Topological quantum edge states

Project leader: Professor Alex Watson
Project manager: Jeff LaComb
Team members: Jonathan Michala, Alex Pierson

Project summary:

We studied the propagation of waves described by Schrödinger’s equation along the interface between two periodic structures (edge states) using numerical and analytical methods. Specifically, we considered the interface between different configurations of the Haldane model, which can exist in `topological' and `non-topological’ phases.  After first studying a simplified one-dimensional model, we worked out the correct Hamiltonian operator for the two-dimensional system, diagonalized it numerically, and then used this information to integrate the Schrödinger equation for different initial conditions. Our computations showed that wave packets propagating along the interface between two distinct 'non-topological’ configurations are reflected by `defects’ of the interface, whereas wave packets propagating along the interface between `topological’ and `non-topological’ configurations propagate past defects almost unaffected.

 

We then interpreted these results by studying the spectrum of the Hamiltonian in detail and using perturbation theory. Future goals of the project are to understand how nonlinearity affects the propagation of edge states, and to understand the propagation of waves at the interface of aperiodic structures.