In a similar way, Landau's Fermi Liquid Theory represents a kind of "Standard Model" for interacting electrons in metals. Like the Standard Model of particle physics, this theory has been phenomenally successful. Also like that other Standard Model, the Landau theory is an "effective theory," in this case valid at long distances and low energies. The Landau theory supposes that interacting electrons at sufficiently low temperatures have energies which are in a 1:1 correspondence to the non-interacting case. The interactions are said to "dress" the electrons into "quasiparticles" which behave as ordinary electrons apart from a renormalized mass and magnetic moment which readjust measureable properties relative to the free electron limit. This picture underlies most of our successful understanding of metallic physics--for example, the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity assumes that Landau quasiparticles pair and the resulting condensation of these pairs produces the superconductivity.
The trouble with the Standard Model of Particle Physics and with the Standard Model of Metal Physics is their very strength: the astonishing descriptive and predictive power they have successfully displayed exerts an overwhelming intellectual tyranny over the field! Physicists in both areas have been hopeful of finding some glimmer of new science that may indicate the breakdown of these theories and generate new work.
Fortunately in the case of Metal Physics, this has begun to occur. The high temperature superconductors, for one, display over a wide range of material parameters a clear breakdown of the Landau theory. Experiment shows that the quasiparticles are not characterized by sharp quantum mechanical levels, and thus cannot represent the fundamental "particles" of these materials. It turns out that another class of materials, the heavy fermion materials (in which interactions drive the electron mass up by a factor of a thousand!) also show this unusual behavior. These materials are also superconducting, and there is strong evidence that the superconductivity is the most unusual yet found (based, for example, upon highly complex phase diagrams).
These heavy fermion materials contain rare earth atoms (like Cerium) or actinide atoms (like Uranium) together with "light electron" atoms (like Copper). These atoms have open f-electron shells, and so can have magnetic and electric moments. It is the interactions between the atomic magnetic and electric moments on the rare earth or actinide atoms which provide the exotic low temperature physics.
Much of my recent research has focused on producing a theory of these unusual materials. I am studying a particular model (the "two-channel Kondo model") in both the extremely dilute limit (one uranium or cerium atom in a metal) and the fully concentrated limit (one uranium or cerium atom in every repeat unit cell of the crystal). These models have low energy states which completely defy a description by Landau theory, and have properties which display a good (if incomplete) correspondence to real materials.
A wonderful theoretical result has been the finding of exotic superconductivity that is fundamentally linked to the breakdown of the Landau theory, and that this superconductivity is indeed the weirdest so far found--the pairs avoid each other in time, and seem to have a net momentum to their center of mass. This steps way outside the BCS paradigm.
The techniques used in my research group and collaborations range from analytic phenomenology, to large scale computation involving Feynman diagram methods or Quantum Monte Carlo techniques. These approaches are sometimes best realized in odd limits (such as infinite spatial dimensionality or infinite number of quantum mechanical components to the magnetic moment) which are a lot of fun to explore and understand. Despite these extreme theoretical wanderings, I always keep an eye on the experimental backdrop (to make sure I stay on this side of the Looking Glass!).
I am also cultivating interests in environmental physics and within a year or two may be looking for students to work with in this area. I am interested in certain problems arising in the study of global warming and biodiversity.
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