Valley-Hall Tight-Binding Lattice — Domain-Wall Edge State (2D)

This is a 2D-native companion to the 3D Valley-Hall waveguide: instead of rendering rods and animating a scripted pulse, it builds the honeycomb lattice's actual tight-binding Hamiltonian — a two-sublattice mass term whose sign flips across an interface — and integrates the time-dependent Schrödinger equation for every lattice site live, with 4th-order Runge–Kutta. The topologically protected edge state along the domain wall, and its immunity to a sharp bend and a local defect, both emerge from that real wave dynamics rather than being asserted by a lookup formula. Switching to the conventional mode swaps in an ordinary barrier-defined channel with no chiral protection, so the same bend and defect now genuinely backscatter the propagating amplitude. Live readouts measure transmission and group velocity directly from the simulated field.