{"title":"On the half-quantized Hall conductance of massive surface electrons in magnetic topological insulator films","authors":"Rui Chen, Shun-Qing Shen","doi":"10.1007/s11433-023-2352-0","DOIUrl":null,"url":null,"abstract":"<div><p>In topological insulators, massive surface states resulting from local symmetry breaking were thought to exhibit a half-quantized Hall conductance, obtained from the low-energy effective model in an infinite Brillouin zone. In a lattice model, the surface band is composed of a combination of surface states and bulk states. The massive surface states alone may not be enough to support an exact one-half quantized surface Hall conductance in a finite Brillouin zone and the whole surface band always gives an integer quantized Hall conductance as enforced by the TKNN theorem. To explore this, we investigate the band structures of a lattice model describing the magnetic topological insulator film that supports the axion insulator, Chern insulator, and semi-magnetic topological insulator phases. We reveal that the gapped and gapless surface bands in the three phases are characterized by an integer-quantized Hall conductance and a half-quantized Hall conductance, respectively. We propose an effective model to describe the three phases and show that the low-energy dispersion of the surface bands inherits from the surface Dirac fermions. The gapped surface band manifests a nearly half-quantized Hall conductance at low energy near the center of Brillouin zone, but is compensated by another nearly half-quantized Hall conductance at high energy near the boundary of Brillouin zone because a single band can only have an integer-quantized Hall conductance. The gapless band hosts a zero Hall conductance at low energy but is compensated by another half-quantized Hall conductance at high energy, and thus the half-quantized Hall conductance can only originate from the gapless band. Moreover, we calculate the layer-resolved Hall conductance of the system. The conclusion suggests that the individual gapped surface band alone does not support the half-quantized surface Hall effect in a lattice model.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":null,"pages":null},"PeriodicalIF":6.4000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11433-023-2352-0.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science China Physics, Mechanics & Astronomy","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11433-023-2352-0","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In topological insulators, massive surface states resulting from local symmetry breaking were thought to exhibit a half-quantized Hall conductance, obtained from the low-energy effective model in an infinite Brillouin zone. In a lattice model, the surface band is composed of a combination of surface states and bulk states. The massive surface states alone may not be enough to support an exact one-half quantized surface Hall conductance in a finite Brillouin zone and the whole surface band always gives an integer quantized Hall conductance as enforced by the TKNN theorem. To explore this, we investigate the band structures of a lattice model describing the magnetic topological insulator film that supports the axion insulator, Chern insulator, and semi-magnetic topological insulator phases. We reveal that the gapped and gapless surface bands in the three phases are characterized by an integer-quantized Hall conductance and a half-quantized Hall conductance, respectively. We propose an effective model to describe the three phases and show that the low-energy dispersion of the surface bands inherits from the surface Dirac fermions. The gapped surface band manifests a nearly half-quantized Hall conductance at low energy near the center of Brillouin zone, but is compensated by another nearly half-quantized Hall conductance at high energy near the boundary of Brillouin zone because a single band can only have an integer-quantized Hall conductance. The gapless band hosts a zero Hall conductance at low energy but is compensated by another half-quantized Hall conductance at high energy, and thus the half-quantized Hall conductance can only originate from the gapless band. Moreover, we calculate the layer-resolved Hall conductance of the system. The conclusion suggests that the individual gapped surface band alone does not support the half-quantized surface Hall effect in a lattice model.
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Science China Physics, Mechanics & Astronomy, an academic journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China, and published by Science China Press, is committed to publishing high-quality, original results in both basic and applied research.
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