This CAREER award supports theoretical and computational research, and education on topological semimetals and the way electrons organize themselves in these materials. Most solids can be thought of as being either insulators or conductors - often metals. A closer examination, however, reveals rich sub-categories including semiconductors such as silicon, that are insulators at the absolute zero of temperature but show substantial conduction at room temperature, and semimetals such as bismuth, that are formally metals at zero temperature but at higher temperatures have several orders-of-magnitude lower conductivities than metals like copper.
Over the past decade, the influx of ideas from mathematics in the area of topology into solid-state physics has spawned a new family of semimetals, namely, topological semimetals, of which graphene and Weyl semimetals are the most famous examples. These materials are "true" semimetals, in the sense that their properties at all temperatures are intermediate between those of metals and of insulators. Topological semimetals are fascinating materials: on one hand, they enable access to the physics related to the fundamental particles that make up matter through table-top experiments, while on the other hand, they tend to have conduction properties which make them attractive platforms for electronic device technologies.
In this project, the PI and his team will theoretically investigate various fundamental aspects of topological semimetals, such as the tendency of electrons confined to their surfaces to organize themselves in states in which the electrons are ordered in some way, like magnetism or the cooperative state of superconductivity in which electrons move without any resistance. The range of the investigation reaches to electronic properties related to how electrons move in single atomic layer and two-layer structures of graphene. These aspects of graphene are challenging to study using existing techniques because standard analytical theoretical descriptions begin to break down while computational approaches are too limited or become prohibitively costly. Thus, the team of researchers will develop a new numerical algorithm tailored for investigating physics in this regime.
The team will integrate the above research with concerted activities that harness technology for surmounting hurdles in education and outreach in the post-COVID era. Specifically, they will design mobile games that teach undergraduate physics content, build an "analogy inventory" to improve communication between physics and other STEM fields, organize a virtual conference on topological semimetals and develop innovative pedagogical strategies suitable for online and social distancing-compliant classrooms.
This CAREER award supports theoretical and computational research, and education on topological semimetals. Topological semimetals (TSMs) are a cornerstone of topological condensed matter and, thanks to their gapless spectrum, present unique challenges and opportunities compared to their gapped counterparts such as topological insulators. The PI will explore, craft innovative tools for and tackle pressing theoretical issues in TSMs to unearth exotic phenomena in both weakly and strongly correlated regimes. This CAREER project is organized in 4 thrusts. Thrust 1 is focused on three-dimensional TSMs, adopting a clever surface-centric approach to reveal qualitatively new weak-correlation physics rooted in the interpolating-dimensional nature of the surface states and their inseparability from the bulk. This includes the quantum effects of weak disorder, spontaneous magnetization, and superconductivity, and also includes robust Majorana wires in mixed real-and-momentum space. Thrust 2 develops the primary tool for Thrust 3, namely, an innovative algorithm that is tailored for probing finite temperature properties of generic, non-integrable systems using the eigenstate thermalization hypothesis. Thrust 3 focuses on the strongly correlated regime of graphene-based systems. In particular, it inspects the microscopic processes that drive hydrodynamic transport in graphene and the finite temperature phases, including possible pseudogap and strange metal phases, in twisted bilayer graphene. Thrust 4 complements the research through concerted activities for surmounting hurdles in education and outreach in the post-COVID era using technology. Specifically, the PI and his team will design mobile games that teach undergraduate physics content, build an “analogy inventory†to improve communication between physics and other STEM fields, organize a virtual conference on TSM-research and develop innovative teaching strategies suitable for online and social distancing-compliant classrooms.
This project is aimed to transform our collective understanding of TSMs by tackling fundamental issues in the field that arise from rapid experimental progress. For instance, Thrust 1 will clarify puzzles in magneto-transport experiments on TSMs, determine whether weak disorder can localize the surface states, provide theoretical support to surface superconductivity seen in TSMs and unveil scenarios where the surface spontaneously orders before the bulk does even though the latter has a higher dimensionality. It will also reveal a new class of non-local Majorana fermions and examine their potential for storing quantum information. The algorithm developed in Thrust 2 is a new approach to strongly correlated systems that could be useful for studying finite temperature equilibrium physics in unsolved regimes plagued by the Monte-Carlo sign-problem such as frustrated spin models and fermionic systems lacking quasiparticles. It transforms the eigenstate thermalization hypothesis from a useful qualitative conjecture to the basis for practical calculation. Thrust 3 will help dissect transport data in experimental graphene samples, which are increasingly approaching the quality needed for the electrons to exhibit hydrodynamic transport. It will also help map out the potentially rich and largely unexplored finite temperature phase diagram of twisted bilayer graphene.
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.
