Existence of a thermally driven BKT transition

Determine whether the gate-tunable InAs/Al Josephson junction arrays undergo a thermally driven Berezinskii–Kosterlitz–Thouless transition as the phase stiffness approaches the universal condition \(\rho_s=(2/\pi)T\).

Background

The classical XY description predicts a BKT transition when the superfluid phase stiffness reaches the universal value $\rho_s=(2/\pi)T$. The measured arrays instead show a smooth suppression of phase stiffness and critical temperatures substantially below expectations from thermal fluctuations alone.

The authors attribute much of the suppression to quantum phase fluctuations, while allowing that a thermal BKT transition could occur at lower stiffness. However, the available measurements do not resolve such a transition, leaving its existence in these arrays uncertain.