Fig. 3: Observation of the Berezinskii–Kosterlitz–Thouless (BKT) transition.
From: Superconductivity and a van Hove singularity confined to the surface of a topological semimetal
a Voltage (V)-current (I) characteristics acquired in the low-current regime, in a logarithmic scale, and for different temperatures. The red, blue, and green dashed lines represent \({V}\propto \,{I}^{3}\), \({V}\propto {I}\), and \(V={I\; R}\)Normal, respectively. b Temperature dependence of the exponent \(a(T)=1+\pi {J}_{S}(T)/{T}\) extracted from fitting the V-I data to \(V\propto {I}^{a\left(T\right)}\). The BKT transition is characterized by \(\pi {J}_{S}({T}_{{{{\rm{BKT}}}}})/{T}_{{{{\rm{BKT}}}}}=2\), leading to \(a({T}_{{{{\rm{BKT}}}}})\,=\,3\), the relation that defines \({T}_{{{{\rm{BKT}}}}}\). The horizontal dashed line indicates the value \(a=3\). \(a(T)\) as a function of \(T\) clearly reveals the BKT transition with \({T}_{{{{\rm{BKT}}}}}\simeq 1.5\) K. c Temperature dependence of the superfluid stiffness, \({J}_{S}.\,{J}_{S}\) drops near \({T}_{{{{\rm{c}}}}}\), as expected from the BCS theory. Above \({T}_{{{{\rm{BKT}}}}}\simeq 1.5\) K, the \({J}_{S}\) decreases more rapidly with increasing T, as shown by the violet dashed lines serving as guides to the eye. d Temperature dependence of the resistance (blue circles), fitted to the Halperin–Nelson theory using the parameters \({T}_{{{{\rm{BKT}}}}}=1.5\) K and \({T}_{{{{\rm{c}}}}}=1.8\) K. The Red curve represents the best fit.
