Critical current density and vortex phase diagram in the superconductor ${\mathrm{Sn}}_{0.55}{\mathrm{In}}_{0.45}\mathrm{Te}$

Critical current density and vortex pinning dynamics have been studied in the superconductor ${\mathrm{Sn}}_{0.55}{\mathrm{In}}_{0.45}\mathrm{Te}$. Analysis of the temperature-dependent lower critical field shows that it has a weakly anisotropic single energy gap. The critical current density $J_c\left(0\right)$ and pinning potential $U_0\left(H\right)$ values reach as high as $2.56\times {10}^3\mathrm{A}/{\mathrm{cm}}^2$ at 1.8 K and $2.1\times {10}^3$ K at ${\mu }_{0}H=0.01\mathrm{T}$, respectively. Based on the collective pinning model, we demonstrate the coexistence of vortex pinning regimes in ${\mathrm{Sn}}_{0.55}{\mathrm{In}}_{0.45}\mathrm{Te}$. One is a $\delta T_{\mathrm{c}}$ pinning regime induced by the spatial fluctuations of the transition temperature in a low field. The other is a dominantly $\delta l$ pinning regime associated with the spatial variations of the charge-carrier mean free path in a higher field. This causes a nonconstant exponent of the power-law behavior $J_c\left(T\right)\propto H^n$. A very weak vortex fluctuation is unveiled by a narrow separation between the irreversibility field ${\mu }_0{H}_{\mathrm{irr}}\left(T\right)$ and upper critical field ${\mu }_0{H}_{\mathrm{c}2}\left(T\right)$ in the vortex phase diagram. We discuss the potential application in superconducting electronics like the single-photon detector in thin film form.

Figure 1

Supercell structures at the face-centered cubic primitive cell basis for (a) SnTe and (b) ${\mathrm{Sn}}_{0.5}{\mathrm{In}}_{0.5}\mathrm{Te}$. (c) High symmetry $k$ path in the Brillouin zone. Band structures include SOC and projected DOS for (d) SnTe and (e) ${\mathrm{Sn}}_{0.5}{\mathrm{In}}_{0.5}\mathrm{Te}$. The Fermi energy (blue dashed lines) is set to zero.

Figure 2

(a) XRD patterns. (b) EDS spectrum. (c) and (d) show the temperature-dependent magnetic susceptibility and resistivity for ${\mathrm{Sn}}_{0.55}{\mathrm{In}}_{0.45}\mathrm{Te}$.

Figure 3

(a) Initial magnetization curves vs. applied field of ${\mathrm{Sn}}_{0.55}{\mathrm{In}}_{0.45}\mathrm{Te}$ at various temperatures. (b) Initial diamagnetization at 1.8 K. Solid line presents a linear fitting curve. Inset shows the difference between experimental and linear fitting data. (c) Temperature-dependent ${\mu }_0{H}_{\mathrm{c}1}$. Solid lines are theoretical fitting curves.

Figure 4

(a) Magnetic hysteresis loops below 5.1 K of ${\mathrm{Sn}}_{0.55}{\mathrm{In}}_{0.45}\mathrm{Te}$. (b) Log-log plot of critical current density $J_c$ versus applied field. The $J_c$ is extracted by Bean's model. The inset shows the exponent versus temperature. (c) Normalized $j_c\left(t\right)$. The inset shows the percentage of the pinning regime. (d) The normalized pinning energy $g\left(t\right)=U\left(t\right)/U\left(0\right)$ versus temperature.

Figure 5

Kramer plot of the $J_c\left(H\right)$ data: $J^{1/2}{H}^{1/4}\sim H$. Inset presents the temperature dependent ${\mu }_0{H}_{\mathrm{irr}}\left(T\right)$ and solid line indicates the fitting curve.

Figure 6

(a) Temperature dependence of resistivity under various fields for ${\mathrm{Sn}}_{0.55}{\mathrm{In}}_{0.45}\mathrm{Te}$. (b) Criterion determining the $T_{\mathrm{c}}$ and $T_{\mathrm{irr}}$. (c) Arrhenius plot: $\text{ln}\left[\rho \right(T,H\left)\right]\sim 1/T$. (d) Field dependence of pinning potential $U_0$. Solid lines are power-law fitting results.

Figure 7

Vortex phase diagram of ${\mathrm{Sn}}_{0.55}{\mathrm{In}}_{0.45}\mathrm{Te}$. The solid and dashed lines are the fitting results. Meissner state: a fully diamagnetic state that does not allow the magnetic field to penetrate inside; Vortex solid: forming the vortex lattice with a well pinning by defects (pinning centers); Vortex liquid: a state that transforms from melting the vortex lattice cannot easily be pinned by defects.