We review low- and high-field magnetotransport in 80-nm-thick strained HgTe, a material that belongs to the class of strong three-dimensional topological insulators. Utilizing a top gate, the Fermi level can be tuned from the valence band via the Dirac surface states into the conduction band and allows studying Landau quantization in situations where different species of charge carriers contribute to magnetotransport. Landau fan charts, mapping the conductivity ${\sigma }_{xx}\left(V_g,B\right)$ in the whole magnetic field–gate voltage range, can be divided into six areas, depending on the state of the participating carrier species. Key findings are (i) the interplay of bulk holes (spin degenerate) and Dirac surface electrons (nondegenerate), coexisting for $E_F$ in the valence band, leads to a periodic switching between odd and even filling factors and thus odd and even quantized Hall voltage values. (ii) We found a similar though less pronounced behavior for coexisting Dirac surface and conduction band electrons. (iii) In the bulk gap, quantized Dirac electrons on the top surface coexist at lower B with nonquantized ones on the bottom side, giving rise to quantum Hall plateau values depending—for a given filling factor—on the magnetic field strength. In stronger $B$ fields, Landau level separation increases; charge transfer between different carrier species becomes energetically favorable and leads to the formation of a global (i.e., involving top and bottom surfaces) quantum Hall state. Simulations using the simplest possible theoretical approach are in line with the basic experimental findings, describing correctly the central features of the transitions from classical to quantum transport in the respective areas of our multicomponent charge carrier system.

中文翻译：

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三维拓扑绝缘体HgTe中的量子霍尔效应和Landau能级

我们回顾了在80 nm厚的应变HgTe中的低磁场和高磁场磁传输，该材料属于强三维拓扑绝缘体。利用顶栅，费米能级可以从价带经狄拉克表面态调谐到导带，并允许在不同电荷载流子促成磁传输的情况下研究朗道量子化。Landau风扇图表，绘制电导率图${\sigma }_{XX}（V_G，乙）$在整个磁场－栅极电压范围内，根据参与的载流子物种的状态，可以分为六个区域。主要发现是（i）体孔（自旋简并）和狄拉克表面电子（未简并）的相互作用，${Ë}_F$在价带中，会导致奇数和偶数填充因子之间的周期性切换，从而导致奇数和偶数量化的霍尔电压值之间的切换。（ii）我们发现共存Dirac表面电子和导带电子具有相似但不太明显的行为。（iii）在体隙中，上表面的量化Dirac电子在下B与下表面的未量化电子共存，从而在给定的填充因子下，取决于磁场强度，产生量子霍尔平稳值。在更强$乙$田间，朗道级分离增加；不同载流子物种之间的电荷转移在能量上变得有利，并导致形成整体（即，涉及顶部和底部表面）量子霍尔态。使用最简单的可能的理论方法进行的仿真与基本的实验结果相符，正确地描述了多组分电荷载流子系统各个区域中从经典输运到量子输运的过渡的中心特征。