Evidence for a new type of superfluid phase in second-layer ${}^4\mathrm{He}$ on graphite has been obtained from simultaneous measurements of torsional-oscillator response and heat capacity on exactly the same sample down to 30 mK, which resolve substrate-related uncertainties in the previous studies. The new phase hosts both superfluidity and enhanced viscoelasticity relative to the low-density quantum liquid, and is stable over a finite interval of ${}^4\mathrm{He}$ areal density, strongly supporting the proposed “superfluid liquid-crystal” hypothesis. A random-Josephson-network analysis shows that the widely reported log-$T$ dependence of the superfluid density is likely due to substrate imperfections.

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• BKT transition
• Structural phase transition
• Helium-4 superfluids
• Superfluids
• Supersolids
• Specific heat measurements