Topological Heat Transport

Brown University, Providence RI

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research and education on topological quantum materials, which are a special class of materials that have been bestowed with exceptionally stable properties. That feature is known as topological protection. Quantum mechanics is responsible for the exceptional properties of topological materials. Consider, for example, electrons, which in reality do not have constituent particles. In certain topological matter, they appear as if they have split into particles, called anyons, which also carry an equally distributed fraction of the original electric charge. These anyons are promising for building the fundamental components of a quantum computer, in which topological protection would help reduce otherwise unavoidable computational errors introduced by the material's interaction with its environment. The PI will develop theoretical approaches for understanding quantum topological materials and their properties. Recent breakthroughs in experiments have uncovered how heat travels through topological matter. A major goal of this project consists of providing a theoretical understanding of quantum heat transport, and also resolving tensions between the existing theoretical framework and the newest experimental data on the behavior of quantum topological matter in two dimensions. The research will advance fundamental understanding of topological matter and quantum transport, both of which are directions of crucial importance for quantum science and technology that have become a national priority. Through research and education opportunities for graduate and undergraduate students, which include collaborations with leading experimentalists, students under the award will be trained to eventually join the future workforce in modern quantum science and technology. TECHNICAL SUMMARY This award supports theoretical research and education on topological quantum materials with a focus on heat transport and the related physics of neutral modes. The non-Abelian fractional statistics of anyons in topological matter may find significant applications in quantum information storage and processing. The understanding of non-Abelian statistics and many other phenomena in topological matter requires experimental access to neutral excitations, which comes from thermal transport experiments. The first research direction is motivated by recent experimental developments and aims at achieving theoretical understanding of thermal equilibration and transport on the edges of quantum Hall liquids, including the effects of upstream neutral modes. The closely related second direction addresses poorly understood quantum Hall states in the second Landau level in GaAs and related systems. The observation of half-integer quantized thermal conductance at filling factor 5/2 strongly supports the existence of non-Abelian anyons in the second Landau level. Yet, many open problems remain, including an apparent conflict between the existing experimental results and numerics. The research builds upon recent experimental results and the breakthrough work by Son on the relation of 2D electron gases and topological insulators. The objective is to reconcile the theory of the 5/2 state with experiments. A third research direction focuses on newly developed topological systems with neutral modes but without charged modes. The methods employed will include a combination of analytical and numerical tools. The research will advance fundamental knowledge of topological matter and quantum transport, both of which are directions of crucial importance for quantum science and technology that have become a national priority. Through research and education opportunities for graduate and undergraduate students, which include collaborations with leading experimentalists, students under the award will be trained to eventually join the future workforce in modern quantum science and technology. 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.