Speaker: Solomon Quinn, Center for Computational Mathematics, Flatiron Institute
Title: Asymmetric transport in continuous topological insulators
Abstract: This talk concerns PDE models for two-dimensional topological insulators. Such systems are characterized by asymmetric transport along a one-dimensional curve representing the interface between two insulating materials. We first demonstrate that a relevant edge current observable is quantized and robust to perturbations for a large class of elliptic Hamiltonians. We then establish a bulk edge correspondence stating that the observable equals an integer-valued bulk difference invariant depending solely on the insulating phases. Finally, we discuss the numerical evaluation of solutions to corresponding source problems. We implement a novel boundary integral equation method for the massive Dirac equation, and present several numerical examples of solutions and scattering effects.
Bio: Solomon Quinn is a Flatiron Research Fellow in the Center for Computational Mathematics (CCM) at the Flatiron Institute. Solomon’s research interests include mathematical physics, partial differential equations and numerical analysis, with applications to topological insulators, waveguides and moiré materials. Before joining CCM, Solomon was a Dunham Jackson Assistant Professor at the University of Minnesota. Solomon obtained his Ph.D. in computational and applied mathematics from the University of Chicago in 2023, under the supervision of Professor Guillaume Bal.
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