Strontium titanate is a bulk insulator that becomes superconducting at remarkably low carrier densities. Even more enigmatic properties become apparent at the strontium titanate/lanthanum aluminate (STO/LAO) interface and it is important to disentangle the effects of reduced dimensionality from the poorly-understood pairing mechanism. Recent experiments measuring the surface photoemission spectrum and bulk tunneling spectrum have found a cross-over, as a function of carrier density, from a polaronic regime with substantial spectral weight associated with strongly coupled phonons, to a more conventional weakly coupled Fermi liquid. Interestingly, it is only the polaronic state that becomes superconducting at low temperatures, although the properties of the superconducting phase itself appear entirely conventional. We interpret these results in a simple analytical model that extends an Engelsberg-Schrieffer theory of electrons coupled to a single longitudinal optic phonon mode to include the response of the electron liquid, and in particular phonon-plasmon hybridization. We perform a Migdal-Eliashberg calculation within our model to obtain this material's unusual superconducting phase diagram.
 Z. Wang et al, Nat. Mater. (2016)
 A.G. Swartz et al, arXiv:1608.05621
Research: Condensed Matter Theory
Advisor: Peter Littlewood
- B.S., Carnegie Mellon University, 2012
- M.S., University of Chicago, 2013
Graduate Student (2012-pres) Dept. of Physics, James Franck Institute
Sachs Felowship, 2013
Condensed matter physics is concerned with the emergent behavior of systems with many strongly interacting constituents. Explicitly tracking every particle - every molecule in a glass of water, say - is computationally infeasible, and in any case frankly uninteresting, whereas the dominant low-energy physics that emerges - for instance the wave that forms when the glass is swirled around, characterized by a few simple parameters like an amplitude and a speed - is both tractable and ultimately the behavior that dominates our observations of the system.
I study strongly correlated electronic systems, so called because the collective behavior of the constituent electrons (among others) is mostly determined by their interactions, departing radically from what could be anticipated from the properties of a single particle. The spectacular phenomena that result, such as superconductivity, defy any description in terms of small departures from a non-interacting gas (as would be appropriate for simple metals, for example). I am particularly interested in certain underrated materials whose peculiarities make it possible to tease out physics that remains elusive elsewhere.
The first is actually a class of synthetic "materials" that can be realized in a variety of systems, from quantum well excitons in dielectric mirrors to cold atoms in cavities, and the effective quasi-particles that emerge when the system is optically pumped are known as polaritons. Most generally, polaritons are hybrid particles of light and matter, and through tuning of the light-matter interaction can inherit properties of each that are desirable for pushing the system into a wide variety of behaviors that are otherwise hard to access. From the light, which is of course massless and non-interacting in free space, polaritons inherit effective masses orders of magnitude smaller than an electron mass and a characteristic dynamical time scale that is much faster than for competing effects from electronic or atomic motions. Meanwhile, polariton-polariton interactions are largely inherited from the interactions of the matter component, which can of course be tuned separately.
For instance, in polaritons based on quantum well excitons, where the polariton-polariton interaction is mostly a weak repulsion, polaritons form a liquid which at low enough temperature undergoes a Bose-Einstein condensation transition and forms a superfluid. The transition temperature is controlled by the ratio of kinetic energy to thermal energy, and for extremely light polaritons can end up as high as room temperature - a feat which has been experimentally achieved and remains far out of reach in other systems. Polaritons are therefore an enticing platform to explore phenomena related to condensation and superfluidity, and have for many years been a rich playground in this field.
My own research focuses on the phases of polaritons that can be realized when interactions become strong and long-ranged, such as the van der Waals repulsion between highly-excited Rydberg states of excitons or atoms. Although this system still supports condensation, the interactions no longer serve to merely thermalize it, and all else being equal would favor an ordered, crystalline state. It turns out that the competition between condensation and crystallization supports a plethora of phases with varying spatial order, including so-called super-solids in which a patterned density coexists with superfluidity. These intriguing states of matter have long been sought, for instance in Helium-4, but with ambiguous results. Polaritons may provide a path to explore these and other heretofore inaccessible states of matter.
A second material I study is the superconductor strontium titanate (STO). STO is a semiconductor but upon light doping becomes superconducting, with a transition temperature which forms a "dome" as a function of carrier density, much like the high-temperature superconducting cuprates. Unlike the cuprates, the superconducting phase appears entirely conventional and well-described by the conventional Bardeen-Cooper-Schrieffer (BCS) theory developed for metals. This is curious because the pairing of electrons in a thin shell around the Fermi energy mediated by acoustic phonons, which is the BCS mechanism of superconductivity, cannot possibly explain the behavior of STO. There is already of course a large industry of proposing unconventional superconductivity mechanisms, but these hypotheses are difficult to unambiguously test in the cuprates where a variety of other electronic phases compete and intertwine with superconductivity. In my work to generate a theory of the comparatively simpler STO, the hope is to find an account that is clean enough to inform new directions in the search for better superconductors.