Abrupt recovery of Fermi-liquid transport following the collapse of the $c$ axis in CaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ single crystals

Single crystals of CaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ are found to exhibit the tetragonal (T) to collapsed-tetragonal (cT) transition at $T_{\mathrm{cT}}\lesssim 100$ K for $x>0.05$. The $c$-axis shrinks by $~9\%$ below $T_{\mathrm{cT}}$, which substantially diminishes the interband nesting between the hole and electron bands. In sharp contrast to the superconducting T phase of $A$Fe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ ($A=$ Ba, Sr), where the anomalous non-Fermi liquid transport properties are observed, the resistivity, Hall coefficient, and magnetoresistance data in the Ca-based system all indicate that the standard Fermi liquid behaviors are recovered abruptly below $T_{\mathrm{cT}}$, and the superconductivity disappears completely. The simultaneous disappearance of the superconductivity and the non-Fermi liquid transport enlightens the essential role of interband-associated fluctuations to the superconductivity in Fe pnictides.

Figure 1

(a) ${\rho }_{\mathit{xx}}(T)$ curves of CaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ in zero field. The inset is an optical photograph of a crystal. (b) Comparison of ${\rho }_{\mathit{xx}}(T)$ curves for nonmagnetic $A$Fe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ ($A=\mathrm{Ba}$, Sr, Ca) near the end point of the SDW ordered phase. (c) $R_H(T)$ at 5 T for various $x$. (d) $x$ dependence of $a$ and $c$ axes lengths, the $z$ coordinate of pnictogen ($z_{\mathrm{Pn}}$) and it’s height $h_{\mathrm{Pn}}$ from the two-dimensional Fe plane, and As-Fe-As bond angle.

Figure 2

(a) Temperature dependence of $a$ and $c$ axis length of $x\approx 5.5\%$ sample, which shows pure cT phase. Inset shows schematic crystal structure. (b–d) Temperature dependence of $c/a$ ratio $z_{\mathrm{Pn}}$, the pnictogen height $h_{\mathrm{Pn}}$, and the tetrahedral angle $\alpha$ ($\beta$) of the same crystal. The collapsed lattice constants at 10 K are $a=3.981(15)$ Å, $c=10.670(38)$ Å, and $z_{\mathrm{Pn}}=0.3671(7)$. The $c$ axis reduces by $~9\%$ and the $a$ axis expands by $~2\%$ from room temperature values. (e, f) Fermi surfaces of $x\approx 5.5\%$ sample at (e) 300 and (f) 10 K calculated by using the experimental lattice parameters.

Figure 3

$T$–$x$ phase diagram of CaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$. The open circles show the T to O phase transition at $T_0$. The closed black circles show $T_{\mathrm{SDW}}$, where ${\rho }_{\mathit{xx}}(T)$ show reductions due to the reduced scattering. The solid down (up) triangles show the T to cT phase transition temperatures $T_{\mathrm{cT}}$ ($T_{\mathrm{cT}}^{*}$), where ${\rho }_{\mathit{xx}}(T)$ shows a jump in cooling (warming) processes. The onset of superconductivity $T_c^{\mathrm{on}}$ and the zero resistivity temperature $T_c^{\mathrm{zero}}$ are shown as closed blue and open red squares.

Figure 4

(a) ${\rho }_{\mathit{xx}}$ and $-R_H$ of $x\approx 5.5\%$ sample plotted against $T^2$. The inset shows ${\rho }_{\mathit{xx}}$ vs. $T^{1.5}$. (b) MR at different temperatures and (c) the Kohler’s plot. Inset in (b) shows the temperature dependence of MR at 14 T.