Wave Interference and Topological Phenomena in Multilayer Systems

PhD Program

Speaker

Duy Hoang Minh Nguyen

When

2026/07/15
11:00

Place

CFM Auditorium, Donostia / San Sebastián

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PhD Thesis defense by Duy Hoang Minh Nguyen

Supervisor: Dario Bercioux (DIPC, Ikerbasque) 

Mesoscopic Wave and Topological Phenomena - Nanophotonics, Condensed Matter Theory

This thesis investigates the emergence of topological phases and complex wave interference in multilayer periodic lattices, driven by structural degrees of freedom such as layer rotation and translation. Utilizing effective continuum models derived from the plane-wave expansion method, we provide a unified theoretical framework to describe and predict novel physical phenomena in both electronic and photonic systems. This approach bridges the gap between microscopic wave properties and macroscopic topological invariants, offering an efficient tool for exploring the physics of mesoscopic systems.

In the realm of photonics, the thesis first explores the topological properties of sliding multilayer gratings. In bilayer configurations, we demonstrate that relative layer translation induces a transition between quantized Thouless pumping and energy trapping. By characterizing the topological phase transition in this system as a competition in strength between two periodic potentials, we design a reconfigurable photonic junction supporting robust interface modes. We further demonstrate the feasibility of topological lasing within this platform, providing a pathway toward multidimensionally tunable and robust light sources.

We then extend this framework to trilayer photonic gratings by utilizing relative displacements as synthetic dimensions. This allows the 1D lattice to simulate the 3D band structure of Weyl semimetals. We numerically demonstrate the reconstruction of surface Fermi arcs at the interface of two simulated Weyl semimetals -- a phenomenon previously predicted theoretically but challenging to observe in solid-state systems. Our results indicate that trilayer gratings are an ideal platform for observing these exotic topological signatures.

Finally, the research addresses electronic interference in twisted bilayer graphene. By employing an atomistic tight-binding model and an effective continuum description, we characterize the chiral structure of quasiparticle interference (QPI) patterns. Our results provide a complete map of scattering processes between Dirac valleys and establish a direct analytical link between QPI patterns and the projected form factor of the energy eigenstates. This finding suggests that QPI can serve as a high-resolution probe for the quantum geometry and topological nature of moire electronic states.

Collectively, this work highlights the versatility of structural tuning in multilayer lattices. By manipulating the "twist" and "slide" of periodic layers, we reveal how trivial constituents can be engineered to host exotic topological phases, providing a foundation for the next generation of integrated topological electronic and photonic devices.