RUI-Unconventional Anisotropic Order in Strongly Correlated Fermi Systems

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NONTECHNICAL SUMMARYThis award supports fundamental theoretical and computational research on systems of electrons that interact strongly with each other leading to novel electronic states that spontaneously develop a preferred direction. How these states respond to say, an applied magnetic or electric field depends on the relative orientation of the field to the preferred direction. The PI will investigate how states with a preferred direction can arise eventhough the fundamental interaction between two electrons depends only on distance between them and so, is the same for any direction. Of particular interest is how anisotropic states emerge in electrons confined to a plane at the interface of two semiconductors and exposed to a perpendicular or nearly perpendicular magnetic field. The PI will investigate quantum mechanical states of electrons that are curiously analogous to the states of long molecules in liquid crystals that form the basis of modern display technology. This research contributes to the intellectual foundations that lead to new electronic and optical device technologies. This research project provides an effective vehicle for involving undergraduate students in research and training them in skills that will be valuable in the modern technical workforce. Undergraduate students, often minority students, will be involved in important aspects of this research. Because the research will require exploring a variety of models using various methods methods, there are many opportunities for undergraduate students to gain important research experience that can help them as they pursue future graduate studies. This project will help to enhance the research and the education infrastructure at the local institution. Through outreach activities, the PI aims to increase interest in science topics at local communities and high schools ultimately contributing to broader participation in science.TECHNICAL SUMMARYThis award supports research and education with the aim to investigate the emergence of unconventional anisotropic order in strongly correlated Fermion systems at absolute zero temperature. The interplay between interactions and quantum effects in this regime may lead to the stabilization of novel quantum phases with unconventional properties. The main goal of this project is to study how various unconventional anisotropic phases with liquid crystalline order can be stabilized in strongly correlated Fermi systems with non-monotonic but isotropic interaction potentials. A focus of this research is to investigate how isotropic interaction potentials trigger anisotropic behavior. The PI and his research team will employ theoretical and computational methods to address outstanding questions regarding the appearance of novel types of anisotropic ordering and phase transitions leading to unconventionally ordered quantum states. The PI aims to develop a framework to understand the emergence of anisotropic order in various correlated Fermion systems by exploring mechanisms ranging from spontaneous Fermi surface deformations to novel anisotropic liquid crystalline phases in a magnetic field. The PI aims to advance understanding of several fundamental issues including: (i) The stabilization of anisotropic Fermi liquid phases due to a non-monotonic interaction potential, namely, how isotropic interaction potentials can drive a correlated Fermi systems towards anisotropic order; (ii) The nature of the recently discovered anisotropic quantum Hall phases in tilted magnetic field for Laughlin-like filling factors in the first excited Landau level; and (iii) The nature of anisotropic liquid crystalline phases in a weak magnetic field in presence of weak anisotropic perturbations that break the rotational symmetry of the dominant interaction potential.This research project provides an effective vehicle for involving undergraduate students in research and training them in skills that will valuable in the modern technical workforce. Undergraduate students, often minority students, will be involved in important aspects of this research. Because the research will require exploring a variety of models using various methods, there are many opportunities for undergraduate students to gain important research experience that can help them as they pursue future graduate studies. This project will help to enhance the research and the education infrastructure at the local institution. Through outreach activities, the PI aims to increase interest in science topics at local communities and high schools ultimately contributing to broader participation in science.