Probing crossover from analogous weak antilocalization to localization by an Aharonov-Bohm interferometer on topological insulator surface

We propose a scanning tunneling microscopy Aharonov-Bohm (AB) interferometer on the surface of a topological insulator (TI) to probe the crossover from analogous weak antilocalization (WAL) to weak localization (WL) phenomenon via the AB oscillations in spin-resolved local density of states (LDOS). Based on our analytical and numerical results, we show that with increasing the energy gap of TI surface states, the ${\mathrm{\Phi }}_0\mathrm{/}2$=$hc\mathrm{/}2e$ periodic AB oscillations in spin-resolved LDOS gradually transit into the ${\mathrm{\Phi }}_0$ periodic oscillations.