Berry-Phase Breakdown and Semiclassical Reconciliation in Topological Dirac Fock-Darwin states

I investigate the two-dimensional Dirac fermion analogue of artificial atoms (Fock-Darwin states, FD) in a circular n-p junction on a topological insulator surface. The FD states in this non-parabolic potential exhibit a unique electron-hole core-shell structure, where the strict Berry-phase switch (BPS) picture breaks down near criticality: the trapped electron-core states evolve into the envelope functions of quantized snake states. This contradicts the sharp BPS seen in experiments. Nevertheless, the BPS scenario remains valid when treating these envelope functions as effective confined states, thereby reconciling theory with experiment. The field-driven evolution from electrostatic to Landau-level confinement is tracked to 14 T experimentally and supported by simulations, establishing topological surface states as a tunable platform for Dirac physics beyond conventional quantum dots.