Heat transport and neutral modes in topological matter

NONTECHNICAL SUMMARY This award supports research, education, and outreach activities with a goal to achieve a fundamental understanding of topological matter with emphasis on the existence and properties of unusual particles known as anyons. Topological matter is a new, important class of materials with uniquely robust properties insensitive to undesirable effects, such as material imperfections or interference from the material's environment. This research project focuses on the understanding of how heat is transported within such matter. This is of major importance to quantum information processing platforms, many of which depend on the use of anyons. Introductory physics textbooks teach us that electrons are truly fundamental particles with no constituent parts. The charge of an electron is understood as the smallest possible charge a particle could have. And yet, in topological matter, stable "quasi"-particles that carry a smaller charge than the charge of an electron can form. They are known as anyons. Anyons exhibit highly counterintuitive behavior when they run around each other, which is directly useful for quantum computing. Indeed, using anyons as building blocks of quantum information devices is expected to dramatically suppress error rates and preserve quantum information from undesirable influences. Presently, the properties and often even the existence of anyons are poorly understood and hotly debated. This proposal focuses on devising new ways to theoretically predict and experimentally probe the physics of anyons in some recently discovered promising classes of topological matter. This award also supports the educational and outreach activities, contributing to the development of US workforce in quantum science and technology and related fields through engaging students in quantum science research. Other planned activities include conference organizing, writing pedagogical review articles, and outreach at the K-12 level. TECHNICAL SUMMARY This award supports research, education, and outreach activities aimed at achieving a fundamental understanding of heat transport and neutral modes in topological states of matter. The last several years have seen dramatic progress in the field of topological matter. One major development was a direct proof of Abelian anyonic statistics via interferometry and of non-Abelian statistics via thermal transport. Another breakthrough resulted from the discovery of new topological states of matter in twisted bilayer molybdenum telluride and multilayer graphene. The proposal is motivated by these achievements and aims at furthering the understanding of the nature of topological orders in real materials, the development of new probes of topological order, and the explanation of surprising data from existing probes. The proposed research involves three directions. The first direction focuses on the nature of the fractional quantum spin Hall effect in molybdenum telluride. Experiments reveal broken time-reversal symmetry, which opens up the possibility of a large number of topological orders. These will be systematically classified and the ways to unambiguously determine the actual topological order will be identified. The second direction addresses interferometry in topological liquids with multiple edge channels. Interferometry in such liquids is poorly understood theoretically, and it is challenging to interpret the available data. Two types of interferometers will be considered: the type that was recently used to probe fractional statistics of the hierarchical state at the filling factor 2/5, as well as a new geometry, proposed by the PI, which inspired the recent observation of fractional statistics at the filling factor 3/7. The third direction focuses on neutral anyonic excitons recently discovered in bilayer graphene. The proposed research will advance the understanding of many-body quantum systems. Besides their importance for basic materials science, the results on non-Abelian topological orders is also relevant for the field of quantum information. This award also supports the educational and outreach activities, contributing to the development of US workforce in quantum science and technology and related fields through engaging students in quantum science research. Other planned activities include conference organizing, writing pedagogical review articles, and outreach at the K-12 level. 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.