This award supports theoretical research and education on soft quantum matter. The PI will use ideas and techniques of soft matter physics, including generalized elasticity and hydrodynamics, and the physics of driven, nonequilibrium systems, to understand the solid and liquid-crystalline phases of two-dimensional electron systems in a quantizing magnetic field, and the phenomenology of supersolids.
In many soft condensed matter systems, a competition between repulsive long range interactions and attractive short range interactions is resolved through the formation of a spatially inhomogeneous mesophase, such as a stripe or bubble phase. Examples include thin ferromagnetic films and the intermediate state of type-I superconductors. This proposal focuses on such phases in two-dimensional electron systems, where the Coulomb interaction provides the long range repulsion and the quantum-mechanical exchange interaction the short-range attraction. Over the past six years a number of transport and microwave conductivity experiments on such systems have provided evidence for electronic "stripe" phases as well lattice phases, including Wigner and bubble crystals. The proposed research will study possible structural phase transitions between different crystal phases and the elastic properties of those phases. These elastic properties will be used as the input for a study of the pinning modes of these crystals in both perpendicular and tilted magnetic fields. Driven Wigner and bubble crystals, specifically their depinning transitions and nonlinear IV characteristics, will also be studied.
Supersolidity is a proposed state of matter in which Bose-Einstein condensation coexists with the crystalline order of a solid. Motivated by recent torsional oscillator experiments on solid helium that claim to have observed this novel state of matter, the PI will study the phenomenology of supersolids. The PI will further develop his recently proposed Landau model for the normal-solid to supersolid transition with the objective of suggesting new experiments that might provide additional evidence for a supersolid phase. The PI will also study the hydrodynamics of a model supersolid and derive its density-density correlation function, which could be measured in a light-scattering experiment.
A strong commitment to education of undergraduate and graduate researchers is accomplished in parallel with the research efforts. The REU program is directly tied to this research.
NON-TECHNICAL SUMMARY:
This award supports theoretical research and education on the discovery and understanding of new states of matter in the quantum world.
One focus of the research is on new states of matter and the transformations that may occur among them that might arise when electrons that are confined to a plane and exposed to a high magnetic field. Another focus of the work is to identify whether experiments are seeing a state of matter in helium that has been solidified and cooled to the lowest temperatures. This curious state was proposed long ago but has remained unseen until recent experiments were performed that rotate a chunk of solid helium. They suggest a fraction of the atoms remain at rest; a curious property for an apparently solid body. The PI will carry out research that aims to find experimental signatures that will aid in the determination of whether this enigmatic state of matter has actually been seen.
The discovery of new states of matter and understanding their properties has led to new technologies from which we all benefit. For example, the discovery of superconductivity, once a laboratory curiosity, has led to the powerful magnets that are used in MRI machines that are now routinely used in medicine. In a similar tradition, this research may contribute to the intellectual foundations of future technology that will benefit society and help keep America competitive.
