Superconducting gap symmetry of the ${\mathrm{BiS}}_2$-based superconductor ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\text{BiSSe}$ elucidated through specific heat measurements

In this study, the superconducting gap symmetry of ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$ is elucidated through specific heat measurements with one single crystal of ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$. A clear jump is observed at 3.95 K in ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$, suggesting bulk superconductivity. From specific heat measurements, $\mathrm{\Delta }{C}_{\mathrm{e}}/\gamma T_{\mathrm{c}}$ and $2\mathrm{\Delta }\left(0\right)/k_{\mathrm{B}}{T}_{\mathrm{c}}$ are obtained as 2.31 and 4.5. These values indicate strong electron-phonon coupling superconductivity. The temperature $\left(T\right)$ and magnetic-field $\left(H\right)$ dependence of the electronic specific heat $C_{\mathrm{e}}(T,H)$ suggests that superconductivity is fully gapped. Our handmade system successfully elucidates superconducting gap symmetry of the ${\mathrm{BiS}}_2$-based compound with a small single crystal.

Figure 1

(a) Crystal structure of the ${\mathrm{BiS}}_2$-based compounds. (b) Single crystal of the ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$ (0.42 mg). (c) $T$ dependence of the electrical resistivity $\rho \left(T\right)$ of ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ and ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$ down to 0.5 K. (d) Setup for specific heat measurements using our handmade calorimeter.

Figure 2

$T$ dependence of the specific heat $C\left(T\right)$ divided by $T$ of background and raw data including sample and background of (a) ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ and (b) ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$ in zero magnetic field. $T$ dependence of the electrical resistivity $\rho \left(T\right)$ of (c) ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ and (d) ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$ in zero magnetic field. $T$ dependence of the specific heat $C\left(T\right)$ divided by $T$ of (e) ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ and (f) ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$ in zero magnetic field.

Figure 3

(a) $T$ dependence of the specific heat $C\left(T\right)$ divided by $T$ of ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$ in magnetic fields of 0, 0.2, and 1 T. The dotted line is the fitting result of $C/T=\gamma +\beta T^2+\delta T^4$. The inset shows the $T^2$ dependence of $C\left(T\right)/T$ at the low-temperature region. (b) Electronic specific heat $C_{\mathrm{e}}\left(T\right)$ divided by $T$. The solid line shows the theoretical calculation of the $\alpha$ model. The dotted lines represent the calculated BCS curve assuming a weak-coupling limit. The inset shows the $H$ dependence of the electronic specific heat $C_{\mathrm{e}}\left(H\right)$ divided by $T$ at 0.5 K.

Figure 4

$T$ dependence of the upper critical field $H_{\mathrm{c}2}\left(T\right)$ of ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$ for (a) $H\left|\right|ab$ and (b) $H\left|\right|c$. The inset shows the $T$ dependence of the electrical resistivity $\rho \left(T\right)$ normalized at ${\rho }_0$ just above $T_{\mathrm{c}}$ in several magnetic fields. The dotted line is the WHH theory with the dirty limit $\left(h^{*}=0.69\right)$. (c) $T$ dependence of the thermodynamic critical field $H_{\mathrm{c}}\left(T\right)$. The inset shows $H_{\mathrm{c}}$ vs $t^2,t=T/T_{\mathrm{c}}$.