Experimental methods for interleaving layers of 2D materials have been developed with endless possibilities for creating stable structures with desired electronic, optical, magnetic and thermal properties. This project will develop mathematical models and computational methods to guide the search and design of 2D materials with optimal properties. This approach makes possible the long-sought goal of atomic-level control of nanostructures as building blocks for creating devices of desirable properties and performance characteristics. The mathematical modeling, analysis, and computation from the atomic to macroscopic scale developed by the project will contribute to the design of new materials leading to applications in incommensurate 2D materials. This effort will impact the development of materials and devices with desired characteristics and performance for a wide range of applications of interest including ultra-fast electronic, opto-electronic, and magnetic devices; nonconventional optical and photonics devices; and communication devices. The challenge of modeling layered incommensurate heterostructures will also promote the development of multiscale models for many other aperiodic materials systems such as composites, atomically engineered structures, and bio-materials. 2D materials research is an ideal platform to motivate new mathematics training and curricula in the analysis, modeling, and computation of quantum electronic structure and transport, and mechanical and topological properties of materials. The project's graduate student training and outreach to underrepresented student populations will broaden the diversity of the mathematical research community.

The main issue encountered in the mathematical modeling of layered 2D materials is that the lattice periodicities of different layers do not match and thus lead to incommensurate structures. New theory and computational methods that do not use Bloch-Fourier methods will be developed to accurately predict material properties in currently inaccessible regimes. This project will utilize the notions of local configuration space and locality to give new formulations and computational methods for the electronic density of states and for transport properties such as conductivity. New momentum space formulations and corresponding fast computational methods will be developed that exploit the structure of the momentum space Hamiltonian. Novel models and computational methods will also be developed and analyzed that extend our model for electronic density of states and conductivity to include mechanical relaxation.

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.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Victor Roytburd
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University of Minnesota Twin Cities
United States
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