Breakdown of Rotational Invariance in Quantum Hall Systems with Anisotropic Interaction

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NONTECHNICAL SUMMARYThe Division of Materials Research and the Division of Human Resource Development contribute funds to this award. It supports fundamental theoretical and computational research on two-dimensional systems of electrons that interact strongly with each other leading to novel electronic states that spontaneously develop a preferred direction. Two-dimensional systems of electrons can be created at the interface of two semiconductors, and they manifest intriguing properties in the presence of a strong perpendicular magnetic field. In that situation, electrons are predicted to form a liquid-like state of matter, exhibiting properties that appear the same in all directions, that is, they are isotropic. However, the presence of an anisotropic or direction-dependent interaction between electrons may drastically change the system's properties, resulting in quantum mechanical states of electrons that are analogous to the states of long molecules in liquid crystals, which form the basis of modern liquid-crystal displays. The PI and his team will use analytical and computational methods to understand the nature of the anisotropy in a system of electrons that interact with an anisotropic interaction potential. The research will contribute to the intellectual foundations that lead to new electronic and optical device technologies.Undergraduate, and often minority, students at the Historically Black Prairie View A & M University will be trained in applying analytical methods and in carrying out numerical simulations. The students will gain important research experience that can help them in their pursuit of future graduate studies, and will help enhance the research and education infrastructure of the institution. The PI will carry out outreach activities that aim to increase interest in science topics at local communities and high schools.TECHNICAL SUMMARYThis award supports theoretical research and education on the emergence of anisotropic orders in strongly correlated quantum Hall systems of electrons in the presence of an anisotropic interaction potential. An anisotropic interaction potential may naturally lead to anisotropic order at regimes where only an isotropic liquid was previously thought possible. These novel quantum phases may possess unconventional properties of great interest to the broad field of theoretical condensed matter physics.The project will develop a framework to understand the emergence of anisotropic order in quantum Hall systems in the presence of an anisotropic interaction potential in the extreme quantum limit. The research aims to explore outstanding issues such as: i) the stability of novel anisotropic quantum Hall liquid phases at odd-denominator filling factors of the lowest Landau level driven by an anisotropic Coulomb interaction potential between electrons, and ii) the stability of novel anisotropic Fermi liquid phases at even-denominator filling factors of the lowest Landau level driven by an anisotropic Coulomb interaction potential between electrons. The PI and his research team will use a combination of analytical and computational methods to carry out the research activities.Undergraduate, and often minority, students at the Historically Black Prairie View A & M University will be trained in applying analytical methods and in carrying out numerical simulations. The students will gain important research experience that can help them in their pursuit of future graduate studies, and will help enhance the research and education infrastructure of the institution. The PI will carry out outreach activities that aim to increase interest in science topics at local communities and high schools.