Disorder, Quasiperiodicity, and Strong Correlations in 2D Materials and Topological Interfaces

NONTECHNICAL SUMMARY Two-dimensional materials are composed of atomically thin sheets of atoms that can be manipulated with an unprecedented level of control. For example, in addition to being able to isolate and stack these atomically thin materials, it is now possible to twist a pair of them to within 0.1 degrees of accuracy. As a result, new arrangements of atoms form when placed on top of each other in this fashion that would not form in nature. At the same time, varying the density of electrons in these devices changes the system from a semiconductor to a superconductor, metal, or insulator providing an amazing amount of control and emergence not previously seen in a single device. These advances raise several new fundamental questions that need to be theoretically and computationally addressed to explain the experimental observations. The amazing tunability of these systems makes them promising candidates for the construction and application of novel technological devices that can be used in future electronics and atomic-scale measurement devices. This research project takes into account realistic effects of the twisted materials to understand how they impact the overall response of the electronic system to imperfections and randomness in the materials, to develop new probes to be used in experiment to ascertain physical effects that are currently out of reach, as well as to find new phases of matter that have yet to be discovered that result from bringing these novel systems in contact. The educational efforts of this proposal focus on career development inside and outside of academia that fosters multifaceted learning and career opportunities for PhD students through direct interactions and exposure with industry professionals and alumni. The PI’s research utilizes a multi-level mentorship program that integrates teaching with research in working with and advising graduate and undergraduate students. Lastly, the computational software developed in the PI’s lab will be made open-source to enhance scientific progress and infrastructure. TECHNICAL SUMMARY This project supports research and education in theoretical condensed matter physics focusing on the role of disorder, quasiperiodicity, and magnetism in twisted two dimensional materials and at interfaces of topological surface states. The rise of two-dimensional materials has ushered in a new era in condensed matter physics, which at the same time has raised several novel questions regarding the microscopic atomic details of the atoms as the layers are twisted and stacked on top of each other. This research aids in the general understanding of these materials by: i) Theoretically investigating the effects of twist-angle disorder in twisted bilayers of graphene and transition-metal dichalcogenides, as well as using vacancies and their scanning-tunneling microscopy response as a probe of twisted bilayer graphene; ii) Determining what kinds of symmetry-broken and strongly correlated states can emerge on the quasiperiodic structures that form from the relaxational process in twisted bilayer graphene close to aligned with hexagonal boron nitride; iii) Understanding how to manipulate the topological Weyl Fermi-arc surface states by coupling them with classical spin ice, quantum spin ice, or a super lattice potential. The PI will employ several computational approaches that combine the kernel polynomial method with the model building capabilities of Wannierization, and many-body approaches that include Hartree-Fock and the dynamical mean-field theory, to describe a wide range of two-dimensional materials that lack translational symmetry. The ultimate goals of this research are first to understand how realistic effects that are innate in these systems affect their behavior, second to use these properties to our advantage to measure physical aspects of the device that have been hitherto out of reach, and lastly to discover novel phases of quantum matter that result when we these systems become strongly interacting. The educational efforts of this proposal focus on career development inside and outside of academia that fosters multifaceted learning and career opportunities for PhD students through direct interactions and exposure with industry professionals and alumni. The PI’s research utilizes a multi-level mentorship program that integrates teaching with research in working with and advising graduate and undergraduate students. Lastly, the computational software developed in the PI’s lab will be made open-source to enhance scientific progress and infrastructure. 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.