The remarkable properties of liquid helium II – such as its ability to creep over the walls of its container – establish it as arguably the most interesting state of condensed matter [1, 2]. It may be represented as a superposition of two fluids: a normal fluid and a superfluid with zero viscosity, with the superfluid fraction increasing towards unity at zero temperature.

Superfluidity is driven by Bose condensation and is thus characterised by the condensate wavefunction. The superfluid velocity is proportional to the gradient of the phase of this semiclassical wavefunction, and vortex excitations appear in the superfluid-velocity field at nonzero temperature. In planar systems, these vortices are bound in neutral pairs at low temperature, but become deconfined above the Berezinskii-Kosterlitz-Thouless (BKT) phase transition [3, 4]. Bishop & Reppy used an oscillating substrate to measure the temperature evolution of the superfluid density in an ultrathin helium film [5] — where this strong experimental evidence for the BKT transition ultimately provided support for its 2016 Nobel Prize.

The condensate phases map to the spin phases of an XY ferromagnetic film, with the systems exhibiting analogous BKT physics [6]. A peculiar consequence of 2D physics means that these planar systems do not exhibit broken symmetry within the traditional mathematical framework, as would be observed below a conventional continuous phase transition. This is explained by the BKT transition being topological in nature, but a broad array of experiments and simulations still suggest broken symmetry in the low-temperature BKT phase. This paradox was resolved by a series of papers showing that symmetry is indeed broken, but within a broader framework than that traditionally used in condensed-matter physics [7, 8].

But symmetry-breaking phase transitions are typically accompanied by strongly correlated system dynamics at the critical point. The new framework for broken symmetry at the BKT transition therefore suggests that strongly correlated dynamics should be observed in experimental systems near the transition. This indeed appears to be the case in simulations of magnetic films [7] and experiments on superconducting films [9] (another BKT system) but a comprehensive theoretical framework still eludes the research community, as does its signal in superfluid films — whose future work we’ll motivate while concluding the talk.

[1] Atkins, Liquid Helium (Cambridge University Press, 1959)

[2] Donelly, Quantized Vortices in Helium II, Cambridge Studies in Low Temperature Physics (Cambridge University Press, 1991)

[3] Berezinskii, Sov. Phys.—JETP 32, 493 (1971)

[4] Kosterlitz & Thouless, J. Phys. C 6, 1181 (1973)

[5] Bishop & Reppy, Phys. Rev. B 22, 5171 (1980)

[6] Bramwell, Faulkner, Holdsworth & Taroni, EPL 112, 56003 (2015)

[7] Archambault, Bramwell & Holdsworth, J. Phys. A 30, 8363 (1997)

[8] Faulkner, Phys. Rev. B 109, 085405 (2024)

[9] Shi et al., Phys. Rev. B 94, 134503 (2016)