BERKELEY, CA — Joseph Orenstein, a staff scientist in Berkeley Lab's Materials Sciences Division and a professor of physics at the University of California at Berkeley, applied a technique called "time-domain terahertz spectroscopy" to study the electronic properties of the high-Tc superconductor BSCCO. When he and his colleagues found peculiar -- and at first unbelievable -- results, their discoveries encouraged Séamus Davis to search for evidence of granular superconductivity in the same material.

The superconducting state
Electrons are fermions, particles that cannot occupy the same quantum state in a system. But when bound together as "Cooper pairs," the pairs are bosons, which can occupy precisely the same quantum state -- all at the same time. Thus electron pairs can form a "condensate" that gives rise to all the spectacular electromagnetic effects displayed by superconductors, including the absence of electrical resistance.

	A spectacular electromagnetic effect of superconductors: a superconductor can levitate a magnet, because after making the transition from the normal to the superconducting state, the superconductor excludes magnetic fields from its interior.

Not every electron finds a partner, however. Unpaired electrons are described as quasiparticles, whose properties include finite lifetimes.

"The standard picture of superconductor electrodynamics is the two-fluid model," says Orenstein, "in which the medium behaves as a superconducting fluid -- a superfluid -- of Cooper pairs, which is permeated by a normal fluid consisting of quasiparticles."

Electrical charge is carried by electrons, but also by the oppositely-charged absences of electrons called holes. Thus Cooper pairs can also be made of holes. Quasiparticles too may be particle-like or hole-like.

Quasiparticles are difficult to study in a superconductor because their properties are usually hidden by the superfluid with which they coexist. The resistance of the normal fluid is undetectable, for example, because it is "shorted out" by the resistanceless condensate. So Orenstein set out to study quasiparticle properties by measuring conductivity using alternating rather than direct current.

When direct current flows through a superconductor, there is no resistance, no voltage, and the electric field strength is exactly zero. While direct current does induce a non-zero magnetic field, it is measurable only near the surface, to a depth known as the penetration depth.

Because the condensate has mass, however, alternating current requires force to repeatedly accelerate and decelerate the charge carriers. Thus there is a measurable electric field and voltage, although no resistance (because current and voltage vary out of phase).

Like a magnetic field, the ac electric field is measurable only to the penetration depth, below which it is "screened." The strength of the screening and the shallowness of the penetration depth vary with the density of the superfluid.

When normal fluid is present, it also contributes to the current. Just as in a normal metal, this current encounters resistance. Energy is converted to heat and dissipates at a rate that peaks when the ac frequency exactly matches the scattering rate of the quasiparticles that make up the normal fluid.

The higher the scattering rate, the shorter the quasiparticle lifetime, an important parameter of various high-Tc superconductors.

The puzzle of quasiparticle lifetimes
When Orenstein began his ac investigations, measurements of quasiparticle lifetime in BSCCO and in a very similar material, YBCO (yttrium barium copper oxide), had yielded quite dissimilar results. Teams who had measured YBCO with microwave frequencies found that quasiparticle lifetimes rapidly increase below the superconducting transition temperature, to more than 100 times that in the normal state.

Microwave measurements of BSCCO, on the other hand, failed to observe a dissipation peak, which is needed to pin down quasiparticle lifetimes.

The high-temperature superconductors BSCCO and YBCO are similar in many respects, including their Perovskite structure, but their electronic properties reveal suprising differences.

At Berkeley Lab's Advanced Light Source, a team headed by Z. X. Shen and Zahid Hussain used a technique called ARPES (angle-resolved photoemission spectroscopy) to measure quasiparticle lifetime in BSCCO; ARPES looks at the electrons emitted from the surface of a material when it is illuminated with high-frequency radiation. Surprisingly, their ARPES measurements suggested that in BSCCO, unlike YBCO, quasiparticle lifetime increased only by a factor of three below the transition temperature.

Were the results different because the materials were different, or because the measurement techniques were incompatible?

"One of the frustrating things about high-Tc superconductors is that we have many experimental probes for investigating them, but each works best on only one or two members of the cuprate family," Orenstein remarks.

Finding the right frequency
It seemed likely that the missing dissipation peak in BSCCO lay at frequencies above the range of typical microwave spectroscopy techniques. Orenstein turned to time-domain terahertz spectroscopy, with frequencies between microwaves and the far infrared. With the terahertz spectrometer he could send a pulsed beam of trillion-cycles-per-second radiation all the way through a slice of BSCCO only 100 billionths of a meter thick.

The terahertz pulse is produced by a short strip of silicon under voltage. When stimulated by optical laser pulses a trillionth of a second long, the strip responds with electric-current pulses that radiate trillion-hertz electromagnetic waves. (In 1888, Heinrich Hertz used a similar system of bigger conductors to produce the first radio waves.)

The terahertz waves are focused on the sample, in which they set up an alternating current of the same frequency. The shape of this wave is altered as it passes through the sample; on the far side, it is detected by a reversed arrangement of focusing elements and a second silicon strip.

In studying superconductors, the terahertz spectrometer's ability to measure the absolute phase of the transmitted pulse is crucial. Conventional detectors read only the intensity of the wave, but Orenstein's spectrometer records its amplitude and phase as well -- all the details of the entire waveform.

"Remember that the quasiparticles dissipate energy, and the superfluid screens," Orenstein says. "The signature of the condensate appears as an out-of-phase component in the waveform, but because quasiparticles respond in phase with the terahertz radiation, they leave a distinct signature in the altered waveform."

Because the relative contributions of the two components to the material's conductivity could be assessed independently, terahertz spectroscopy seemed the ideal technique for seeking BSCCO's quasiparticle dissipation peak.

The improbable truth
The terahertz measurements produced a startling result: the two-fluid model itself seemed to fail.

Terahertz electromagnetic pulses set up alternating current in a thin sample; the shape of the wave is altered as it passes through the sample, conveying information about electronic states.

"The two-fluid model suggests that when you cool a superconductor down, you expect the normal charge carriers to convert to superconducting pairs. The dissipative component should go down, and the screening component should go up," Orenstein says. In BSCCO, both increased. "When we added up the dissipation below the superconducting transition temperature, we found some 30 percent of the total unaccounted for by the normal fluid."

Orenstein says that "eventually, we could come up with only one explanation for this anomaly. The extra dissipation could only arise if the superfluid density was not uniform throughout the sample. Variations from place to place had to be almost 50 percent of the average superfluid density! It was an extreme idea, and I never thought anybody would believe it. I spent most of a summer worrying about it."

Learning of the Orenstein group's conclusions, Séamus Davis, using scanning tunneling microscopy, set out to explore the possibility that there were actual spatial variations in the conductive properties of BSCCO's superconducting layers.

"Essentially, Séamus looks at electronic properties on the top copper-oxygen layer of BSCCO," Orenstein explains. "He measures energy gaps, which we believe are proportional to the density of the condensate. His images and our measurements, which look at some 40 to 60 layers, are in good quantitative agreement."

The story is far from over, but so far, says Orenstein, "It's been fun. We had this prediction from looking at clues, like Sherlock Holmes. And then Séamus goes out and actually sees the culprit."

Additional information:

• More about time-domain terahertz spectroscopy
• More about Orenstein's investigations of high-temperature superconductors