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der optimal conditions it should be higher than it is in bilayer graphene, where the occurrence of this effect is hotly debated. Once the exciton condensate is formed, vortices can be nucleated by applying an in-plane mag- netic field. Since the exciton condensate is itself insulat- ing, the main conduction channel in this situation will be through vortices, each carrying − e/ 2 charge. Frac- tional charge of the carriers then can be detected using established techniques. 35,36 

## VI. OUTLOOK AND OPEN QUESTIONS 

Predicted more than 30 years ago in the context of high-energy physics, but never before observed in a real or numerical experiment, the Witten effect is realized in a strong topological insulator. A unit magnetic monopole inserted in a model STI binds electric charge − e/ 2 in accordance with the prediction 18 and furnishes a rare ex- ample of charge fractionalization and spin-charge sepa- ration in 3 spatial dimensions. In the special case when the underlying system possesses particle-hole symmetry and when the Zeeman term (15) can be neglected, the ap- pearance of fractional charge follows from the same ‘zero- mode’ arguments that underlie charge fractionalization in a one-dimensional system of fermions coupled to a scalar 

field with a soliton profile 28,29 as realized in dimerized polyacetylene. 30 In the more general case when the Zee- man term or weak disorder are present, there exist no ex- act zero modes in the spectrum of electrons yet the frac- tional charge remains precisely quantized. This reflects the more subtle topological order that underlies the axion response of a STI, which is robust against any weak per- turbation that respects time reversal symmetry. 7,8,14,15 

An interesting open question is the fate of the Witten effect in the presence of magnetic disorder. Experimen- tally, this can be implemented by adding a small con- centration of magnetic ions (such as Fe or Mn) into a topological insulator. Although at the microscopic level θ is no longer quantized in the presence of T -breaking perturbations, we expect its effective value, relevant to the physics at long lengthscales, to remain pinned at π as long as the magnetic moments stay disordered. This is because the net magnetic moment in a macroscopic region containing many impurities will effectively vanish. Qualitatively, this suggests that the Witten effect may survive inclusion of a moderate concentration of mag- netic dopants with randomly oriented moments. At low temperatures moments may order ferromagnetically. 37 In this case both T and the inversion symmetry are bro- ken (the latter due to the random position of magnetic dopants) and the effective θ can acquire an arbitrary 

