Quantum Critical Behavior In The Superfluid Density Of High-Temperature Superconducting Thin Films

A central question in the physics of high-temperature superconductors is how superconductivity is lost at the extreme ends of the superconducting phase diagram, underdoping and overdoping. When mobile holes are removed from optimally doped cuprates, the transition temperature T_C and superfluid density n_S(0) decrease in a surprisingly correlated fashion. I succeeded in producing and measuring homogeneous underdoped high-temperature superconducting films by partially substituting Ca⁺² for Y⁺³ in YBa₂Cu₃O_7-d films with reduced oxygen concentrations in the CuO chains.

I test the idea that the physics of underdoped cuprates is dominated by phase fluctuations by measuring the temperature dependence of superfluid density n_S(T) and by changing the dimensionality of the system from 3D thick samples to 2D ultrathin films. Thick Y_1-xCa_xBa₂Cu₃O_7-d films are in agreement with previous measurements of pure YBa₂Cu₃O_7-d samples and do not show any 2D or 3D-XY critical regimes in the temperature dependence of superfluid density. Moreover, the transition temperature has a square-root dependence on absolute superfluid density at zero temperature, rather than showing the predicted linear dependence in the case of strong thermal phase fluctuations. When superfluid density is measured in underdoped 2D Y_1-xCa_xBa₂Cu₃O_7-d films as thin as only 2 unit cells for all doping levels, n_S(T) has a dramatic downturn consistent with a 2D vortex-antivortex pair unbinding transition and, at severe underdoping, T_C is linearly proportional to n_S(0). This dimensionality-dependent scaling relation is the result of quantum phase fluctuations that suppress superconductivity near a Quantum Critical Point at zero temperature. Further measurements in an additional family of high-temperature superconductors, La_2-xSr_xCuO₄, are consistent with my results in underdoped Y_1-xCa_xBa₂Cu₃O_7-d.

La_2-xSr_xCuO₄, also provided the opportunity to study the other extreme end of the superconducting phase diagram. In the overdoped region, as carrier density increases, supefluid density and the transition temperature are both suppressed. While it still remains uncertain what produces this suppression, a plausible interpretation is that only a small fraction of the hole carriers contribute to the superfluid density and the pair breaking effects are so important that they destroy superconductivity.