields for sample 1. The curves are measured at the same temperature but different magnetic fields are scaled nicely by adjusting the value of $\Gamma$. The inset presents the angular dependence of resistance for the Rb${}_{0.76}$Fe${}_{1.62}$Se${}_2$ single crystal (sample 1).

Figure 7

Scaling of the resistivity versus $\mathrm{H̃}=H\sqrt{\sin {}^2(\theta )+{\Gamma }^2\cos {}^2(\theta )}$ at 29 K, 30 K in different magnetic fields for sample 2. The curves are measured at the same temperature, but different magnetic fields are scaled nicely by adjusting the value of $\Gamma$. The inset presents the angular dependence of resistance for the Rb${}_{0.8}$Fe${}_{1.68}$Se${}_2$ single crystal (sample 2).

Figure 8

The comparison of anisotropy for the Rb${}_{0.76}$Fe${}_{1.62}$Se${}_2$, Rb${}_{0.8}$Fe${}_{1.68}$Se${}_2$, Ba${}_{0.6}$K${}_{0.4}$Fe${}_2$As${}_2$, and Ba(Fe${}_{0.92}$Co${}_{0.08}){}_2$As${}_2$ single crystals.