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Magnetotransport properties of the Quantum Spin Hall and Quantum Hall states in an inverted HgTe/CdTe and InAs/GaSb quantum wells

The quantum spin Hall (QSH) states discovered in an inverted band of InAs/GaSb and HgTe/CdTe quantum wells categorize them among the very superior candidates for topological insulators. In the presence of a magnetic field, these QSH states persist up to a magnetic field equal to the critical field, beyond which the edge states would consist of normal quantum Hall (QH) states. We provide the expression of this critical field which is found consistent with some previous literature. The critical field partitioned the spectrum into two types of quantum states, \textit{viz}. , the Quantum spin Hall (QSH) and Quantum Hall (QH) states. We present a theoretical study of the magnetotransport properties based on the Bernevig-Hughes-Zhang Hamiltonian that describes these QSH states. Our results of the Hall conductivity show the different responses at these two different topological regions. Around the low Fermi energy level, the system has a high Hall conductivity in the QH region, while the same is less dominant in the QSH region. Our results of the Hall conductivity thus help differentiate the type topological phase of the given quantum well.