Latest revision as of 23:33, 23 May 2026

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Quantum anomalous Hall effect (QAHE) is the "quantum" version of the anomalous Hall effect. While the anomalous Hall effect requires a combination of magnetic polarization and spin-orbit coupling to generate a finite Hall voltage even in the absence of an external magnetic field (hence called "anomalous"), the quantum anomalous Hall effect is its quantized version. The Hall conductivity acquires quantized values proportional to integer multiples of the von Klitzing constant ( $e^{2} / h$ ) (also called conductance quantum). In this respect the QAHE is similar to the quantum Hall effect. The integer here is equal to the Chern number which arises out of topological properties of the material band structure. These effects are observed in systems called quantum anomalous Hall insulators (also called Chern insulators).^[1]

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 {{Short description|Effect in quantum mechanics where conductivity acquires quantized values
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-'''Quantum anomalous Hall effect''' (QAHE) is the "quantum" version of the [[Physics:Hall effect#Anomalous Hall effect|anomalous Hall effect]]. While the anomalous Hall effect requires a combination of magnetic polarization and [[Physics:Spin–orbit interaction|spin-orbit coupling]] to generate a finite Hall voltage even in the absence of an external magnetic field (hence called "anomalous"), the quantum anomalous Hall effect is its quantized version. The Hall conductivity acquires quantized values proportional to integer multiples of the von Klitzing constant (<math>e^2/h</math>) (also called  [[Physics:Conductance quantum|conductance quantum]]). In this respect the QAHE is similar to the [[Physics:Quantum Hall effect|quantum Hall effect]]. The integer here is equal to the [[Chern class|Chern number]] which arises out of topological properties of the material [[Physics:Electronic band structure|band structure]]. These effects are observed in systems called quantum anomalous Hall insulators (also called Chern insulators).<ref>{{cite arXiv|title = The quantum anomalous Hall effect|eprint= 1508.07106|date = 2015-08-28|first1 = Chao-Xing|last1 = Liu|first2 = Shou-Cheng|last2 = Zhang|first3 = Xiao-Liang|last3 = Qi|class= cond-mat.mes-hall}}</ref>
+'''Quantum anomalous Hall effect''' (QAHE) is the "quantum" version of the anomalous Hall effect. While the anomalous Hall effect requires a combination of magnetic polarization and spin-orbit coupling to generate a finite Hall voltage even in the absence of an external magnetic field (hence called "anomalous"), the quantum anomalous Hall effect is its quantized version. The Hall conductivity acquires quantized values proportional to integer multiples of the von Klitzing constant (<math>e^2/h</math>) (also called  conductance quantum). In this respect the QAHE is similar to the [[Physics:Quantum Hall effect|quantum Hall effect]]. The integer here is equal to the Chern number which arises out of topological properties of the material band structure. These effects are observed in systems called quantum anomalous Hall insulators (also called Chern insulators).<ref>{{cite arXiv|title = The quantum anomalous Hall effect|eprint= 1508.07106|date = 2015-08-28|first1 = Chao-Xing|last1 = Liu|first2 = Shou-Cheng|last2 = Zhang|first3 = Xiao-Liang|last3 = Qi|class= cond-mat.mes-hall}}</ref>
 The effect was observed experimentally for the first time in 2013 by a team led by [[Biography:Xue Qikun|Xue Qikun]] at Tsinghua University.<ref>{{Cite journal|title = Experimental Observation of the quantum Anomalous Hall Effect in a Magnetic Topological Insulator|journal = Science|date = 2013-04-12|issn = 0036-8075|pmid = 23493424|pages = 167–170|volume = 340|issue = 6129|doi = 10.1126/science.1234414|language = en|first1 = Cui-Zu|last1 = Chang|first2 = Jinsong|last2 = Zhang|first3 = Xiao|last3 = Feng|first4 = Jie|last4 = Shen|first5 = Zuocheng|last5 = Zhang|first6 = Minghua|last6 = Guo|first7 = Kang|last7 = Li|first8 = Yunbo|last8 = Ou|first9 = Pang|last9 = Wei|bibcode = 2013Sci...340..167C |arxiv = 1605.08829| s2cid=29455044 }}</ref>
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-[[File:File not found.png|thumb|280px|No image available.]]
+[[File:Quantum_anomalous_Hall_effect_concept_map.svg|thumb|280px|anomalous Hall effect in the Quantum Collection.]]
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