Anomalous upper critical field in the quasicrystal superconductor Ta$_{1.6}$Te

Superconductivity in quasicrystals poses a new challenge in condensed matter physics. We measured the resistance and ac magnetic susceptibility of a Ta$_{1.6}$Te dodecagonal quasicrystal, which is superconducting below $T_c \sim$ 1 K. We show that the upper critical field increases linearly with a large slope of $-$4.4 T/K with decreasing temperature down to 0.04 K, with no tendency to level off. The extrapolated zero-temperature critical field exceeds the Pauli limit by a factor of 2.3. We also observed flux-flow resistance with thermally activated behavior and an irreversibility field that is distinct from the upper critical field. We discuss these peculiarities in terms of the nonuniform superconducting gap and spin--orbit interaction in quasicrystal structures.