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Breakthrough in the Understanding
of High-Tc Superconductors
Cooper Pairs Observed
Above Tc
Joseph Orenstein
A research team led by Joe Orenstein has made an important breakthrough in the understanding of high-Tc superconducting materials. They have detected the persistence of Cooper pairing in the normal (non-superconducting) state and identified the mechanism of the vanishing of "quantum phase coherence" which takes place above the critical temperature (Tc).
The binding of electrons to form "Cooper pairs" is essential in creating the superconducting state. The remarkable manifestations of superconductivity--zero resistance and expulsion of all magnetic flux--also require that pairs of Cooper pairs share the same phase ("quantum phase coherence"). The superconducting transition temperature corresponds to the temperature at which thermal agitation destroys long-range phase coherence. In principle, therefore, Cooper pairs with short-range coherence could survive above Tc; in fact, theorists have speculated that Cooper pairing together with short-range coherence may persist to temperatures as high as 100 K above Tc in cuprate superconductors. It has been difficult, however, to obtain direct experimental evidence to test this prediction. The primary problem is that small phase-coherent regions in the superconductor decay very rapidly and are invisible to standard low-frequency probes.
The MSD team approached this problem by performing measurements of the conductivity, at very high frequencies. The measurements were performed on 50 nm films of Bi2Sr2CaCu2O8+d using time-dependent transmission spectroscopy in the 100-600 GHz range. The high-frequency conductivity directly measures the superconductor's "phase-stiffness energy," the energy required to change the phase of Cooper pairs in one region relative to another.
The accompanying figure shows the measured phase-stiffness energy as a function of temperature for two samples with different O contents and, therefore, different Tcs. In the plot the phase-stiffness energy is converted to an effective temperature, Tphase, using Boltzmann's constant. In a conventional superconductor, Tphase would vanish at Tc, regardless of the measurement frequency. The MSD team found that rather than vanishing at Tc, Tphase exhibits an abrupt crossover from a frequency-independent to frequency-dependent quantity. The frequency-dependent phase-stiffness energy above Tc is direct evidence for the persistence of Cooper pairing. However, the most exciting conclusions emerge from a comparison of this crossover phenomenon in different samples. The MSD team found that the value of Tphase at the crossover is 8/p times the temperature at which the crossover occurs (see figure). This is precisely the universal relationship between phase-stiffness energy and transition temperature predicted by Kosterlitz and Thouless in the early 1970's to describe coherent-to-incoherent transitions in two spatial dimensions. The Kosterlitz-Thouless transition is mediated by the thermal generation of topological defects in the phase, known as vortices. Thus the MSD work not only demonstrates the persistence of Cooper pairing in the normal state, but unambiguously identifies the mechanism for the vanishing of their phase coherence at Tc.
In future work the MSD team will use their powerful technique to probe the vanishing of phase coherence at "quantum phase transitions." In such transitions, phase coherence can be destroyed even near absolute zero temperature by varying quantum mechanical control parameters, such as chemical potential and disorder.
Joe Orenstein (510.486-5880), Materials Sciences Division (510.486-4755), E. O. Lawrence Berkeley National Laboratory.
J. Corson, R. Mallozzi, J. Orenstein, J. N. Eckstein, I. Bozovic, "Vanishing of phase coherence in underdoped Bi2Sr2CaCu2O8+d," Nature, March 18, 398 :221-223 (1999).