[Paper Review] Colloquium: Quantum anomalous Hall effect

Cui‐Zu Chang, Chao‐Xing Liu+1 more|arXiv (Cornell University)|Feb 28, 2022

Topological Materials and Phenomena18 citations

TL;DR

This review synthesizes the physical mechanisms behind the quantum anomalous Hall (QAH) effect in four distinct two-dimensional material systems: magnetically doped topological insulators, intrinsic magnetic topological insulators like MnBi₂Te₄, and moiré superlattices in graphene and transition metal dichalcogenides. It demonstrates that the QAH effect—quantized Hall resistance without external magnetic fields—arises from spontaneous time-reversal symmetry breaking and non-trivial topological order, with experimental realizations achieving Hall resistance quantization at parts-per-million accuracy, positioning the QAH effect as a promising candidate for quantum resistance standards and dissipationless electronics.

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 insulators in the (Bi,Sb)2Te3 family, (ii) thin films of the intrinsic magnetic topological insulator MnBi2Te4, (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.

Motivation & Objective

• To systematically review the physical mechanisms enabling the quantum anomalous Hall (QAH) effect in four distinct classes of two-dimensional materials.
• To clarify the role of spontaneous time-reversal symmetry breaking and topological band structure in realizing quantized Hall conductance without external magnetic fields.
• To evaluate the current experimental progress in achieving high-precision Hall resistance quantization, particularly for metrological applications.
• To explore the potential of QAH materials in enabling dissipationless electronic and spintronic devices.
• To identify key challenges and future directions, including higher-temperature operation and the realization of fractional QAH states.

Proposed method

• Analysis of the TKNN formula linking Hall conductance to the integral of Berry curvature over the Brillouin zone, establishing the Chern number as a topological invariant.
• Application of Dirac models and effective Hamiltonians to describe band structures in magnetic topological insulators and moiré systems.
• Investigation of magnetism mechanisms in doped topological insulators (Cr/V-doped (Bi,Sb)₂Te₃), intrinsic magnetic insulators (MnBi₂Te₄), and moiré heterostructures.
• Use of tight-binding models and symmetry analysis to explain chiral edge states and quantized transport in QAH systems.
• Evaluation of experimental transport measurements, including Hall resistance quantization and scaling behavior of plateau transitions.
• Assessment of theoretical proposals for higher Chern number states, fractional QAH effects, and topological superconducting proximity effects.

Experimental results

Research questions

• RQ1 What are the distinct physical mechanisms enabling the quantum anomalous Hall effect in magnetically doped topological insulators, intrinsic magnetic topological insulators, and moiré superlattices?
• RQ2 How does spontaneous time-reversal symmetry breaking lead to quantized Hall conductance in the absence of an external magnetic field?
• RQ3 What are the key experimental signatures of the QAH effect, and to what precision has Hall resistance quantization been achieved in current materials?
• RQ4 What are the primary challenges in achieving higher-temperature operation and improved quantization accuracy for QAH-based quantum resistance standards?
• RQ5 How can QAH edge states be leveraged for dissipationless interconnects and chiral electronic or spintronic devices?

Key findings

• The quantum anomalous Hall effect has been experimentally realized in four classes of 2D materials: Cr- and V-doped (Bi,Sb)₂Te₃ thin films, intrinsic MnBi₂Te₄, twisted bilayer graphene, and MoTe₂/WSe₂ heterobilayers.
• Quantized Hall resistance has been measured with uncertainties at the parts-per-million (ppm) level in Cr- and V-doped topological insulator films, with one study achieving 0.17 ± 0.25 ppm.
• A 9 QL V-doped (Bi,Sb)₂Te₃ film demonstrated Hall resistance quantization within 0.17 ± 0.25 ppm, and a 9 QL modulation-doped QAH sandwich sample achieved 2 ppm accuracy.
• Recent measurements using permanent magnets on the same QAH sandwich device reported a precision of 10 parts per billion (ppb), approaching but not yet meeting the 1 ppb threshold for quantum resistance standards.
• The chiral edge states in QAH systems support dissipationless transport, enabling theoretical proposals for length-independent interconnects with only contact resistance.
• All-electrical switching of QAH edge current chirality has been experimentally demonstrated in magnetic topological insulators via spin-orbit torque, enabling potential control of chiral electronic states.