Quantum Anomalous Hall Effect in Magnetic Doped Topological Insulators and Ferromagnetic Spin‐Gapless Semiconductors—A Perspective Review

Abstract

between intrinsic magnetization and spin-orbit coupling (SOC). Unlike spindegenerate chiral edge states in integer quantum Hall effect where time-reversal symmetry (TRS) is broken through external magnetic field, the trademark of QAH effect is the spinless/spinful chiral edge states. Such macroscopic quantum phenomenon, originating from the bulk topology of QAH systems, is ideal for transport in both electronics and spintronics devices. After seminal proposal by Haldane, [1] a number of theoretical models were proposed for the realization of QAH effect in realistic condensed mater systems sharing the same key feature-achieving simultaneous control over intrinsic magnetization and SOC. This aim is associated with two decisive energy scales for the observation of QAH effect: association of the SOC with the bulk topological bandgap and the association of ferromagnetism with the Curie temperature. The smaller of these two energy scales defines the upper limit for the observable temperature of QAH effect. As a result, to assess the realistic temperature scale for QAH effect, the necessity of a delicate interplay between these two energy scales plays the key role in the search of suitable materials. Quantum anomalous Hall effect, with a trademark of dissipationless chiral edge states for electronics/spintronics transport applications, can be realized in materials with large spin-orbit coupling and strong intrinsic magnetization. After Haldane's seminal proposal, several models have been presented to control/ enhance the spin-orbit coupling and intrinsic magnetic exchange interaction. After brief introduction of Haldane model for spineless fermions, following three fundamental quantum anomalous Hall models are discussed in this perspective review: i) low-energy effective four band model for magnetic-doped topological insulator (Bi,Sb) 2 Te 3 thin films, ii) four band tight-binding model for graphene with magnetic adatoms, and iii) two (three) band spinful tight-binding model for ferromagnetic spin-gapless semiconductors with honeycomb (kagome) lattice where ground state is intrinsically ferromagnetic. These models cover 2D Dirac materials hosting spinless, spinful, and spin-degenerate Dirac points where various mass terms open bandgap and lead to quantum anomalous Hall effect. With emphasis on the topological phase transition driven by ferromagnetic exchange interaction and its interplay with spin-orbit-coupling, various symmetry constraints on the nature of mass term and the materialization of these models are discussed. This study will shed light on the fundamental theoretical perspectives of quantum anomalous Hall materials.

Mn‐Rich MnSb2Te4: A Topological Insulator with Magnetic Gap Closing at High Curie Temperatures of 45–50 K

“…[1] The idea to combine ferromagnetism with topological insulators for this purpose [2][3][4] has fuelled the materials science. [5,6] It led to the experimental discovery of the QAHE in Cr-and V-doped (Bi, Sb) 2 Te 3 [7][8][9][10][11] with precise quantized values of the Hall resistivity down to the sub-part-per-million level. [12][13][14][15] The stable 3+ configuration of V or Cr substitutes the isoelectronic Bi or Sb [3,16,17] enabling ferromagnetism by coupling the magnetic moments of the transition metal atoms.…”

Optimizing Topological Switching in Confined 2D-Xene Nanoribbons via Finite-Size Effects

“…In passing, it is noted and will be be presented in a separate study, longitudinal momentum and width dependence of gate-induced inter-edge coupling can also be employed to tune the exchange interaction in 2D magnetic topological insulators. [49][50][51][52][53][54][55][56][57] For example, critical regime in an antiferromagnetic topological insulators can be optimized to design a topological spin transistor via gate induced topological switching of edge state spin transport.…”

Topological One-Way Edge States in an Air-Hole Honeycomb Gyromagnetic Photonic Crystal

“…Topological physics is flourishing as an active field, which has drawn extensive attention in both fundamental research and applied science [1]. Topological insulator commonly features the striking phenomenon of topologically protected one-way transport, exhibiting edge states or surface states that are strongly robust against defects, disorders, obstacles, sharp corners and so on [2,3]. Inspired from the discovery of condensed quantum Hall effect, many studies have shown that topological states show essentially single-particle behavior of electrons and one can establish an analogy relationship with photon behaviors called topological photonic state (or topological one-way edge state) [4][5][6][7].…”