Wei Liu introduced her talk by a description of the superconducting transition as seen in the thermal dependance of the resistance. She divided the curve into three main parts: a normal state behavior at high temperature, a superconducting fluctuations region when the curve bends down at the transition and a superconducting state characterized by a zero resistance. She emphazised that the critical region of the transition is divided into an amplitude fluctuation region at the beginning of the downturn of the curve and a phase fluctuation region at lower temperature. In the phase fluctuation region, free vortices are thermally generated down to the Berezinsky–Kosterlitz–Thouless (BKT) transition where these fluctuations are frozen out. The speaker described different signatures of this BKT transition: a universal resistance curve [P. Minnhagen (1987)] and the non linear I-V characteristic [K. Epstein (1982)].The critical temperature of the BKT transition is theoretically signalled by a jump in the exponent of this charactreristic (not seen in transport measurements as far as the blogger knows). A related universal jump has indeed been seen in the damping rate of a torsion oscillator immersed inHe3/He4 mixtures. The method used by Wei Liu is based on the frequency dependance of the superfluid stifness. Although it was not the premature end of her talk, she immediately anticipated her conclusions: the microwave complex conductivity can characterize two-dimensionnal quantum systems by providing an experimental signature of the superfluid stifness. She observed that the dynamic slows down at the transition.
The experiment relies on the Corbino geometry of the sample which allows a broadband spectrometric study (100 MHz-40 GHz with 1Hz resolution). The measurement consists in recording, with a network analyser, the microwave reflexion of a line ended by the sample cooled down to 300 mK. Both the real and imaginary components of the complex impedance can thus be obtained.
The sample was a 30 nm thick amorphous Indium oxide film with a sheet resistance below 1500 Ohms. An Azlamazov-Larkin paraconductivity analysis of the thermal dependance of the resistance gives a superconducting temperature sligthly below 3 K.
Weil Liu showed the real and imaginary part of the conductance of this film as a function of frequency for different temperatures. In the real conductance, the spectral weight moves to lower frequency as the temperature is decreased. In the supercondsucting state, a gap in the frequency opens and a delta function peak appears at zero frequency as expected for a superconductor with zero DC resistance. The plot of the logarithm of the imaginary conductance shows a linear behavior whose slope continuously changes from a positive value at high temperature to a negative one at low temperature. This imaginary component times the frequency is a direct measure of the energy scale of the superfluid stiffness. The latter becomes frequency dependent above T_BKT (approximately 2.3K) and while its value should be four times T_BKT at this temperature (according to BKT theory), the speaker rather estimates it around 12 K. However, the audience found that there was not such a discrepancy between theory and measurements, taking into account the width of the experimental curves.
The real part of the conductance was also shown for different temperature and a peak above T_BKT could be observed that shifts to even higher temperature when the AC frequency is increased. This peak unveils the superfluid density.
The last part of the talk consisted in a scaling analysis of the phase and the amplitude of the complex impedance. Both quantities could be rescaled on universal curves for a significant range of temperature above the transition. This analysis allowed Wei Liu to extract a characteristic relaxation frequency which decreases rapidly above T_BKT. Such an observation is consistent with a vortex activation scenario. However the blogger did not understand whether the extracted vortex core energy was in agreement or not with BCS theory.
During the discussion, the validity of the BKT interpretation of the data in such a disordered superconductor was questionned. Indeed, one expects the vortex to be pinned. It was recognized that edge pinning was irrelevant because of the Corbino geometry. However, internal pinning could be detrimental. Whether the short length scales probed by these high frequency measurements allows disregarding pinning remains an open question.
Blogged by Claude Chapelier
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