Colloquium: Quantum anomalous Hall effect

Abstract

The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators -topologically non-trivial states of two-dimensional matter with broken time-reversal symmetry. In Chern insulators, non-trivial bulk band topology is expressed by chiral states that carry current along sample edges without dissipation. The quantum anomalous Hall (QAH) effect refers to QH effects that occur in the absence of external magnetic fields due to spontaneously broken time-reversal symmetry. The QAH effect has now been realized in four different classes of two-dimensional materials: (i) thin films of magnetically (Cr-and/or V-) doped topological insulator (Bi,Sb) 2 Te 3 family, (ii) thin films of the intrinsic magnetic topological insulator MnBi 2 Te 4 , (iii) moiré materials formed from graphene, and (iv ) moiré materials formed from transition metal dichalcogenides. In this Article, we review the physical mechanisms responsible for each class of QAH insulator, highlighting both differences and commonalities, and comment on potential applications of the QAH effect.

Topological $p_x+ip_y$ inter-valley coherent state in Moiré MoTe$_2$/WSe$_2$ heterobilayers

“…For example, there have been experimental observations of quantum anomalous Hall (QAH) states in twisted bilayer graphene [2,3] and AB stacked MoTe 2 /WSe 2 heterobilayers [4,5]. Unlike other QAH state platforms, such as magnetic doped topological insulator thin film [6][7][8][9][10][11] and MnBi 2 Te 4 [12] in which the topological states can be understood from singleparticle band structures, the bands in moiré materials are typically very narrow (several to tens of meV) so that Coulomb interactions cannot be neglected. A possible path to obtain QAH states is to first create moiré Chern bands at each valley and lift the valley degeneracy through interactions.…”

Progress and prospects in the quantum anomalous Hall effect

“…The quantum anomalous Hall (QAH) effect represents one of the triumphs in conceptualizing topological aspects of electronic states in condensed matter physics [1][2][3][4][5][6][7][8][9][10]. It constitutes an ever-evolving family of Hall effects [11].…”

Electron spin resonance study of mixed Bi2Se3 topological insulator-magnetic insulator nanoparticles

“…2,3 The backscattering-free spin-polarized current of quantum anomalous Hall insulators and the quantized magnetoelectric effect of axion insulators are expected to pave the way for spintronics and quantum computing. [1][2][3][4][5] Recently, the magnetic proximity effect at the interface between a magnetic material and a topological insulator has attracted a lot of attention along with several controversies as one of the methods to break the time-reversal symmetry of the topological insulator surface. 2,3,[6][7][8][9][10][11][12] Anomalous Hall effect measurements and spin-polarized neutron reflectivity measurements in bilayers of magnetic materials and topological insulators reported proximity-induced ferromagnetic ordering at the topological insulator surface.…”