Type-I superconductivity in single-crystal ${\mathrm{Pb}}_2\mathrm{Pd}$

We have investigated the superconducting properties in a single crystal of the superconductor ${\mathrm{Pb}}_2\mathrm{Pd}$ via various techniques including, magnetization, AC transport, transverse field muon spin rotation and relaxation, and heat capacity. All measurements confirm the superconducting transition temperature $T_C=3.0\pm 0.1\mathrm{K}$. Electronic specific-heat data are well described by the BCS expression, suggesting that ${\mathrm{Pb}}_2\mathrm{Pd}$ opens an isotropic gap on entering the superconducting state. Specific-heat jump and the ${\lambda }_{e\text{−}ph}$ value categorize ${\mathrm{Pb}}_2\mathrm{Pd}$ as a moderately coupled superconductor. Magnetization and transverse field muon spin rotation measurements along with the Ginzburg-Landau parameter, $\kappa$ < $1/\sqrt{2}$ demonstrates that ${\mathrm{Pb}}_2\mathrm{Pd}$ is a type-I superconductor.

Figure 1

The powder XRD pattern of ${\mathrm{Pb}}_2\mathrm{Pd}$ obtained at room temperature is shown by red circles whereas the black line represents the Rietveld refinement. The crystal image (left-up) and crystal structure of ${\mathrm{Pb}}_2\mathrm{Pd}$ where blue circles represent Pb atoms, whereas gray circles represent a Pd atom (right-up). The back Laue x-ray diffraction pattern of a ${\mathrm{Pb}}_2\mathrm{Pd}$ single crystal (rightmost).

Figure 2

Zero-field temperature variation of electrical resistivity in the range of $1.9\mathrm{K}\le T\le 300\mathrm{K}$ where the solid red line is a fit to the parallel resistor model. The inset (bottom right): A sharp superconducting transition at $T_C=3.0\mathrm{K}$ whereas the top left inset shows the Hall resistivity with respect to field ($\pm 9\mathrm{T}$) at $T=50\mathrm{K}$.

Figure 3

(a) Temperature dependence of the moment collected via ZFCW and FCC under an applied magnetic field of 1 mT. (b) Magnetization as a function of applied field for $1.8\mathrm{K}\le T\le 2.8\mathrm{K}$. (c) Magnetization vs magnetic field at 1.8 K of ${\mathrm{Pb}}_2\mathrm{Pd}$.

Figure 4

Temperature dependence of the critical field from various measurements. The inset: $\rho \left(T\right)$ at different fields starting from 0 to 25 mT.

Figure 5

(a) Zero-field $C/T$ variation with respect to $T^2$ where the solid line represents a fit to $\frac{C}{T}={\gamma }_n+{\beta }_3{T}^2+{\beta }_5{T}^4$. Inset: Specific-heat data exhibiting a superconducting transition at $T_C=2.95\mathrm{K}$. (b) $s$-wave fitting to the normalized electronic specific-heat data shown by the solid line.

Figure 6

The Fourier transform of $\mu \mathrm{SR}$ asymmetry representing the local field distribution and asymmetry spectra at different fields and temperatures. (a)–(c) show field distribution in the Meissner, intermediate, and normal state whereas (d)–(f) consists of corresponding asymmetry spectra. The solid lines are fit to the data using Eq. (5).

Figure 7

(a) Internal field as a function of temperature in the normal region of ${\mathrm{Pb}}_2\mathrm{Pd}$. (b) Superconducting volume fraction with respect to temperature at a 100-G applied field.

Figure 8

The plot of Uemura and co-workers showing the superconducting transition temperature $T_c$ vs the effective Fermi temperature $T_F$, where ${\mathrm{Pb}}_2\mathrm{Pd}$ is shown as a solid red marker. Other data points plotted between the blue solid lines are the different families of unconventional superconductors [44, 45, 46].