Nodeless superconducting gaps in noncentrosymmetric superconductor ${\mathrm{PbTaSe}}_2$ with topological bulk nodal lines

Low-temperature thermal conductivity measurements were performed on single crystal of ${\mathrm{PbTaSe}}_2$, a noncentrosymmetric superconductor with topological bulk nodal lines in the electronic band structure. It is found that the residual linear term ${\kappa }_0/T$ is negligible in zero magnetic field. Furthermore, the field dependence of ${\kappa }_0/T$ exhibits an $\mathsf{S}$-shaped curve. These results suggest that ${\mathrm{PbTaSe}}_2$ has multiple nodeless superconducting gaps. Therefore, the spin-triplet state with gap nodes does not play an important role in this noncentrosymmetric superconductor with strong spin-orbital coupling. The fully gapped superconducting state also meets the requirement of a topological superconductor, if ${\mathrm{PbTaSe}}_2$ is indeed the case.

Figure 1

(a) X-ray diffraction pattern of ${\mathrm{PbTaSe}}_2$ single crystal. Only ($00l$) Bragg peaks show up, demonstrating that the largest surface is $ab$ plane. Inset: Optical image of our ${\mathrm{PbTaSe}}_2$ single crystals. (b) The dc magnetization at $H=10$ Oe for a ${\mathrm{PbTaSe}}_2$ single crystal, measured with zero-field-cooled (ZFC) process. (c) The resistive superconducting transition of ${\mathrm{PbTaSe}}_2$ single crystal at zero field. The dashed line is a fit of the normal-state resistivity between 4.5 and 12 K to $\rho ={\rho }_0+A{T}^2$. Inset: The temperature dependence of resistivity up to 297 K.

Figure 2

(a) Low-temperature resistivity of ${\mathrm{PbTaSe}}_2$ single crystal in magnetic field up to 0.25 T. Inset: The magnetoresistance of ${\mathrm{PbTaSe}}_2$ single crystal at 0.3 K and above $H=1$ T. (b) Temperature dependence of the upper critical field $H_{c2}\left(T\right)$, defined by $\rho =0$. The dashed line is a guide to the eye, which points to $H_{c2}\left(0\right)\approx 0.22$ T.

Figure 3

Low-temperature thermal conductivity of ${\mathrm{PbTaSe}}_2$ single crystals (a) in zero field, and (b) in magnetic fields applied perpendicular to the $ab$ plane. The solid lines represent the fits to $\kappa /T=a+b{T}^{\alpha -1}$ for the data in different $H$. The dashed lines are the normal-state Wiedemann-Franz law expectation $L_0/{\rho }_0$(0.1 T), with the Lorenz number $L_0=2.45\times {10}^{-8}\mathrm{W}\mathrm{\Omega }{\mathrm{K}}^{-2}$ and ${\rho }_0$(0.1 T) = $1.21\mu \mathrm{\Omega }$ cm.

Figure 4

Normalized residual linear term ${\kappa }_0/T$ of ${\mathrm{PbTaSe}}_2$ as a function of $H/H_{c2}$, with bulk $H_{c2}=0.10$ T. For comparison, similar data are shown for the clean $s$-wave superconductor Nb [20], the dirty $s$-wave superconducting alloy InBi [21], the multiband $s$-wave superconductor ${\mathrm{NbSe}}_2$ [16], and an overdoped $d$-wave cuprate superconductor Tl-2201 [17].