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

by Iulian Hetel, Thomas R. Lemberger & Mohit Randeria

Journal club talk by Ganesh Ramachandran
Summary by Brandon Ramakko



This week's talk by Ganesh focused on experimental results for thin films of underdoped YBCO. To begin the discussion, he briefly explained the temperature-doping phase diagram for this HTSC. The transition in the overdoped regime of the superconducting dome can be explained by a mean-field transition but it is not clear what causes the transtion in the underdoped regime. This paper aims to explain the transition in this regime using their experimental results.

The speaker then discussed a plot of superfluid density versus temperature for Helium films. The superfluid density is constant and drops discontinuously to zero at Tc. The size of this drop increases linearly. This is characteristic of a 2D Kosterlitz-Thouless-Berezinski transition. So if the plot of superfluid density for YBCO has the same bahaviour, you could conclude that it is indeed a 2D Kosterlitz-Thouless-Berezinski transition.

The speaker went on to explain the two-coil mutual-inductance method used by the authors. The sample is placed between two coils and an AC current running through the first coil produces a flux which induces an EMF in the sample which drives a current. The flux due to the current in the sample goes through the second coil and by measuring the voltage in the second coil you can calculate the conductivity. Using London's equations you can get the superfluid density.

The speaker then discusses the experiental plot of superfluid density versus temperature. There is no discontinuous drop as expected in a Kosterlitz-Thouless-Berezinski transition. The drop is probably smoothed out due to complexities such as the measurement being taken at a frequency of 50 kHz, inhomogeneities, vortex pinning and possible new physics. A line was added that seems to go through each curve where the density starts to decrease quickly. This seemed to be consistent over a range of doping values. The Tc values were determined from this fit.

It was asked how thick the layers used were and the speaker replied that the thinnest sample was 2 layers thick. It was also asked why the behaviour of the density for T less than Tc was quadratic when it should be linear. This difference in behaviour might be due to disorder or the frequency of 50 kHz (intead of 0) being used.

The speaker then discussed a plot of Tc versus superfluid density(T=0). The measurements show a linear relationship consistent with a 2D Kosterlitz-Thouless-Berezinski transition for small doping or low temperature. It was asked at what temperature it stops behaving linearly. The speaker aswered that at 10K, Tc behaves like the square root of the density. Josephson scaling near a quantum critical point (QCP) implies that the critical point in the underdoped regime is a 2D QCP. Since the transition is mediated by vortex-antivortex pairs, if these could be suppressed you could have a room temperature superconductor.

Patrick Morales commented on the difficulty of the experiment. Having attemped similar experiments he said that the split coil experiment on a thin film is difficult because you have weak signals with large noise. You need a large homogeneous sample. He mentioned it is extremely difficult to get a nice uniform thin sample because YBCO does not grow well in the underdoped regime and it is very hard to remove oxygen in a homogeneous manner.