Electron Transport in Low-Dimensional and Mesoscopic Topological Solids

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NONTECHNICAL SUMMARYThis award supports research that is aimed at developing theoretical tools for characterizing and harnessing the properties of various technologically relevant materials. Progress in quantum electronics, from bendable screens of hand-held devices to future quantum information machines, hinges on the development of materials with desirable mechanical and electrical properties. Recent decades have brought remarkable experimental and theoretical discoveries in the physics of materials. Isolation of graphene, a one-atom thick two-dimensional crystal cleaved out of graphite, boosted the discovery of new two-dimensional materials made out of various other elements. Theoretical prediction of topological solids – conductors, semiconductors, and insulators with highly unusual electronic properties – have paved the way for the synthesis of these novel materials in the laboratory. Some of them are truly unique by naturally combining the properties of an insulator in the bulk and of a conductor at the surface. The rapid progress in such materials discovery calls for the development of new theoretical methods to understand the properties of these novel materials, explain experimental findings, and help in guiding new experimental discoveries. This project aims at building the theory needed to achieve these goals.The research addresses a set of electrical conduction and microwave response characteristics of novel low-dimensional topological materials. These characteristics are associated with the materials’ unique electronic structure and with the dynamics of their charge carriers. The three specific directions of the research cover the microwave properties of low-dimensional topological superconductors, theory of electron transport in two-dimensional topological solids, and magnetic and electronic characteristics of a class of topological conductors, called Weyl metals. Graduate students will be actively involved in the research; they will be mentored and trained in a broad range of theoretical techniques. The PI also plans to deliver a set of lectures introducing the frontiers of quantum materials theory to non-expert audiences.TECHNICAL SUMMARYThis award supports research that is focused on theoretical investigations of the dc and ac response functions of several low-dimensional and mesoscopic systems with nontrivial band topology. The emphasis is placed on theory applicable to experiments with superconducting nano-circuits, flat-band two-dimensional conductors, and surfaces of Weyl semimetals. The motivation comes from the advances in synthesis of new materials, experimental techniques enabling the high precision measurements of static and dynamic responses, and from the challenges the evaluation of these responses presents for the theory.The first part of the project is devoted to developing new methods of studying topological superconducting phases. The main goal of this part is to elucidate the joint effect of disorder and topology of a superconducting phase on the microwave response functions of bulk superconductors and their junctions. The second part of the project aims at developing a hydrodynamic theory of electrons in narrow-band two-dimensional conductors, with or without spontaneously-broken symmetries. The goal is to understand the recently-measured tunneling spectra, predict the electron flow patterns in constrained geometries, and find the corresponding conductance. The third part of the project addresses the magnetic oscillations of the transport and thermodynamic properties associated with a surface of a Weyl metal. The goal is to identify the oscillatory contributions to conductivity and magnetic susceptibility which are associated with a surface, but do not rely on electron trajectories connecting the opposite surfaces.All parts of the project are geared towards the needs of experimental mesoscopic physics. Solving the problems formulated in the project is expected to explain existing experimental results, help in planning new experiments, and develop theoretical methods broadly applicable to low-dimensional quantum condensed matter. Graduate students will be actively involved in the research; they will be mentored and trained in a broad range of theoretical techniques. The PI also plans to deliver a set of lectures introducing the frontiers of quantum materials theory to non-expert audiences.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.