Pigeonholing quantum phase transitions

Classification of quantum phenomena critical to high-temp superconductivity

A team of physicists led by researchers at Rice University has developed the first thermodynamic method for systematically classifying quantum phase transitions, mysterious electromagnetic transformations that are widely believed to play a critical role in high-temperature superconductivity.

The new research is described in two papers – one theoretical and one experimental – in the Aug. 8 issue of Physical Review Letters. The theoretical paper predicts that a mathematical irregularity called a divergence occurs at every “quantum critical point,” a stage materials pass through as they change phases. The experimental paper reports the observation of such a divergence in the quantum critical points of two metals with very different quantum signatures.

“One of the biggest questions in condensed matter physics today is whether high-temperature superconductivity arises out of quantum critical points,” said lead researcher Qimiao Si, associate professor of physics and astronomy at Rice. “Classification of quantum critical points is an important step toward answering this question.”

Matter commonly transforms itself via phase changes. Melting ice and boiling water are examples of phase transitions that arise from changes in temperature, which can easily be described using classical physics. Within the past decade, physicists have detected quantum phase transitions, changes that arise entirely from quantum fluctuations — the jittering of subatomic particles as described by Heisenberg’s uncertainty principle.

Every phase transition, whether classical or quantum, is marked by a change in the way matter is ordered. For example, when ice melts, water molecules change from an ordered crystal lattice to a disordered fluid. In quantum phase transitions, which occur in rare earth metals called heavy fermions, electrons change from magnetic to paramagnetic. As the metals change quantum phases, they pass through a stage known as the “critical point” in which all electrons throughout the material respond collectively and can no longer be regarded as individual particles.

The new theoretical work by Si and Rice graduate student Lijun Zhu, in collaboration with Achim Rosch’s group at the University of Karlsruhe, Germany, sprang from the fact that thermodynamic quantities — like specific heat — often diverge at classical critical points. The team predicted that the Grüneisen ratio — the relative value of thermal expansion to specific heat — would diverge in a very predictable manner in any material as it approached a quantum critical point.

To test the theory, Si and Zhu collaborated with Frank Steglich’s experimental group from the Max-Planck Institute for Chemical Physics of Solids in Dresden, Germany. Steglich, together with his colleagues John Mydosh, Philipp Gegenwart and Robert Küchler, chose two heavy fermion compounds that are based on cerium and ytterbium. The quantum critical points for each occur at absolute zero, the coldest temperature possible.

Since it is impossible to achieve absolute zero in a laboratory, the team cooled the metals to within a few hundredths of a degree above absolute zero. They found that the Grüneisen ratio diverged as predicted in both metals as they approached absolute zero.

From the divergences, the researchers concluded that the two metals belong to two different classes of quantum phase transition. One of these is the locally-critical quantum phase transition, a new class of quantum phase transition first proposed by Si and colleagues in an article in Nature two years ago.

“If our classification system is born out through experiments on additional materials, the discipline will, for the first time, have a general thermodynamic means to systematically understand quantum critical points,” Si said. “Such understandings could prove very valuable for physicists studying high-temperature superconductors.”

Materials scientists are interested in superconductors because they conduct electricity with no resistance. In standard conductors, like copper or aluminum, a significant percentage of power is lost due to resistance, the tendency of the wires to convert some electricity into heat. Most superconductors must be cooled to near absolute zero before they superconduct. High temperature superconductors operate at temperatures as high as minus 164 degrees Fahrenheit, far above the boiling point of liquid nitrogen, an important milestone for those interested in designing practical systems that are both technologically and economically feasible.

Heavy fermion metals are prototype systems for quantum criticality. When these metals reach their quantum critical point, the electrons within them act in unison and the effects of even one electron moving through the system cause widespread effects throughout. This is very different from the electron interactions in a common wiring material like copper. It is these collective effects that have increasingly convinced physicists of a possible link between superconductivity and quantum criticality.

Contact: Jade Boyd, jadeboyd@rice.edu