Three-dimensional quantum Hall effect and metal–insulator transition in ZrTe5

Abstract

Symmetry, dimensionality, and interaction are crucial ingredients for phase transitions and quantum states of matter. As a prominent example, the integer quantum Hall effect (QHE) represents a topological phase generally regarded as characteristic for two-dimensional (2D) electronic systems, and its many aspects can be understood without invoking electron-electron interaction. The intriguing possibility of generalizing QHE to three-dimensional (3D) systems was proposed decades ago, yet it remains elusive experimentally. Here, we report for the first time clear experimental evidence for the 3D QHE, observed in bulk ZrTe5 crystals. Owing to the extremely high sample quality, the extreme quantum limit with only the lowest Landau level occupied can be achieved by an applied magnetic field as low as 1.5 T. Remarkably, in this regime, we observe a dissipationless longitudinal resistivity ≅ accompanied with a well-developed Hall resistivity plateau = ( ± . ) ( , ) , where , is the Fermi wavelength along the field direction ( axis). This striking result strongly suggests a Fermi surface instability driven by the enhanced interaction effects in the extreme quantum limit. In addition, with further increasing magnetic field, both and increase dramatically and display an interesting metal-insulator transition, representing another magnetic field driven quantum phase transition. Our findings not only unambiguously reveal a novel quantum state of matter resulting from an intricate interplay among dimensionality, interaction, and symmetry breaking, but also provide a promising platform for further exploration of more exotic quantum phases and transitions in 3D systems.Since its discovery in 1980, the QHE has been established and well understood in a variety of 2D electron systems, including the traditional 2D electron gas 1,2 , and 2D materials like graphene 3,4 , etc. The hallmark of QHE is that the Hall conductivity takes precisely quantized values as 2 /ℎ while the longitudinal conductivity vanishes 1,2 . Here, the prefactor is the filling factor which counts the number of filled Landau levels, is the elementary charge, and ℎ is Plank's constant. Soon after its

Unraveling the topology of ZrTe5 by changing temperature

“…This prediction has sparked intense experimental and theoretical activity on this material system, not only in the monolayer form but also in the bulk. Additionally, ZrTe 5 has proved a fertile ground for the discovery of a number of exciting properties: chiral magnetic effect 5 , log-periodic quantum oscillations 6 , three-dimensional quantum Hall effect 7 and quantized thermoelectric Hall conductivity 8 , to list just a few.…”

Approaching three-dimensional quantum Hall effect in bulk HfTe5

“…Contrast to the quasi-2D case, the single-particle electronic bands under the magnetic field are gapless since the interlayer coupling is much larger than the Landau level spacing. An energy gap near the Fermi energy is evidenced by transport measurements originating from the formation of charge density wave driven by Coulomb interaction 8,14 .…”

Quantum transport in topological semimetals under magnetic fields (II)

“…Recently, a new experiment uses this thickness-dependent phase shift to demonstrate the contribution of the Weyl orbit in the observed quantized Hall resistance [219]. The 3D quantum Hall effect can also be supported by the CDW mechanism [255], which has been observed recently in ZrTe 5 [256]. More works will be inspired to verify the mechanism and realize the 3D quantum Hall effect in the future [257].…”