Searching materials for three-dimensional quantum Hall effect

Many new quantum effects were recently found in bulk single crystals, demonstrating great surprises since it was believed that quantum confinement appears in super-clean thin-film structures only. The electron behaviour dramatically changes in magnetic field and the Hall conductivity gets quantized values of ve2/h together with vanishing the longitudinal conductivity. Where e is the elementary charge, v is the filling factor of Landau level, and h is Planck's constant [1]. Depending on the fraction or integer value of v, QHE is known as fractional QHE or integral QHE. Recently, v has been recognized as Chern number, representing the topological character of the QHE and topology in materials is now a central topic of research in condensed matter physics. The QHE has intensively been investigated in two-dimensional electron gas systems, but it was also proposed earlier to appear in three-dimensional materials: for electrons in periodic or quasiperiodic potential and if the Fermi level lies in an energy gap, the longitudinal conductivity vanishes and the Hall conductivity σxy or Hall resistivity ρxy is

σxy = (e2/h)*(1/λQ) or ρxy = (h/e2)*λQ

where λQ is the period of potential in real space. In the presence of a magnetic field, electrons get localized and the mutual interaction enhanced, that together create an instability to the Fermi surface [2]. This instability can come from many sources, for example, charge density wave, spin density wave, excitonic insulator etc. Our notion is to search for compounds that exhibit a three-dimensional QHE by creating an instability to the Fermi surface in presence of a magnetic field. Very recently, the first 3D QHE was realized in ZrTe5 [3]. Candidates with small Fermi surface, resulting low charge-carrier concentrations and an electronic instability are the preliminary criterion.

[1] K. von Klitzing, G. Dorda, and M. Pepper
New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance
Phys. Rev. Lett. 45, 494 (1980)
[2] B.I. Halperin
Possible States for a Three-Dimensional Electron Gas in a Strong Magnetic Field
Jpn. J. Appl. Phys. 26, 1913 (1987)
[3] F. Tang, Y. Ren, P. Wang, R. Zhong, J. Schneeloch, S.A. Yang, K. Yang, P.A. Lee, G. Gu, Z. Qiao, and L. Zhang
Three-dimensional quantum Hall effect and metal–insulator transition in ZrTe5
Nature 569, 537541 (2019)

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