Superfluidity in the Second Layer of ^{4}He on Graphite.

Evidence for a new type of superfluid phase in second-layer ^{4}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}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.