Quantum anomalous Hall effect in magnetic topological insulators

Jing Wang, Biao Lian, Shou Cheng Zhang

Research output: Contribution to journalConference articlepeer-review

82 Scopus citations


The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimensions (2D) and three-dimensions (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. We present the phase diagram in thin films of a magnetic topological insulator and review the basic mechanism of ferromagnetic order in magnetically doped topological insulators. We also review the recent experimental observation of the QAH effect. We discuss more recent theoretical work on the coexistence of the helical and chiral edge states, multi-channel chiral edge states, the theory of the plateau transition, and the thickness dependence in the QAH effect.

Original languageEnglish (US)
Article number014003
JournalPhysica Scripta
Issue numberT164
StatePublished - Dec 1 2015
Externally publishedYes
Event156th Nobel Symposium on New Forms of Matter: Topological Insulators and Superconductors - Lidingo, Sweden
Duration: Jun 12 2014Jun 15 2014

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics
  • Condensed Matter Physics


  • quantum anomalous hall effect
  • quantum spin hall effect
  • surface state
  • topological insulator


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