Topological Phases and Correlation Phenomena in Complex Materials

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

TECHNICAL SUMMARY This award supports theoretical research and education to study several problems in two general areas of theoretical condensed matter physics. The first area of research concerns topological phases of electronic and atomic systems: the PI will study the properties and instabilities of partially filled bands with nontrivial topology and how topological states could be created at surfaces and interfaces, for example in the unconventional two-dimensional gas at the surface of a 3D topological insulator. The PI will investigate connections between topological or geometric field theories of topological states and plausible experiments. The second area of research is on how a combination of numerical matrix-product-state methods and analytic theory can lead to insights into some challenging problems in strong-correlation physics in low dimensions. The two goals for this section of the project are to understand one-dimensional models of many-body localization in interacting disordered systems, and to develop predictive methods for some open two-dimensional classical or quantum statistical physics problems. This section builds upon previous work on understanding how quantum information theory concepts such as entanglement can aid the numerical simulation of correlated materials. The educational component of this proposal is significant, and the largest expenditure is for graduate student support. This will contribute to the development of a scientifically sophisticated workforce. The PI will carry out new course development and undergraduate student research supervision within the university, in addition to his ordinary teaching load and lectures at advanced schools elsewhere. For outreach beyond the academic community, the PI will expand his lecturing and writing about recent developments and historical highlights of condensed matter physics. NON-TECHNICAL SUMMARY This award supports theoretical research and education to study new kinds of electronic materials. Recent years have seen the creation of several new kinds of electronic materials. One example is the discovery of electrical insulators with atomically thin metallic surfaces that are extremely robust to the most common types of impurities and disorder. These new insulators are called topological insulators as the connection between their bulk insulating behavior and surface metallic behavior is described by the branch of mathematics known as topology, which studies properties invariant under continuous changes. More familiar insulators usually have no surface metallic layer, and if they do, it is much less stable to disorder. Another interesting property of the robust surface metallic layer in topological insulators is that the electrons moving in the layer are effectively massless, in that their energy is linearly proportional to their momentum. Electrons in solids exhibit a remarkable variety of collective phenomena including magnetism and superconductivity. Superconductivity is a state of electrons with the signature that resistance to the flow of electric current vanishes at low temperatures. These collective behaviors result from the interactions between electrons. One goal of this project is to understand how topological insulators and related materials, which are currently understood at the level of individual electrons, could lead to new collective phenomena when the interactions between electrons are included. The PI also seeks to understand how new electronic states could be created using interfaces between different materials. Methods used range from advanced techniques originally developed for particle physics to computational simulations, where ideas drawn from the theory of quantum information have had a major impact on our ability to simulate systems in low dimensions. Quantum information generalizes the classical information theory which describes the operation of modern computers and data systems, using ideas specific to quantum systems. One important idea is entanglement, which is a kind of subtle correlation in which the best possible description of a large system does not imply a complete description of its parts. Work on topological order influences many other areas of condensed matter physics and some areas of technology; it contributes to the intellectual foundation for future devices. Several education and outreach efforts will be supported in order to convey to a broad audience the importance and excitement of theoretical materials research. The educational component of this proposal is significant, and the largest expenditure is for graduate student support. This will contribute to the development of a scientifically sophisticated workforce. The PI will carry out new course development and undergraduate student research supervision within the university, in addition to his ordinary teaching load and lectures at advanced schools elsewhere. For outreach beyond the academic community, the PI will expand his lecturing and writing about recent developments and historical highlights of condensed matter physics