Wei Li
DePaul University, IL·Mathematics & Statistics
Some materials act as insulators on the inside but let waves travel along their surfaces, and those surface waves keep going even around corners and past manufacturing defects. Materials with this property are called topological insulators, first found for electrons and later built for light.
- Fields
Mathematics & Statistics
Physics
- Topics
photonic topological insulators
topological edge states
partial differential equations
- Grants
- 1 known grant, through Aug 2027
What they work on
- Prove the existence of and characterize edge states, the waves that travel along a boundary, on sharp interfaces formed by joining photonic materials with various symmetries, within a partial differential equation framework.
- Analyze edge states arising in the photonic quantum Hall and quantum spin Hall settings and in photonic topological insulators built on square lattices, geometries that current models do not address.
- Identify edge states on sharply truncated edges for different truncation locations and boundary conditions, determining how where a lattice is cut affects the surface waves it supports.
- Construct a family of materials satisfying the no-fold assumption, a spectral condition under which edge states emerge when degeneracies are weakly perturbed, using layer potentials and asymptotic analysis.
More about the research
The light-carrying version, a photonic topological insulator, is attractive for compact on-chip communication and data processing, for optical isolators that let light pass one way only, for topological lasers, for uncompressed video transmission and for ultra-thin electrical shielding. The practical catch is that the robust edge waves are usually described mathematically only for smooth, gradual interfaces, while the devices that are easiest to fabricate have sharp joins and abrupt edges. This project supplies the missing theory.
Why it matters
Photonic devices built from sharply joined or truncated materials are the easiest to manufacture, but existing theory does not cover them, leaving designers without reliable predictions of whether robust light-guiding edge states will exist. Rigorous results for these geometries could guide the design and simplify fabrication of on-chip optical communication components, optical isolators and topological lasers, while advancing the mathematics of layer potentials and asymptotic analysis.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Dmitri Feldman
Brown University, RI·Physics
Classify the possible topological orders behind the fractional quantum spin Hall effect in twisted bilayer molybdenum telluride, where time-reversal symmetry is broken, and identify measurements that can show which order is present.
Gregory Berkolaiko
Texas A&M University-College Station, TX·Mathematics & Statistics
Derive explicit formulas for the number of edge-state eigenvalues in spectral gaps of tight-binding Hamiltonians for topological insulators, using the Maslov index and its numerically computable discrete version, the Duistermaat index.
Roman Shterenberg
University of Alabama at Birmingham, AL·Mathematics & Statistics
Analyze mathematical models of almost-periodic operators from quantum mechanics to explain the mechanism of electrical conductivity in modulated, non-repeating crystals.
The school
DePaul University: 4 labs on PI Pages, $11M a year on research, 47 research doctorates a year.
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