Three-dimensional Quantum Hall Effect Research Articles

Three-dimensional quantum Hall effect in acoustic crystals

Three-dimensional quantum Hall effect in acoustic crystals

High-Mobility Topological Semimetals as Novel Materials for Huge Magnetoresistance Effect and New Type of Quantum Hall Effect.

The quantitative description of electrical and magnetotransport properties of solid-state materials has been a remarkable challenge in materials science over recent decades. Recently, the discovery of a novel class of materials-the topological semimetals-has led to a growing interest in the full understanding of their magnetotransport properties. In this review, the strong interplay among topology, band structure, and carrier mobility in recently discovered high carrier mobility topological semimetals is discussed and their effect on their magnetotransport properties is outlined. Their large magnetoresistance effect, especially in the Hall transverse configuration, and a new version of a three-dimensional quantum Hall effect observed in high-mobility Weyl and Dirac semimetals are reviewed. The possibility of designing novel quantum sensors and devices based on solid-state semimetals is also examined.

Chern number and Hall conductivity in three-dimensional quantum Hall effect in Weyl semimetals

Chern number and Hall conductivity in three-dimensional quantum Hall effect in Weyl semimetals

Quantum oscillations and three-dimensional quantum Hall effect in ZrTe5

Recent experiments have reported a lot of spectacular transport properties in topological materials, such as quantum oscillations and three-dimensional (3D) quantum Hall effect (QHE) in ${\mathrm{ZrTe}}_{5}$. In this paper, by using a strong topological insulator model to describe ${\mathrm{ZrTe}}_{5}$, we study the magnetotransport property of the 3D system. With fixed carrier density, we find that there exists a deferring effect in the chemical potential, which favors distinguishing the saddle points of the inverted LLs. On the other hand, with fixed chemical potential, the features of 3D QHE are demonstrated and we attribute the underlying mechanisms to the interplay between Dirac fermions, magnetic field, and impurity scatterings.

Realization of a three-dimensional quantum Hall effect in a Zeeman-induced second-order topological insulator on a torus

We propose a realization of a quantum Hall effect (QHE) in a second-order topological insulator (SOTI) in three dimensions (3D), which is mediated by hinge states on a torus surface. It results from the nontrivial interplay of the material structure, Zeeman effect, and the surface curvature. In contrast to the conventional 2D- and 3D-QHE, we show that the 3D-SOTI QHE is not affected by orbital effects of the applied magnetic field and exists in the presence of a Zeeman term only, induced e.g. by magnetic doping. To explain the 3D-SOTI QHE, we analyze the boundary charge for a 3D-SOTI and establish its universal dependence on the Aharonov-Bohm flux threading through the torus hole. Exploiting the fundamental relation between the boundary charge and the Hall conductance, we demonstrate the universal quantization of the latter, as well as its stability against random disorder potentials and continuous deformations of the torus surface.

Understanding the three-dimensional quantum Hall effect in generic multi-Weyl semimetals

The quantum Hall effect in three-dimensional Weyl semimetal (WSM) receives significant attention for the emergence of the Fermi loop where the underlying two-dimensional Hall conductivity, namely, sheet Hall conductivity, shows quantized plateaus. In tilt multi-Weyl semimetals (mWSMs) lattice models, we systematically study Landau levels (LLs) and magneto-Hall conductivity both under the parallel and perpendicular magnetic field (referenced to the Weyl node's separation), i.e., $\mathbit{B}\ensuremath{\parallel}z$ and $\mathbit{B}\ensuremath{\parallel}x$, to explore the impact of tilting and nonlinearity in the dispersion. We make use of two (single) node low-energy models to qualitatively explain the emergence of mid-gap chiral (linear crossing of chiral) LLs on the lattice for $\mathbit{B}\ensuremath{\parallel}z$ $(\mathbit{B}\ensuremath{\parallel}x)$. Remarkably, we find that the sheet Hall conductivity becomes quantized for $\mathbit{B}\ensuremath{\parallel}z$ even when two Weyl nodes project onto a single Fermi point in two opposite surfaces, forming a Fermi loop with ${k}_{z}$ as the good quantum number. On the other hand, the Fermi loop, connecting two distinct Fermi points on two opposite surfaces, with ${k}_{x}$ being the good quantum number, causes the quantization in sheet Hall conductivity for $\mathbit{B}\ensuremath{\parallel}x$. The quantization is almost lost (perfectly remained) in the type-II phase for $\mathbit{B}\ensuremath{\parallel}x$ $(\mathbit{B}\ensuremath{\parallel}z)$. Interestingly, the jump profiles between the adjacent quantized plateaus change with the topological charge for both cases. The momentum-integrated three-dimensional Hall conductivity is not quantized; however, it bears the signature of chiral LLs resulting in the linear dependence on $\ensuremath{\mu}$ for small $\ensuremath{\mu}$. The linear zone (its slope) reduces (increases) as the tilt (topological charge) of the underlying WSM increases.

Anisotropic Three-Dimensional Quantum Hall Effect and Magnetotransport in Mesoscopic Weyl Semimetals.

Weyl semimetals are emerging to become a new class of quantum-material platform for various novel phenomena. Especially, the Weyl orbit made from surface Fermi arcs and bulk relativistic states is expected to play a key role in magnetotransport, leading even to a three-dimensional quantum Hall effect (QHE). It is experimentally and theoretically important although yet unclear whether it bears essentially the same phenomenon as the conventional two-dimensional QHE. We discover an unconventional fully three-dimensional anisotropy in the quantum transport under a magnetic field. Strong suppression and even disappearance of the QHE occur when the Hall-bar current is rotated away from being transverse to parallel with respect to the Weyl point alignment, which is attributed to a peculiar absence of conventional bulk-boundary correspondence. Besides, transport along the magnetic field can exhibit a remarkable reversal from negative to positive magnetoresistance. These results establish the uniqueness of this QHE system as a novel three-dimensional quantum matter.

Generalization of the theory of three-dimensional quantum Hall effect of Fermi arcs in Weyl semimetal

The quantum Hall effect (QHE), which is usually observed in two-dimensional systems, was predicted theoretically and observed experimentally in three-dimensional (3D) topological semimetal. However, there are some inconsistencies between the theory and the experiments showing the theory is imperfect. Here, we generalize the theory of the 3D QHE of Fermi arcs in Weyl semimetal. Through calculating the sheet Hall conductivity of a Weyl semimetal slab, we show that the 3D QHE of Fermi arcs can occur in a large energy range and the thickness dependences of the QHE in different Fermi energies are distinct. When the Fermi energy is near the Weyl nodes, the Fermi arcs give rise to the QHE which is independent of the thickness of the slab. When the Fermi energy is not near the Weyl nodes, the two Fermi arcs form a complete Fermi loop with the assistance of bulk states giving rise to the QHE which is dependent on the sample thickness. We also demonstrate how the band anisotropic terms influence the QHE of Fermi arcs. Our theory complements the imperfections of the present theory of 3D QHE of Fermi arcs.

Theoretical study of the three-dimensional quantum Hall effect in a periodic electron system

The existence of a three-dimensional quantum Hall effect (3D QHE) due to spontaneous Fermi surface instabilities in strong magnetic fields was proposed decades ago, and has stimulated recent progress in experiments. The reports in recent experiments show that the Hall plateaus and vanishing transverse magnetoresistivities (TMRs) (which are two main signatures of 3D QHE) are not easily observed in natural materials. Two main explanations for the slowly varying slopelike Hall plateaus and nonvanishing TMRs [which can be referred to as the quasiquantized Hall effect (QQHE)] have been proposed. By studying the magnetotransport with a simple effective periodic 3D system, we show how 3D QHE can be achieved in certain parameter regimes. We find two mechanisms that may give rise to QQHE. One mechanism is the ``low'' Fermi energy effect, and the other is the ``strong'' impurity effect. Our studies also prove that an artificial superlattice is an ideal platform for realizing 3D QHE with a high layer barrier periodic potential.

Three-dimensional quantum Hall effect and magnetothermoelectric properties in Weyl semimetals

We numerically study the three-dimensional (3D) quantum Hall effect (QHE) and magnetothermoelectric transport of Weyl semimetals in the presence of disorder. We obtain a bulk picture that the exotic 3D QHE emerges in a finite range of Fermi energy around the Weyl points determined by the gap between the $n=\ensuremath{-}1$ and $n=1$ Landau levels (LLs). The quantized Hall conductivity is attributable to the chiral zeroth LLs traversing the gap, and is robust against disorder scattering for an intermediate number of layers in the direction of the magnetic field. Moreover, we predict several interesting characteristic features of the thermoelectric transport coefficients in the 3D QHE regime, which can be probed experimentally. This may open an avenue for exploring Weyl physics in topological materials.

Three-dimensional quantum Hall effect in Weyl semimetals

We analytically study the three-dimensional (3D) quantum Hall effect (QHE) in a thin film of a Weyl semimetal from the perspective of bulk states. We derive the Chern numbers for $B\ensuremath{\ne}0$ from the Chern numbers for $B=0$ through a topological analysis and obtain a phase diagram of Chern numbers in Weyl semimetals. We demonstrate how the relative alignment of the Weyl nodes and the thickness of the film influence the quantum Hall plateaus and predict a peculiar phase diagram for the QHE in a thin film of a Weyl semimetal. Our work reveals the nature of the 3D QHE in Weyl semimetals from the bulk states.

Three-dimensional quantum Hall effect in the excitonic phase of a Weyl semimetal

The quantum Hall effect (QHE) is usually observed in two-dimensional systems. Recently, the QHE has been proposed to exist in three-dimensional (3D) Weyl semimetals when the Fermi energy is precisely at the Weyl nodes at zero temperature, which is hardly achievable experimentally. However, the QHE has been experimentally realized in the 3D topological semimetal ${\text{Cd}}_{3}{\text{As}}_{2}$ at finite temperatures. It has been found that a Weyl semimetal may translate to a chiral excitonic insulator due to the interplay between the interaction and band topology. In a Weyl semimetal slab, we show that the Fermi arc surface states can exist not only in the Weyl semimetal but also in the chiral excitonic insulator. As long as the Fermi energy crosses the Fermi arc states, the QHE can be generated under the combined action of bulk states and Fermi arc surface states. Therefore, the integer quantization of Hall conductivity can be observed for a finite energy range, or equivalently at finite temperatures.

Proposal for engineering 3D quantum Hall effect in an electronic superlattice

The three-dimensional (3D) quantum Hall effect (3DQHE) was initially proposed to be realized in systems with spontaneous charge-density-wave (CDW) or spin-density-wave (SDW), which has stimulated recent experimental progress in this direction. Here, instead of such intrinsic scenarios, we propose to realize the 3DQHE in a synthetic semiconductor superlattice. The superlattice is engineered along one direction, which is modeled by the Kronig-Penney type periodic potential. By applying a magnetic field along this direction, quantized 3D Hall conductivity can be achieved in certain parameter regimes, along with a vanishing transverse conductivity. We show that such results are robust against the disorder effect and can be hopefully realized by state-of-the-art fabrication techniques. Our work opens a new research avenue for exploring the 3DQHE in electronic superlattice structures.

Level Statistics Crossover of Chiral Surface States in a Three-Dimensional Quantum Hall SystemSupported by the National Natural Science Foundation of China (Grant No. 11674282), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000).

Recent experiments have demonstrated the realization of the three-dimensional quantum Hall effect in highly anisotropic crystalline materials, such as ZrTe5 and BaMnSb2. Such a system supports chiral surface states in the presence of a strong magnetic field, which exhibit a one-dimensional metal-insulator crossover due to suppression of surface diffusion by disorder potential. We study the nontrivial surface states in a lattice model and find a wide crossover of the level-spacing distribution through a semi-Poisson distribution. We also discover a nonmonotonic evolution of the level statistics due to the disorder-induced mixture of surface and bulk states.

Enhanced anisotropic superconductivity in the topological nodal-line semimetal InxTaS2

Coexistence of topological bands and a charge density wave (CDW) in topological materials has attracted immense attention because of their fantastic properties, such as an axionic CDW, the three-dimensional quantum Hall effect, etc. In this work, the nodal-line semimetal ${\mathrm{In}}_{x}{\mathrm{TaS}}_{2}$ characterized by a CDW and superconductivity is successfully synthesized, whose structure and topological bands (two separated Weyl rings) are similar to ${\mathrm{In}}_{0.58}{\mathrm{TaSe}}_{2}$. A $2\ifmmode\times\else\texttimes\fi{}2$ commensurate CDW is observed at low temperature in ${\mathrm{In}}_{x}{\mathrm{TaS}}_{2}$, identified by transport properties and scanning tunneling microscopy measurements. Moreover, superconductivity emerges below 0.69 K, and the anisotropy ratio of the upper critical field $[\mathrm{\ensuremath{\Gamma}}={H}_{c2}^{||ab}(0)/{H}_{c2}^{||c}(0)]$ is significantly enhanced compared to 2H-${\mathrm{TaS}}_{2}$, which shares the same essential layer unit. According to the Lawrence-Doniach model, the enhanced $\mathrm{\ensuremath{\Gamma}}$ may be explained by the reduced effective mass in the ${k}_{x}\text{\ensuremath{-}}{k}_{y}$ plane, where Weyl rings locate. Therefore, this type of layered topological systems may offer a platform to investigate highly anisotropic superconductivity and to understand the extremely large upper critical field in the bulk or in the two-dimensional limit.

Unconventional Hall response in the quantum limit of HfTe5

Interacting electrons confined to their lowest Landau level in a high magnetic field can form a variety of correlated states, some of which manifest themselves in a Hall effect. Although such states have been predicted to occur in three-dimensional semimetals, a corresponding Hall response has not yet been experimentally observed. Here, we report the observation of an unconventional Hall response in the quantum limit of the bulk semimetal HfTe5, adjacent to the three-dimensional quantum Hall effect of a single electron band at low magnetic fields. The additional plateau-like feature in the Hall conductivity of the lowest Landau level is accompanied by a Shubnikov-de Haas minimum in the longitudinal electrical resistivity and its magnitude relates as 3/5 to the height of the last plateau of the three-dimensional quantum Hall effect. Our findings are consistent with strong electron-electron interactions, stabilizing an unconventional variant of the Hall effect in a three-dimensional material in the quantum limit.

Theory of the fractional quantum Hall effect in Weyl semimetals

We develop a hydrodynamic field theory of the three-dimensional fractional quantum Hall effect, which was recently proposed to exist in magnetic Weyl semimetals, when the Weyl nodes are gapped by strong repulsive interactions. This theory takes the form of a BF theory, which contains both one-form and two-form gauge fields, coupling to quasiparticle and loop excitations correspondingly. It may be regarded as a generalization of the Chern-Simons theory of two-dimensional fractional quantum Hall liquids to three dimensions.

Topological Lifshitz transitions and Fermi arc manipulation in Weyl semimetal NbAs

Surface Fermi arcs (SFAs), the unique open Fermi-surfaces (FSs) discovered recently in topological Weyl semimetals (TWSs), are unlike closed FSs in conventional materials and can give rise to many exotic phenomena, such as anomalous SFA-mediated quantum oscillations, chiral magnetic effects, three-dimensional quantum Hall effect, non-local voltage generation and anomalous electromagnetic wave transmission. Here, by using in-situ surface decoration, we demonstrate successful manipulation of the shape, size and even the connections of SFAs in a model TWS, NbAs, and observe their evolution that leads to an unusual topological Lifshitz transition not caused by the change of the carrier concentration. The phase transition teleports the SFAs between different parts of the surface Brillouin zone. Despite the dramatic surface evolution, the existence of SFAs is robust and each SFA remains tied to a pair of Weyl points of opposite chirality, as dictated by the bulk topology.

Elastic gauge fields and zero-field three-dimensional quantum Hall effect in hyperhoneycomb lattices

Dirac materials respond to lattice deformations as if the electrons were coupled to gauge fields. We derive the elastic gauge fields in the hyperhoneycomb lattice, a three dimensional (3D) structure with trigonally connected sites. In its semimetallic form, this lattice is a nodal-line semimetal with a closed loop of Dirac nodes. Using strain engineering, we find a whole family of strain deformations that create uniform nearly flat Landau levels in 3D. We propose that those Landau levels can be created and tuned in metamaterials with the application of a simple uniaxial temperature gradient. In the 3D quantum anomalous Hall phase, which is topological, we show that the components of the elastic Hall viscosity tensor are multiples of $\eta_{H}=\beta^{2}\sqrt{3}/\left(8\pi a^{3}\right)$, where $\beta$ is an elastic parameter and $a$ is the lattice constant.

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

The discovery of the quantum Hall effect (QHE)1,2 in two-dimensional electronic systems has given topology a central role in condensed matter physics. Although the possibility of generalizing the QHE to three-dimensional (3D) electronic systems3,4 was proposed decades ago, it has not been demonstrated experimentally. Here we report the experimental realization of the 3D QHE in bulk zirconium pentatelluride (ZrTe5) crystals. We perform low-temperature electric-transport measurements on bulk ZrTe5 crystals under a magnetic field and achieve the extreme quantum limit, where only the lowest Landau level is occupied, at relatively low magnetic fields. In this regime, we observe a dissipationless longitudinal resistivity close to zero, accompanied by a well-developed Hall resistivity plateau proportional to half of the Fermi wavelength along the field direction. This response is the signature of the 3D QHE and strongly suggests a Fermi surface instability driven by enhanced interaction effects in the extreme quantum limit. By further increasing the magnetic field, both the longitudinal and Hall resistivity increase considerably and display a metal-insulator transition, which represents another magnetic-field-driven quantum phase transition. Our findings provide experimental evidence of the 3D QHE and a promising platform for further exploration of exotic quantum phases and transitions in 3D systems.