Exotic Quantum Liquid Phases Due to Intrinsic Degrees of Anisotropy

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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 and education involving the study of electrons confined to two dimensions and subject to interactions and crystal environments that lead to a preferred direction.Atoms and molecules are made of elementary particles such as electrons, protons, and neutrons. Electrons are often tightly bound to their atoms. Materials are made of many billions of atoms, and in metals and semiconductor materials some electrons can move relatively freely. These electrons can behave like a liquid and can easily respond to externally applied fields, such as electric fields, magnetic fields, and applied pressure. For example, a copper wire conducts electricity in response to an applied electric field.Since many interesting properties of materials are determined by the behavior of such free electrons, it is natural to study the nature of the possible states of electronic matter that arise in large systems of electrons and the dependence of their properties on external parameters, such as temperature, electron density, and applied magnetic field. The PI will study electronic states in materials where free electrons are restricted to two-dimensions where the interaction between electrons and quantum effects may combine leading to new phenomena and new electronic states of matter. The electrons may be in a uniform liquid state of matter if interactions are not very strong. The properties of such a liquid state would be isotropic - the same in all directions. However, it is possible that effective interactions between electrons are anisotropic or direction dependent. The presence of the crystalline lattice of atoms makes electrons behave as though they have an effective mass that can depend on the direction of their motion. This may lead to electrons behaving like a liquid of elongated rods leading to electronic states analogous to those assumed by the rod-like molecules in a liquid crystal display. The PI will investigate electronic states that may arise as a consequence of anisotropy. This includes externally induced anisotropy, such as the anisotropic states that could arise under the application of a strong magnetic field perpendicular to the 2D world of the electrons. The investigation of new electronic states adds to the intellectual foundations that lead to new electronic device technologies. The research activities conducted in this project will lead to research opportunities for economically challenged students in the setting of a HBCU, will enhance research and education in an undergraduate environment, and will improve the preparation of undergraduate students for graduate studies. Overall, this project will help to enhance the research and the education infrastructure at the local institution, and lead to broader participation of underrepresented groups in science.TECHNICAL SUMMARYThe Division of Materials Research and the Division of Human Resource Development contribute funds to this award. It supports fundamental theoretical and computational research to investigate the emergence of novel anisotropic exotic quantum liquid phases in strongly correlated Fermi systems. The PI will study two-dimensional systems of electrons in the quantum Hall regime and two-dimensional Fermi liquid phases with deformed Fermi surfaces in presence of some internal degree of anisotropy. The PI aims to understand how anisotropic electronic ordered states arise in various quantum phases in response to intrinsic anisotropy of the system. The PI will also investigate the nature of novel exotic anisotropic phases such as anisotropic quantum Hall liquid phases driven by an anisotropic interaction potential and anisotropic Fermi liquid phases with deformed Fermi surfaces driven by a combination of anisotropic effective mass and an anisotropic interaction potential between electrons.The theoretical approaches can be applied to experiments on two-dimensional electron systems with strong mass anisotropy where unusual anisotropic transport in the quantum Hall regime is anticipated. The ideas of this research can be relevant to understand experiments in two-dimensional systems of electrons confined in aluminum arsenide quantum wells and related systems. The electron effective mass anisotropy ratios can be almost one order of magnitude in these systems. Of particular interest is how tuning piezoelectric properties effects the anisotropic effective electron interactions, and the resulting experimentally observable consequences. Experiments may be proposed to detect signatures in transport properties resulting from the interplay of different sources of anisotropy. The PI will consider other physical systems as well, including ultracold atoms in anisotropic lattice traps. The PI and his team will use a combination of theoretical and computational methods, including exact diagonalization and quantum Monte Carlo, to carry out the research. Students will use methods suited to their skills, such as variational or perturbation methods from quantum theory, or computer simulations, in order to enhance their educational experience as appropriate. The research provides a setting for education and mentoring to enhance interest in science and leading careers in STEM. This project will help broaden participation of minority and economically challenged students in science and engineering through enhancing the pipeline.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.