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 σ_xy or Hall resistivity ρ_xy is

σ_xy = (e²/h)*(1/λ_Q) or ρ_xy = (h/e²)*λ_Q

where λ_Q 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.

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