Project Details
Description
NONTECHNICAL SUMMARY
This award supports theoretical research and education on new electronic states of matter that emerge from correlated motion of electrons that arise from the interactions among them. The understanding of emergent states is an important challenge in modern condensed matter physics. The system of electrons confined to a plane at an interface between semiconductors has proved to be fertile for the investigation of new states of matter, producing a large variety under the application of a high magnetic field. This award supports research that will provide insight into the nature of liquid and crystal phases, the role of spin - a quantum mechanical property of the electron, and effects of the confined environment on electrons. The PI will perform detailed calculations of compressibility, an important thermodynamic quantity, incorporating nontrivial many body effects, and also explore the applicability of other theoretical methods, to non-uniform fractional quantum Hall states.
This research contributes to the knowledgebase that supports new technology and to education. The study of the fractional quantum Hall effect in various contexts has led to new discoveries and new ideas, such as topological insulators, Chern insulators, Majorana fermions, abelian and non-abelian anyons, and the idea of manipulating quantum-Hall-like, or topological, states to perform computation. The study of fractional quantum Hall effect has also been a driving force for improvements in the quality of semiconductor materials, necessary for other technological innovations.
The graduate students supported by this grant will receive broad training in forefront areas of research, will master condensed matter theory on the one hand and computational methods on the other, and will be exposed to international collaborative research. The PI and students involved in the project will devote a portion of their time to working with middle school, high school and undergraduate students to expose them to ideas that become relevant in low dimensions, and to motivate them into physics research. This will be done through existing outreach activities at Penn State as well as through organization of a summer school.
TECHNICAL SUMMARY
This award supports theoretical research and education concerning new phenomena in solid and liquid phases that occur when two-dimensional electrons are exposed to a strong magnetic field. It will focus on several problems on which substantial progress can now be made as a result of the very accurate theoretical understanding that has been developed in recent years. Some of the specific projects are as follows. The crystal in the lowest Landau level has been shown to be a nontrivial, inherently quantum mechanical state, which has non-trivial defects called bubble interstitials. The spin physics of the crystal will be studied using theoretical methods as well as Monte Carlo simulation. The PI will investigate the role of strong correlations in the bubble crystal believed to occur in the second Landau level. The recent understanding of the role of anisotropic effective mass will be extended to a larger variety of fractional states. The compressibility of the correlated system will be calculated as a function of the filling factor, incorporating the variety of liquid and crystal states. The applicability of methods such as the density functional theory will be explored to describe non-homogeneous situations. These questions are of relevance to experiments being performed on semiconductor heterojunction and graphene two-dimensional systems. In all of these cases, the aim will be to obtain detailed quantitative predictions as a function of various parameters, such as Landau level mixing and the width and shape of the transverse wave function, which can be varied in experiments in a controllable manner. A combination of analytical methods, exact diagonalization and Monte Carlo techniques will be used as needed.
The graduate students supported by this grant will receive broad training in forefront areas of research, will master condensed matter theory on the one hand and computational methods on the other, and will be exposed to international collaborative research. The PI and students involved in the project will devote a portion of their time to working with middle school, high school and undergraduate students to expose them to ideas that become relevant in low dimensions, and to motivate them into physics research. This will be done through existing outreach activities at Penn State as well as through organization of a summer school.
Status | Finished |
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Effective start/end date | 6/15/15 → 9/30/18 |
Funding
- National Science Foundation: $309,000.00