Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin copper oxide films

A central challenge in the physics of high-temperature superconductors is to understand superconductivity within a single copper oxide layer or bilayer, the fundamental structural unit, and how superconductivity is lost with underdoping of charge carriers. A seminal property of crystals and thick films(1-4) is that when mobile holes are removed from optimally doped CuO2 planes, the transition temperature, T-c, and superfluid density, n(s)(0), decrease in a surprisingly correlated fashion. We elucidate the essential physics of strongly underdoped bilayers by studying two-dimensional (2D) samples near the critical doping level where superconductivity disappears. We report measurements of n(s)(T) in films of Y1- xCaxBa2Cu3O7- delta as thin as two copper oxide bilayers with T c values as low as 3 K. In addition to seeing the 2D Kosterlitz - Thouless - Berezinski transition(5,6) at T-c, we observe a remarkable scaling of T-c with n(s)(0), which indicates that the disappearance of superconductivity with underdoping is due to quantum fluctuations near a 2D quantum critical point.