Time Dependence and Textures in Low Dimensional Electron Systems

Indiana University, Bloomington IN

Investigators

Abstract

NON-TECHNICAL SUMMARY: This award supports theoretical research and education on the role of specially arranged external disturbances in creating novel electronic states in materials. Topology in the context of condensed matter systems provides a way of understanding how electrons are organized in a material, as well as predicting robust properties of how they move through and along the edges of the material. The concept has become increasingly recognized as an important facet of the physics of condensed matter systems. In this project, the PI will explore how topological characteristics of electronic states in materials can be manipulated using periodic time-dependent disturbances, such as light or electric and magnetic fields that vary in time. The resulting systems are generically known as Floquet systems, and they share the ability of supporting "textures," regions where discrete properties, such as the direction of the intrinsic magnetism of the electron, vary in ways which, when combined for the system as a whole, lead to patterns with interesting properties. The research is focused on ways to understand and predict when such patterns should be present, and furthermore in developing useful models of how such reorganization and patterning of microscopic properties leads to measurable electronic consequences. The PI will also explore, in the case of Floquet systems, the possibility of exploiting textures as possible resources in quantum information processing. This project will be conducted with the full participation of graduate students, who will be trained in modern methods of condensed matter physics, preparing them for careers in science and technology. Scientists from the US and abroad will be collaboratively involved in the work. In addition, the PI will be involved in an educational initiative specifically for high-school students from rural and/or low-income areas in Indiana: the creation of an online introductory physics course for Indiana high-school students without access to an Advanced Placement physics course. Included will be discussions about the remarkable modern materials relevant to this proposal, such as graphene and carbon nanotubes. TECHNICAL SUMMARY: This award supports theoretical research and education on the roles of topology in Floquet materials. Floquet systems are defined by periodic time-dependent potentials, for example by shining strong, circularly polarized light normally onto a two dimensional electron system. In some cases such potentials can induce texture and topology in a band of states, which may not be present, or may have a different form, in the corresponding static system. The PI seeks to answer fundamental questions about these systems. The research will include studies of edge-state structure and transport properties, which appear to be related in a more complicated way than in analogous static topological systems. As part of this, the PI and coworkers will explore topological invariants that directly address transport coefficients, and investigate how they relate to the edge states they support. Studies of disorder effects, including localization and disorder-induced transitions among different topological states, will be undertaken. Also explored will be new concepts in optically generated "valleytronics" which might be realized for certain Floquet systems. The studies will also include simpler models with an eye towards defining density matrices for Floquet systems, with the eventual goal of developing methods in which contacts and/or thermal baths need not be explicitly included in modeling a Floquet system. Textures can also be present in real space, and have particularly interesting realizations in quantum Hall systems, for which they carry physical charge. In the project, such physics will be explored in multicomponent Dirac systems, in particular graphene and topological insulator surfaces, where different possible broken symmetries may compete to yield the lowest energy ground state. Textures introduced by doping such systems away from integer fillings should result in states that combine different types of orderings in spatially non-uniform patterns. These systems offer rich phase diagrams and novel transitions, both quantum and thermal, between different phases. The PI and collaborators will seek to fully characterize and understand such systems. In addition, an exploration of edge theories of thin topological insulators in which interactions induce coherence between transverse surfaces will be conducted. This impacts the spectrum and physical behavior of electrons at the edge both at the mean-field level, and when fluctuations of the surface ordering are incorporated. This project will be conducted with the full participation of graduate students, who will be trained in modern methods of condensed matter physics, preparing them for careers in science and technology. Scientists from the US and abroad will be collaboratively involved in the work. In addition, the PI will be involved in an educational initiative specifically for high-school students from rural and/or low-income areas in Indiana: the creation of an online introductory physics course for Indiana high-school students without access to an Advanced Placement physics course. Included will be discussions about the remarkable modern materials relevant to this proposal, such as graphene and carbon nanotubes.