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We study transport across a time-dependent magnetic barrier present on thesurface of a three-dimensional topological insulator. We show that such abarrier can be implemented for Dirac electrons on the surface of athree-dimensional topological insulator by a combination of a proximatemagnetic material and linearly polarized external radiation. We find that theconductance of the system can be tuned by varying the frequency and amplitudeof the radiation and the energy of an electron incident on the barrierproviding us optical control on the conductance of such junctions. We firststudy a $\delta$-function barrier which shows a number of interesting featuressuch as sharp peaks and dips in the transmission at certain angles ofincidence. Approximate methods for studying the limits of small and largefrequencies are presented. We then study a barrier with a finite width. Thisgives rise to some new features which are not present for a $\delta$-functionbarrier, such as resonances in the conductance at certain values of the systemparameters. We present a perturbation theory for studying the limit of largedriving amplitude and use this to understand the resonances. Finally, we use asemiclassical approach to study transmission across a time-dependent barrierand show how this can qualitatively explain some of the results found in theearlier analysis. We discuss experiments which can test our theory.

Transport on a topological insulator surface with a time-dependent magnetic barrier