Quantum Critical Point - Quantum Critical Endpoints

Quantum Critical Endpoints

Quantum critical points arise when a susceptibility diverges at zero temperature. There are a number of materials (such as CeNi₂Ge₂) where this occurs serendipitously. More frequently a material has to be tuned to a quantum critical point. Most commonly this is done by taking a system with a second-order phase transition which occurs at finite temperature and tuning it—for example by applying pressure or magnetic field or changing its chemical composition. CePd₂Si₂ is such an example, where the antiferromagnetic transition which occurs at about 10K under ambient pressure can be tuned to zero temperature by applying a pressure of 28,000 atmospheres. Less commonly a first-order transition can be made quantum critical. First-order transitions do not normally show critical fluctuations as the material moves discontinuously from one phase into another. However if the first order phase transition does not involve a change of symmetry then the phase diagram can contain a critical endpoint where the first-order phase transition terminates. Such an endpoint has a divergent susceptibility. The transition between the liquid and gas phases is an example of a first-order transition without a change of symmetry and the critical endpoint is characterized by critical fluctuations known as critical opalescence.

A quantum critical endpoint arises when a finite temperature critical point is tuned to zero temperature. One of the best studied examples occurs in the layered ruthenate metal, Sr₃Ru₂O₇ in a magnetic field. This material shows metamagnetism with a low-temperature first-order metamagnetic transition where the magnetization jumps when a magnetic field is applied within the directions of the layers. The first-order jump terminates in a critical endpoint at about 1 kelvin. By switching the direction of the magnetic field so that it points almost perpendicular to the layers, the critical endpoint is tuned to zero temperature at a field of about 8 teslas. The resulting quantum critical fluctuations dominate the physical properties of this material at nonzero temperatures and way from the critical field. The resistivity shows a non-Fermi liquid response, the effective mass of the electron grows and the magnetothermal expansion of the material is modified all in response to the quantum critical fluctuations.