Correlated Electron Transport in Mesoscopic Structures

Yale University, New Haven CT

Investigators

Abstract

NON-TECHNICAL SUMMARY This award supports theoretical research and education to investigate the electronic properties of a new class of insulating materials. Quantum physics has established the underlying reason that leads to two broad classes of materials: those which conduct electricity, conductors, and those that do not, insulators. The distinction comes from the existence in the insulators of an "energy gap" that charged particles have to overcome in order to produce an electric current. Quantum mechanics also explains the properties of semiconductors, the materials from which transistors are made. By strict classification these are insulators, but with a relatively small energy gap. Semiconductor physics has developed ways to control the gap, and thus to control the properties of semiconductors, making them able to conduct electricity or interrupt the conduction at will. Built on these principles semiconductor devices have fueled the information technology revolution. Recently application of quantum mechanics has predicted the existence of a new kind of insulator called "topological insulators." These materials must have an energy gap for charge carriers in the bulk of the material; however, the bulk insulator coexists with conducting channels at the surfaces and edges of the material. At sufficiently low temperatures the edge channels are predicted to be ideal conductors for electrons. Yet another remarkable prediction is that the edge channels at the interface between a topological insulator and a superconductor must house so-called Majorana states. At sufficiently low temperature, superconducting materials develop a new quantum state that has no resistance to electric current. Majorana states are qualitatively new quantum mechanical states which may be used as the foundation for a quantum computer; thus carrying a promise to revolutionize the digital technology once again. However, in reality the electron energy gap in the bulk of any existing topological insulator is quite small, even by the standards of semiconductor physics. The smallness of the gap amplifies the adverse effects of materials imperfections and makes it difficult to control the conduction of topological insulators and to harvest the unusual properties of the edge channels. The goal of this project is to determine the mechanisms that obscure the ideal conductance of edge channels in topological insulators, find ways to detect Majorana states by measuring how well microwaves are absorbed by systems of topological insulators combined with superconductors, and to explore ways of increasing the robustness of Majorana states. The systems considered in this research hold promise to be potential elements of a future electronics technology. Therefore this fundamental science project may have a technological impact. The work on this project develops understanding of real materials and proficiency in modern methods of condensed matter theory. It provides a good training ground for graduate students and post-doctoral research associates. TECHNICAL SUMMARY This award supports theoretical research and education to investigate the frequency dependent responses of mesoscopic systems. The emphasis is placed on theory applicable to experiments involving the edge states in two-dimensional topological insulators and with superconducting nanocircuits. 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 of evaluation of these responses present for the theory. The search for manifestations of symmetries and non-perturbative interaction effects in the response functions of the two mesoscopic systems forms the common theme that unites all parts of the proposal. The first part of the project is devoted to investigation of the finite-temperature resistance and magnetoresistance of one-dimensional electron channels at the edges of a two-dimensional topological insulator. Understanding the resistance and magnetoresistance calls for the development of a theory of charge disorder and spin correlations mediated by the one-dimensional helical electron states. The second part of the project is aimed to develop new methods in the search for Majorana fermions in condensed matter. The main goal is to find the signatures of Majorana states in low-frequency response functions and in microwave spectra of Josephson junctions between semiconductor nanowires. The third part of the project addresses the excitation spectra and dynamic responses of one-dimensional Fermi systems with strong pairing interactions and spin-orbit coupling. The goal is to develop theory methods applicable to a variety of novel condensed matter systems. All parts of the project are motivated by experimental mesoscopic physics. Solving the problems formulated in the project may explain the existing experimental results, help in planning new experiments, and lead to developing theoretical methods broadly applicable to low-dimensional quantum condensed matter.