Scientists from the U.S. Department of Energy’s Lawrence Berkeley National
Laboratory (Berkeley Lab) and the Univ.
of California at Berkeley
have joined with researchers at Stanford
Univ. and the SLAC
National Accelerator Laboratory to mount a three-pronged attack on one of the
most obstinate puzzles in materials sciences: what is the pseudogap?
A collaboration organized by Zhi-Xun Shen, a member of the Stanford
Institute for Materials and Energy Science (SIMES) at SLAC and a professor of
physics at Stanford Univ., used three complementary experimental approaches to investigate
a single material, the high-temperature superconductor Pb-Bi2201 (lead bismuth
strontium lanthanum copper-oxide). Their results are the strongest evidence yet
that the pseudogap phase, a mysterious electronic state peculiar to
high-temperature superconductors, is not a gradual transition to
superconductivity in these materials, as many have long believed. It is in fact
a distinct phase of matter.
“This is a paradigm shift in the way we understand high-temperature
superconductivity,” says Ruihua He, lead author with Makoto Hashimoto of the
paper in Science that describes the team’s findings. “The involvement
of an additional phase, once fully understood, might open up new possibilities
for achieving superconductivity at even higher temperatures in these
materials.” When the research was done Hashimoto and He were members of SIMES,
of Stanford’s Department of Applied Physics, and of Berkeley Lab’s Advanced Light
Source (ALS), where He is now a postdoctoral fellow.
The pseudogap mystery
Superconductivity is the total absence of resistance to the flow of
electric current. Discovered in 1911, it was long thought to occur only in
metals and only below a critical temperature (Tc) not far above absolute zero.
“Ordinary” superconductivity commonly takes place at 30 K or less, equivalent
to more than 400 degrees below zero Fahrenheit. Awkward as reaching such low
temperatures may be, ordinary superconductivity is widely exploited in
industry, health, and science.
High-Tc superconductors were discovered in 1986. “High” is a relative term;
the highest-Tc superconductors function at temperatures five times higher than
ordinary superconductors but still only about twice that of liquid nitrogen.
Many high-Tc superconductors have been found, but the record holders for
critical temperature remain the kind first discovered, the cuprates—brittle
oxides whose structure includes layers of copper and oxygen atoms where current
flows.
In all known superconductors electrons join in pairs (Cooper pairs) to move
in correlated fashion through the material. It takes a certain amount of energy
to break Cooper pairs apart; in ordinary superconductors, the absence of
single-electron states below this energy constitutes a superconducting gap,
which vanishes when the temperature rises above Tc. Once in the normal state
the electrons revert to unpaired, uncorrelated behavior.
Not so for cuprate superconductors. A similar superconducting gap exists
below Tc, but when superconductivity ceases at Tc the gap doesn’t close. A
“pseudogap” persists and doesn’t go away until the material reaches a higher
temperature, designated T* (T-star). The existence of a pseudogap in the normal
state is itself anything but normal; its nature has been heatedly debated ever
since it was identified in cuprates more than 15 years ago.
Attempts to explain what’s going on in the pseudogap have coalesced around
two main schools of thought. Traditional thinking holds that the pseudogap
represents a foreshadowing of the superconducting phase. As the temperature is
lowered, first reaching T*, a few electron pairs start to form, but they are
sparse and lack the long-range coherence necessary for superconductivity—they
can’t “talk” to one another. As the temperature continues to fall, more such
pairs are formed until, upon reaching Tc, virtually all conducting electrons
are paired and act in correlation; they’re all talking. In this scheme, there’s
only a single phase transition, which occurs at Tc.
Another school of thought argues that the appearance of the pseudogap at T*
is also a true phase transition. The pseudogap does not represent a smooth
shift to the superconducting state but is itself a state distinct from both
superconductivity and normal “metallicity” (the usual state of delocalized,
uncorrelated electrons). This new phase implies the existence of a “quantum
critical point”—a point along a line at zero temperature where competing phases
meet. In theory, with competing phases wildly fluctuating in the neighborhood
of a quantum critical point, there may be entirely new routes to
superconductivity.
“Promising as the ‘quantum critical’ paradigm is for explaining a wide range
of exotic materials, high-Tc superconductivity in cuprates has stubbornly
refused to fit the mold,” says Joseph Orenstein of Berkeley Lab’s Materials
Sciences Division, a professor in physics at UC Berkeley, whose group conducted
one of the research team’s three experiments. “For 20 years, the cuprates
managed to conceal any evidence of a phase-transition line where the quantum
critical point is supposed to be found.”
In recent years, however, hints have emerged. “New ultrasensitive probes
have found fingerprints of phase transitions in high-Tc materials,” Orenstein
says, “although there’s been no smoking gun. The burning question is whether we
can discover the nature of the new phase or phases.”
A multipronged attack on the
pseudogap
In the Stanford-Berkeley study, three groups of researchers joined forces
to probe the pseudogap phase on the same sample.
“Pb-Bi2201 was chosen because, first, it is structurally simple, and second,
it has a relatively wide temperature range between Tc and T*,” says Ruihua He.
“This permits a clean separation of any remnant effect of superconductivity
from genuine pseudogap physics.”
Groups led by Z.-X. Shen at beamline 5?4 of the Stanford Synchrotron
Radiation Lightsource (SSRL) at SLAC and by Zahid Hussain, ALS Division Deputy
for Scientific Support, at beamline 10.0.1 of Berkeley Lab’s ALS, studied the
sample with angle-resolved photoemission spectroscopy (ARPES). In ARPES, a beam
of x-rays directed at the sample surface excites the emission of valence
electrons. By monitoring the kinetic energy and momentum of the emitted
electrons over a wide temperature range the researchers map out the material’s
low-energy electronic band structure, which determines much of its electrical
and magnetic properties.
At Stanford, researchers led by Aharon Kapitulnik of SIMES, a professor in
applied physics at Stanford
Univ., studied the same
crystal of Pb-Bi2201 with the magneto-optical Kerr effect. In light reflected
from the sample under a zero magnetic field, tiny rotations of the plane of
polarization are measured as the temperature changes. The rotations are
proportional to the net magnetization of the sample at different temperatures.
Finally, Orenstein’s group at Berkeley
applied time-resolved reflectivity to the sample. A pump pulse from a laser
excites electrons many layers of atoms deep, temporarily affecting the sample’s
reflectivity. Probe pulses, timed to follow less than a trillionth of a second
after the pump pulses, reveal changes in reflection at different temperatures.
All these experimental techniques had previously pointed to the possibility
of a phase transition in the neighborhood of T* in different cuprate materials.
But no single result was strong enough to stand alone.
ARPES experiments performed in 2010 by the same group of experimenters as in
the present study revealed the abrupt opening of the pseudogap at T* in
Pb-Bi2201. Variations in T* in different materials and even different samples,
as well as in the surface conditions to which ARPES is sensitive, had left room
for uncertainty, however.
In 2008, the Kerr effect was measured in another cuprate, also by the same
group as in the present study, and showed a change in magnetization from zero
to finite across T*. This was long-sought thermodynamic evidence for the
existence of a phase transition at T*. But compared to the pronounced spectral
change seen by ARPES, the extreme weakness of the Kerr-effect signal left doubt
that the two results were connected.
Finally, since the late 1990s various experiments with time-resolved
reflectivity in different cuprates have reported signals setting in near T* and
increasing in strength as the temperature drops, until interrupted by the onset
of a separate signal below Tc. The probe is complex and there was a lack of
corroborating evidence for the same cuprates; the results did not receive wide
attention.
Now the three experimental approaches have all been applied to the same
material. All yielded consistent results and all point to the same conclusion:
there is a phase transition at the pseudogap phase boundary—the three
techniques put it precisely at T*. The electronic states dominating the
pseudogap phase do not include Cooper pairs, but nevertheless intrude into the
lower-lying superconducting phase and directly influence the motion of Cooper
pairs in a way previously overlooked.
“Instead of pairing up, the electrons in the pseudogap phase organize
themselves in some very different way,” says He. “We currently don’t know what
exactly it is, and we don’t know whether it helps superconductivity or hurts
it. But we know the direction to take to move forward.”
Says Orenstein, “Coming to grips with a new picture is a little like trying
to steer the Titanic, but the fact that all three of these techniques
point in the same direction adds to the mounting evidence for the phase
change.”
Hussain says the critical factor was bringing the Stanford and Berkeley scientists
together. “We joined forces to tackle a more complex problem than any of us had
tried on our own.”