Spin-Momentum Locking — the 2D Momentum-Space Companion

The conducting surface of a 3D topological insulator hosts a single Dirac cone whose spin is rigidly locked perpendicular to momentum. This 2D companion solves the same gapped Dirac Hamiltonian E(k) = ±√[(ħv_F k)² + m²] independently on a flat canvas: an E(k) dispersion cut shows the mass gap opening at k=0, and a kx–ky spin-texture map shows the Fermi circle with arrows whose in-plane length and colour (not a 3D tilt) encode the spin's canting out of the surface plane. Firing an electron wavepacket at a fixed impurity runs the same Monte-Carlo backscattering test as the 3D version, and the live measured-vs-theory readout is a genuine statistical self-check that non-magnetic disorder cannot backscatter a helical Dirac electron until a magnetic gap breaks time-reversal symmetry.