Semi-metal-insulator transition on the surface of a topological insulator with in-plane magnetization

Abstract

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, the parity is also broken, since the Dirac fermions become massive. This leads in turn to the generation of a topological Chern-Simons term by quantum fluctuations. On the other hand, for an in-plane magnetization the surface states remain gapless for the non-interacting Dirac fermions. In this work we study the possibility of spontaneous breaking of parity due to a dynamical gap generation on the surface in the presence of a local, Hubbard-like, interaction of strength $g$ between the Dirac fermions. 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. We discuss our results in the context of recent experiments in EuS/Bi_2Se_3 heterostructures.

v3: Extended version; 11 pages, 2 figures, typos corrected. This version matches published version

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• Conformality loss and quantum criticality in topological Higgs electrodynamics in 2+1 dimensions
• Finite temperature fluctuation-induced order and responses in magnetic topological insulators
• Thermal screening at finite chemical potential on a topological surface and its interplay with proximity-induced ferromagnetism
• Topological magnetic dipolar interaction and non-local electric magnetization control in topological insulator heterostructures
• Nematic order on the surface of a three-dimensional topological insulator
• Formation of bound states from the edge states of 2D topological insulator by macroscopic magnetic barriers
• Strong photon coupling to high-frequency antiferromagnetic magnons via topological surface states
• Fermi surface instabilities of symmetry-breaking and topological types on the surface of a three-dimensional topological insulator