On the Novel 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, and is stable over a finite density interval, 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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