Anomalous metallic state above the upper critical field of the conventional three-dimensional superconductor AgSnSe${}_2$ with strong intrinsic disorder

We report superconducting properties of AgSnSe${}_2$, which is a conventional type II superconductor in the very dirty limit due to intrinsically strong electron scatterings. While this material is an isotropic three-dimensional (3D) superconductor with a not-so-short coherence length where strong vortex fluctuations are not expected, we found that the magnetic-field-induced resistive transition at fixed temperatures becomes increasingly broader toward zero temperature and, surprisingly, that this broadened transition is taking place largely above the upper critical field determined thermodynamically from the specific heat. This result points to the existence of an anomalous metallic state possibly caused by quantum phase fluctuations in a strongly disordered 3D superconductor.

Figure 1

(a) Face-centered cubic structure of AgSnSe${}_2$. Note that Ag and Sn atoms are randomly distributed in the cation sites. (b) XRD pattern of the AgSnSe${}_2$ sample. All the diffraction peaks can be well indexed using a cubic cell with the F$m$3$m$ space group. (c) Temperature dependence of ${\rho }_{xx}$ of the AgSnSe${}_2$ sample. Lower inset shows an enlarged view of the data near the superconducting transition for ${\rho }_{xx}$ (right axis) and for the dc magnetic susceptibility measured upon zero-field-cooling (left axis, shown in terms of the shielding fraction). Upper inset shows the magnetic-field dependence of ${\rho }_{yx}$ at 5 K; its slope gives $n_e$ $=$ 2.0 $\times$ 10${}^{22}$ cm${}^{-3}$.

Figure 2

(a) Temperature dependencies of $c_p/T$ measured in 0 and 9 T. Inset shows $c_p/T$ plotted as a function of $T^2$ for the 9-T data, where the superconductivity is completely suppressed; the solid line presents the best fit to the data using the Debye model (see Ref. 33). (b) Temperature dependence of $c_{\mathrm{el}}/T$ in 0 T. The dash-dotted line is the calculated $c_{\mathrm{el}}/T$ curve given by the weak-coupling BCS theory; the solid line is the best fit using a modified BCS theory with $\alpha$ $=$ 1.925. The horizontal solid line denotes ${\gamma }_{\mathrm{n}}$.

Figure 3

(a) $M\left(B\right)$ curves measured after zero-field cooling to various temperatures. The dashed line marks the initial linear behavior. (b) Plot of $B_1$ vs $T$; the solid line is a fit to the data using the local dirty limit formula. The $B_{\mathrm{c}1}$(0) obtained after the demagnetization correction is marked by an arrow. Inset shows the $B$ dependenices of $\Delta M$ $\equiv$ $M-M_{\mathrm{lin}}$, where $M_{\mathrm{lin}}$ denotes the initial Meissner contribution; the data are shifted vertically for clarity. The determined $B_1$ value for each temperature is shown by arrows. (c) Temperature dependencies of $M_{\mathrm{sc}}\equiv M-{\chi }_{0}B$ under various magnetic fields. The $T_{\mathrm{c}}^{\mathrm{Mag}}\left(B\right)$ values are indicated by arrows. (d) $B_{\mathrm{c}2}^{\mathrm{Mag}}$ vs $T$ phase diagram; the solid line is a WHH fit to the data.

Figure 4

(a) and (b) Superconducting transition measured in the temperature dependence of the specific heat under various magnetic fields. (c) $B_{c2}^{Cp}$ vs $T$ phase diagram; the solid line is a WHH fit to the data. For comparison, $B_{c2}^{\mathrm{Mag}}\left(T\right)$ and its WHH fitting are shown with filled squares and a dashed line, respectively.

Figure 5

Magnetic-field-induced resistive transition measured at various temperatures. The level of ${\rho }_{xx}$ that is used for determining $B_{10\%}$, $B_{50\%}$, and $B_{90\%}$ are indicated by dashed lines.

Figure 6

Plots of $B_{\mathrm{irr}}$, $B_{10\%}$, $B_{50\%}$, and $B_{90\%}$ obtained from the resistive transition data, together with $B_{c2}$ determined thermodynamically from specific-heat measurements (solid line).