## Tuesday, December 10, 2013

### Another workshop + some links

It's been a very hectic end-of-semester, between classes, research, and writing.  Thank all of you for your replies concerning power outages.  Perhaps recurring power problems are actually some secret motivator to get all of us to work on alternative energy research - I'll invent an arc reactor just to guarantee reliable power.

Right now, my colleagues and I here at Rice are hosting another workshop, this one on heavy fermions and quantum criticality.  For those who don't know, "heavy fermions" are found in materials where there are particular magnetic interactions between mobile charge carriers and localized (usually 4f) electrons.  Think of it this way:  the comparatively localized electrons have a very flat, narrow band dispersion (energy as a function of momentum).  (In the limit of completely localized states and isolated atoms, the "band" is completely flat, since the 4f states are identical for all the same atoms.)  If you hybridize those comparatively localized electrons with the more delocalized carriers that live in s and p bands, you end up with one band of electron states that is quite flat.  Since $E \sim (\hbar^2/2m*)k^2$, a very flat $E(k)$ would be equivalent to a really large effective mass $m*$.  Heavy fermion materials can have electron-like (or hole-like) charge carriers with effective masses several hundred times that of the free electron mass.   These systems are interesting for several reasons - they often have very rich phase diagrams (in terms of magnetic ordered states), can exhibit superconductivity (!), and indeed can share a lot of phenomenology with the high temperature superconductors, including having a "bad metal" normal state.  In the heavy fermion superconductors, it sure looks like spin fluctuations (related to the magnetism) are responsible for the pairing in the superconducting state.

Quantum criticality has to do with quantum phase transitions.  A quantum phase transition happens when you take a system and tune some parameter (like pressure, temperature, doping, etc.), and find that there is a sharp change (like onset of magnetic order or superconductivity) in the properties (defined by some order parameter) of the ground state (at zero temperature) at some value of that tuning (the quantum critical point).  Like an ordinary higher temperature phase transition, one class of quantum phase transitions is "second order", meaning (among other things) that fluctuations of the order parameter are important.  In this case, they are quantum fluctuations rather than thermal fluctuations, and there are particular predictions for how these things survive above $T = 0$ - for example, plotting properties as a function of $\omega/T$, where $\omega$ is frequency, should collapse big data sets onto universal curves.  There appears to be an intriguing correlation between quantum critical points, competition between phases, and the onset of superconductivity.  Fun stuff.