Flavio S. Nogueira, Ilya Eremin
A thin film of ferromagnetically ordered material proximate to the surface of a three-dimensional topological insulator explicitly breaks the time-reversal symmetry of the surface states. For an out-of-plane ferromagnetic order parameter on the surface, parity is also broken, since the Dirac fermions become massive. This leads in turn to the generation of a Chern-Simons term by quantum fluctuations. On the other hand, for an in-plane magnetization the surface states remain metallic. In this work we study the possibility of spontaneous breaking 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 spontaneous gap generation. In the presence of a local, Hubbard-like, interaction of strength g, a gap and a Chern-Simons term are generated for g larger than some critical value, g_c, provided the number of Dirac fermions, N, is odd. For an even number of Dirac fermions the masses are generated in pairs having opposite signs, and no Chern-Simons term is generated. Our result offers a possible explanation to recent experiments showing a gap opening even when the topological insulator is proximate to a planar ferromagnet.
View original:
http://arxiv.org/abs/1304.2933
No comments:
Post a Comment