Anisotropic upper critical field in the van der Waals superconducting quasicrystal (Ta$_{0.7}$Nb$_{0.3}$)$_{1.6}$Te
We investigated the upper critical field of a large single grain of the Nb-substituted van der Waals layered quasicrystal (Ta$_{0.7}$Nb$_{0.3}$)$_{1.6}$Te. The sample exhibits a sharp superconducting transition at $T_{\mathrm{c}}$ = 1.35 K, the highest value reported to date among quasicrystal superconductors. The angular dependence of the critical field exhibits a pronounced criterion dependence: the field determined using the 10% $R_{\mathrm{N}}$ ($R_{\mathrm{N}}$: normal-state resistance) criterion is well described by the anisotropic Ginzburg-Landau model, whereas those determined using the 65% and 90% $R_{\mathrm{N}}$ criteria exhibit Tinkham-like angular dependence characteristic of two-dimensional superconductivity. The high-field part of the resistive transition is well described by a surface-superconductivity model and exhibits a pronounced excitation-current dependence for magnetic fields close to the $ab$ plane, supporting the presence of surface superconductivity on the quasiperiodic $ab$-plane surfaces. The bulk $H_{\mathrm{c2}}$ is strongly anisotropic, with the in-plane $H_{\mathrm{c2}}$ exceeding the weak-coupling Pauli limit by a factor of approximately 2.5. For both field orientations, $H_{\mathrm{c2}}(T)$ deviates upward from the conventional dirty-limit Werthamer-Helfand-Hohenberg prediction at low temperatures. A phenomenologically modified Ginzburg-Landau-Abrikosov-Gorkov model incorporating a spatial distribution of the electronic diffusivity substantially improves the description of $H_{\mathrm{c2}}(T)$, suggesting that spatial variations in electronic transport properties may contribute to its anomalous temperature dependence.