Thermodynamic evidence for full-gap superconductivity in the dodecagonal quasicrystal Cu-doped Ta$_{1.6}$Te
We report the superconducting gap in the van der Waals layered quasicrystal Cu-doped Ta$_{1.6}$Te, using a fast relaxation technique that removes the large nuclear contribution of $^{181}$Ta. The initial-slope method enabled detection of the electronic specific heat down to 60~mK, revealing a fully gapped state with $\Delta(0)/k_{\rm B} = 1.43$~K. Both the gap magnitude and specific-heat jump are smaller than BCS predictions, while quasiparticle excitations are strongly suppressed, consistent with a theoretical expectation for aperiodic systems. AC-susceptibility measurements show a large upper critical field and pronounced anisotropy, reflecting the quasi-two-dimensional structure. These results provide the first thermodynamic evidence for a full-gap superconducting state in a quasicrystal and highlight unconventional pairing mechanisms beyond periodic lattices.