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\nA thin film of ferrom agnetically ordered material proximate to the surface of a three-dimen sional topological insulator explicitly breaks the time-reversal symme try of the surface states. For an out-of-plane ferromagnetic order par ameter on the surface\, parity is also broken\, since the Dirac fermio ns become massive. This leads in turn to the generation of a Chern-Sim ons term by quantum fluctuations. On the other hand\, for an in-plane magnetization the surface states remain metallic.

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\nWe con sider a theory for a two-dimensional interacting conduction electron s ystem with strong spin-orbit coupling on the interface between a topol ogical insulator and the magnetic (ferromagnetic or antiferromagnetic) layer. For the ferromagnetic case we derive the Landau-Lifshitz equat ion\, which features a contribution proportional to a fluctuation-indu ced electric field obtained by computing the topological (Chern-Simons ) contribution from the vacuum polarization. We also show that fermion ic quantum fluctuations reduce the critical temperature T*c at the int erface relative to the critical temperature Tc of the bulk\, so that i n the interval T*c ≤T

\nIn addition we study the possibility of spontaneous breakin g of parity due to a dynamical gap generation on the surface. We find that in the absence of interaction between the fermions there is no sp ontaneous gap generation. In the presence of a local\, Hubbard-like\, interaction of strength g\, a gap and a Chern-Simons term are generate d for g larger than some critical value provided the number of Dirac f ermions\, N is odd. For an even number of Dirac fermions the masses ar e generated in pairs having opposite signs\, and no Chern-Simons term is generated. Our result offers a possible explanation to recent exper iments showing a gap opening even when the topological insulator is pr oximate to a planar ferromagnet.

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\n[1] F.S. Noguiera and Il ya Eremin\, Phys. Rev. Lett. 109\, 237203 (2012)

\n[2] F.S. Noguie ra and Ilya Eremin\, arXiv:1304.2933 (unpublished).

\n URL:https://www.physics.wisc.edu/twap/?id=2996 END:VEVENT END:VCALENDAR