Condensed matter physics
Topological materials
Explore bulk energy bands and edge states in a topological insulator (SSH-style model). Observe how in-gap edge states appear and vanish as mass/disorder parameters change.
Equipment
- Bulk-band model and finite 1D chain with edges
- Four sliders: mass m, symmetry disorder, model parameter, time
- In-gap energy/state display and "Pause" button
Procedure
Observe bulk bands and the gap
In figure 1 "Bulk bands and edge states", see the two band branches and the gap between them. Set "Mass m" small: the gap closes — the system approaches a metal; increase m: the gap opens and edge states appear inside it, the topological character of the phase.
Test the robustness of edge states
With the gap open, raise the "Symmetry disorder" slider: the edge state survives until disorder is strong enough to close the gap — the signature of topological protection. In figure 2 "Spin and protecting symmetry", observe the spin–momentum locking of the edge state.
Vary the model parameter and conclude
Sweep "Model parameter" and "Time" to see the edge state propagate/localize at the boundary. Summarize the bulk–boundary rule: the bulk band's topological invariant (winding/Chern number) dictates the number of edge states that must exist — changing it requires closing the gap, i.e., a topological phase transition.