Kosterlitz-Thouless transition in uniformly confined $^4$He

Abstract

This study investigates the Kosterlitz-Thouless (KT) transition in superfluid $^4$He confined within uniform nanochannels. While the universal jump in superfluid density is a well-established phenomenon, predicting the absolute transition temperature ($T_{KT}$) based on film geometry has remained a long-standing challenge, often relying on empirical fits. Using on-chip nanofluidic Helmholtz resonators with channel heights of 10, 15, and 20 nm, we probe the transition using 4th sound resonant modes.We demonstrate that the observed shift in the transition temperature relative to the bulk lambda point ($T_{\lambda}$) is accurately accounted for by including two-dimensional thermal excitations, specifically 2D rotons. By incorporating these roton-like excitations into the static KT theory, we can predict absolute transition temperatures that align with our experimental measurements and historical data without invoking traditional coherence length scaling arguments. Furthermore, we show that the dynamical extension of the KT theory (AHNS) fully describes the dissipation peaks observed near the transition without requiring ad-hoc free vortex contributions. These results provide compelling evidence that roton excitations, rather than correlation length scaling, govern the finite-size behaviour of confined superfluid $^4$He