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 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 rho_xx=0 accompanied with a well-developed Hall resistivity plateau rho_xy=(1\pm0.1) h/e^2 (\lambda_(F,z)/2), where \lambda_(F,z) is the Fermi wavelength along the field direction (z 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 rho_xx and rho_xy 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.

• The paper demonstrates the first experimental evidence of the 3D quantum Hall effect in ZrTe₅ by observing a dissipationless longitudinal resistivity and quantized Hall plateau.
• It employs Hall bar geometry and Shubnikov–de Haas oscillations to characterize Landau level quantization under a low magnetic field (~1.3 T).
• The study identifies a metal-insulator transition and highlights interaction-driven instabilities with potential applications in quantum computing and magnetic storage.

Analyzing the Three-Dimensional Quantum Hall Effect and Metal-Insulator Transition in ZrTe₅

In the study conducted by Tang et al., significant insights into the three-dimensional (3D) quantum Hall effect (QHE) were achieved through experimental observations using high-quality bulk ZrTe₅ crystals. Historically, the QHE is a well-established phenomenon in two-dimensional (2D) electron systems, characterized by quantized Hall conductivity and vanishing longitudinal resistivity. Although theoretical extensions and models have long posited the presence of a 3D version, empirical evidence remained scarce until this investigation provided clarity through ZrTe₅, a material noted for its structural and electronic properties.

Methodology and Key Findings

The researchers utilized ZrTe₅ due to its orthorhombic layered structure, which supports extremely low carrier density and high electron mobility, both crucial conditions for achieving the extreme quantum limit essential for 3D QHE observation with a relatively small magnetic field (~1.3 T). Employing Hall bar geometry for transport measurements, they documented dissipationless longitudinal resistivity and a persistent Hall resistivity plateau at extremely low Landau levels. This provided clear experimental evidence of 3D QHE, fulfilling the predictions of Halperin's theoretical framework regarding interaction-driven instabilities in a 3D electron gas under strong magnetic fields.

In particular, the observations revealed a dissipationless longitudinal resistivity and a well-developed Hall resistivity plateau, suggesting the manifestation of a stable quantum state. Notably, the 3D QHE in ZrTe₅ was verified by measuring a distinctive metal-insulator transition. Critical examination of Fermi surface morphology and quantum oscillations through Shubnikov-de Haas studies provided insights into Fermi surface topology, indicating the coexistence of 3D quantum behavior with Dirac-like electronic dispersion.

Implications and Theory

The manifestations observed can be attributed primarily to enhanced interaction effects augmented by several factors: the Landau level quantization effect that lowers electronic dimensionality, the anisotropic mass and Fermi velocity distribution in ZrTe₅, and the unique innate Fermi surface topology facilitating nesting conducive to charge density wave (CDW) instabilities.

Such a comprehensive investigation provides profound implications on fundamental understanding and potential applications. The controlled demonstration of 3D QHE suggests the emergence of unexplored quantum phases and transitions, possibly furthering quantum computation and compact, high-capacity magnetic storage technologies. Moreover, the results and methodologies applied here may offer pertinent experimental protocols optimizable for other topological and quantum materials.

Future Considerations

While the data presented represents a significant advancement in the quantum behavior of 3D systems under extreme conditions, several avenues remain for exploitation and exploration. Future efforts should focus on the nature of the insulating phase at elevated magnetic fields, potentially ascribing its genesis to Wigner crystallization or other localized phenomena. Additionally, the transition-free plateaus observed suggest underlying fractional quantization mechanisms that merit further theoretical and experimental scrutiny to elucidate a potential precursor to a fractional 3D quantum Hall state.

In conclusion, the study by Tang et al. decisively demonstrates for the first time the existence of 3D QHE under attainable experimental conditions, owed significantly to the material properties of ZrTe₅. This work represents a substantial step forward in the quest to achieve a deeper understanding of quantum phase transitions in three-dimensional systems. As such, it lays the groundwork for subsequent inquiries into exotic quantum states of matter and their practical applications.