Superfluid density ofH4econfined in nanopores

Abstract

Helicity modulus in one-dimensional (1D) and anisotropic two-dimensional (2D) classical $XY$ models is calculated. In finite-size 1D lattice, it is unity at absolute zero and rapidly vanishes as temperature increases due to proliferating phase slippage. Similarly, in anisotropic 2D lattice with large aspect ratio, helicity modulus in the direction of the longer side diminishes at a temperature much smaller than Kosterlitz-Thouless transition temperature ${T}_{\text{KT}}$. This finding is in contrast to the recent observation of finite superfluid density below ${T}_{\text{KT}}$ in $^{4}\text{H}\text{e}$ films adsorbed on 1D nanopores. We argue that the superfluid density observed in the experiment is not affected by phase slippage and that is the reason why finite superfluid density was observed. Furthermore, we discuss the observability of genuine 1D behavior of superfluid density in 1D nanopores.