Nonlinear uniaxial pressure dependence of $T_c$ in iron-based superconductors

We have systematically studied the effects of in-plane uniaxial pressure $p$ on the superconducting transition temperature $T_c$ in many iron-based superconductors. The change of $T_c$ with $p$ is composed of linear and nonlinear components. The latter can be described as a quadratic term plus a much smaller fourth-order term. In contrast to the linear component, the nonlinear $p$ dependence of $T_c$ displays a pronounced in-plane anisotropy, which is similar to the anisotropic response of the resistivity to $p$. As a result, it can be attributed to the coupling between the superconducting and nematic orders, in accordance with the expectations of a phenomenological Landau theory. Our results provide direct evidences for the interplay between nematic fluctuations and superconductivity, which may be a common behavior in iron-based superconductors.

Figure 1

(a) Uniaxial pressure dependence of the resistance for ${\mathrm{BaFe}}_{1.9}{\mathrm{Ni}}_{0.1}{\mathrm{As}}_2$ with $p$ along the (100) direction. The temperature varies from 20 to 19.2 K with a step of 0.05 K as shown by the arrow. (b) Similar to panel (a) but for $p$ along the (110) direction. The temperature varies from 20.3 to 19.6 K with a step of 0.05 K. [(c), (d)] Converted temperature dependence of the resistance for $p$ along the (100) and (110) directions at 12 and $-12$ MPa, respectively. The reason why $T_c$ of these two samples are different is because the current densities are different in the measurements due to their different cross sections. (e) Uniaxial pressure dependence of $\mathrm{\Delta }{T}_c$ along the (100) (circles) and (110) (squares) directions. (f) Uniaxial pressure dependence of $\mathrm{\Delta }{T}_c^{nl}$ along the (100) (circles) and (110) (squares) directions. The solid line for the case $p\parallel \left(110\right)$ is fitted as described in the main text.

Figure 2

[(a)–(c)] Uniaxial pressure dependence of $\mathrm{\Delta }{T}_c$ along the (100) (circles) and (110) (squares) directions for $x=0.13$, 0.16, and 0.2, respectively. [(d)–(f)] Uniaxial pressure dependence of $\mathrm{\Delta }{T}_c^{nl}$ for $x=0.13$, 0.16, and 0.2, respectively. The lines are the fitted results as described in the main text.

Figure 3

[(a)–(f)] Uniaxial pressure dependence of $\mathrm{\Delta }{T}_c$ (left panels) and $\mathrm{\Delta }{T}_c^{nl}$ (right panels) for the optimally doped ${\mathrm{Ba}}_{0.67}{\mathrm{K}}_{0.33}{\mathrm{Fe}}_2{\mathrm{As}}_2$ [(a), (b)], ${\mathrm{KFe}}_2{\mathrm{As}}_2$ [(c), (d)], and ${\mathrm{LaFeAsO}}_{0.74}{\mathrm{F}}_{0.26}$ [(e), (f)]. The circles and squares correspond to pressure along the (100) and (110) directions, respectively. The solid lines are fitted results as described in the main text. The inset in panel (d) shows the temperature dependence of ${\chi }_n$, which is proportional to the change of resistivity under $p$ as reported previously [9, 10].

Figure 4

The linear coefficient $B$ and the quadratic coefficient $C$ in ${\mathrm{BaFe}}_{2\text{−}x}{\mathrm{Ni}}_x{\mathrm{As}}_2$ (circles), ${\mathrm{Ba}}_{0.67}{\mathrm{K}}_{0.33}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (squares), ${\mathrm{KFe}}_2{\mathrm{As}}_2$ (diamonds), and ${\mathrm{LaFeAsO}}_{0.74}{\mathrm{F}}_{0.26}$ (hexagons). The open and solid symbols correspond to $p$ parallel to (100) and (110) directions, respectively. The error bars are estimated by considering the uncertainties from measurements of the cross sections, the zero-pressure positions, and the fitting processes.

Figure 5

The quartic coefficient $D$ in BFNA, BKFA, KFA, and LFAOF. The circles and square symbols correspond to uniaxial pressure $p$ parallel to (100) and (110) directions, respectively.

Figure 6

(a) Uniaxial pressure dependence of resistance for optimal doping Bi-2212 with pressure $p$ along the (100) direction near superconducting transition temperature. The temperature varies from 91 to 88 K with a step of 0.1 K indicated by right gradient arrow. (b) Similar to panel (a) but for $p$ along (110) direction. Temperature varies from 94 to 90.5 K with 0.1-K step. Note that the orthorhombic notation is used. (c) Temperature dependence of resistance subtracted from panels (a) and (b) at $p=0$ Mpa. Although the two samples are cut from same batch, the $T_c$'s are slightly different, which mainly comes from their different current densities. (d) Uniaxial pressure dependence of $\mathrm{\Delta }R$ with pressure along (100) (blue circles) and (110) (red squares) directions. The specific temperatures are the maximum temperature of $dR/dT$ with $T=$ 89.9 and 91.4 K, respectively.

Figure 7

(a) Uniaxial pressure dependence of $\mathrm{\Delta }{T}_c$ along (100) (circles) and (110) (squares) directions. (b) Uniaxial pressure dependence of $\mathrm{\Delta }{T}_c^{nl}$ along (100) (circles) and (110) (squares) directions.