Half-integer Quantum Hall Effect Research Articles

Research progress of quantum Hall effect in topological insulator

Three-dimensional topological insulators (TIs) with gapless topological surface states (TSSs) have attracted considerable attention because of their unique properties. The transport of TSS is an essential means to explore the novel properties. The quantum Hall effect (QHE) of TSS is an important content in the study of topological insulator, for it is an important characteristic of the pure TSS transport. This paper briefly reviews the recent research progress of QHE in TIs. Firstly, we introduce the fundamental concepts of the QHE in TIs. In a three-dimensional TI, each TSS contributes to a half-integer QHE. An integer QHE should be observed due to the existence of top and bottom surface in TI. Then, we review the realization and development of QHE. With the optimization of TI materials, the QHE of TSS is observed in bulk-insulating TIs. Next, the phase transition and scaling law behavior of QHE in TIs are discussed. The dominance of electron-electron interaction of the TSS is revealed by the anomalous critical exponent. Also, the experimental studies of the magnetic proximity and gate voltage modulation of the QHE are reviewed in detail. Finally, the perspectives of QHE in TIs are discussed.

High-Temperature Quantum Hall Effect in Graphite-Gated Graphene Heterostructure Devices with High Carrier Mobility.

Since the discovery of the quantum Hall effect in 1980, it has attracted intense interest in condensed matter physics and has led to a new type of metrological standard by utilizing the resistance quantum. Graphene, a true two-dimensional electron gas material, has demonstrated the half-integer quantum Hall effect and composite-fermion fractional quantum Hall effect due to its unique massless Dirac fermions and ultra-high carrier mobility. Here, we use a monolayer graphene encapsulated with hexagonal boron nitride and few-layer graphite to fabricate micrometer-scale graphene Hall devices. The application of a graphite gate electrode significantly screens the phonon scattering from a conventional SiO2/Si substrate, and thus enhances the carrier mobility of graphene. At a low temperature, the carrier mobility of graphene devices can reach 3 × 105 cm2/V·s, and at room temperature, the carrier mobility can still exceed 1 × 105 cm2/V·s, which is very helpful for the development of high-temperature quantum Hall effects under moderate magnetic fields. At a low temperature of 1.6 K, a series of half-integer quantum Hall plateaus are well-observed in graphene with a magnetic field of 1 T. More importantly, the ν = ±2 quantum Hall plateau clearly persists up to 150 K with only a few-tesla magnetic field. These findings show that graphite-gated high-mobility graphene devices hold great potential for high-sensitivity Hall sensors and resistance metrology standards for the new Système International d'unités.

Graphene: A Path-Breaking Discovery for Energy Storage and Sustainability.

The global energy situation requires the efficient use of resources and the development of new materials and processes for meeting current energy demand. Traditional materials have been explored to large extent for use in energy saving and storage devices. Graphene, being a path-breaking discovery of the present era, has become one of the most-researched materials due to its fascinating properties, such as high tensile strength, half-integer quantum Hall effect and excellent electrical/thermal conductivity. This paper presents an in-depth review on the exploration of deploying diverse derivatives and morphologies of graphene in various energy-saving and environmentally friendly applications. Use of graphene in lubricants has resulted in improvements to anti-wear characteristics and reduced frictional losses. This comprehensive survey facilitates the researchers in selecting the appropriate graphene derivative(s) and their compatibility with various materials to fabricate high-performance composites for usage in solar cells, fuel cells, supercapacitor applications, rechargeable batteries and automotive sectors.

Half-integer anomalous currents in 2D materials from a QFT viewpoint

Charge carriers in Dirac/Weyl semi-metals exhibit a relativistic-like behavior. In this work we propose a novel type of intrinsic half-integer Quantum Hall effect in 2D materials, thereby also offering a topological protection mechanism for the current. Its existence is rooted in the 2D parity anomaly, without any need for a perpendicular magnetic field. We conjecture that it may occur in disturbed honeycomb lattices where both spin degeneracy and time reversal symmetry are broken. These configurations harbor two distinct gap-opening mechanisms that, when occurring simultaneously, drive slightly different gaps in each valley, causing a net anomalous conductivity when the chemical potential is tuned to be between the distinct gaps. Some examples of promising material setups that fulfill the prerequisites of our proposal are also listed to motivate looking for the effect at the numerical and experimental level.

Role of the third dimension in searching for Majorana fermions in α−RuCl3 via phonons

Understanding phonons in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ is critical to analyze the controversy around the observation of the half-integer thermal quantum Hall effect. While many studies have focused on the magnetic excitations in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, its vibrational excitation spectrum has remained relatively unexplored. We investigate the phonon structure of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ via inelastic neutron-scattering experiments and density-functional-theory calculations. Our results show excellent agreement between experiment and first-principles calculations. After validating our theoretical model, we extrapolate the low-energy phonon properties. We find that the phonons in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ that either propagate or vibrate in the out-of-plane direction have significantly reduced velocities and therefore have the potential to dominate the observability of the elusive half-integer plateaus in the thermal Hall conductance. In addition, we use low-energy interlayer phonons to resolve the low-temperature stacking structure of our large crystal of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, which we find to be consistent with that of the $R\overline{3}$ space group, in agreement with neutron diffraction.

Enhancing spin–orbit coupling in high-mobility graphene by introducing chiral space curvature

Graphene is an excellent two-dimensional materials with high-mobility and relativistic electronic linear dispersion. Its rich physical properties such as half-integer quantum Hall effect and device application potential have been continuously attracting great attention. However, light carbon atoms also imply negligible intrinsic spin–orbit coupling (SOC) strength which hinders its spintronic application. To enhance the SOC effect, we introduce a special deformation vector with chiral curvature, borrowed from the Einstein theory of general relativity, to mimic space warping and twisting. The derived Rashba type pseudospin–spin coupling locks the spin orientation of an electron with respect to its pseudospin. Combined with the original Dirac type Hamiltonian specifying the pseudospin orientation of an electron with respect to its wavevector, it lifts the spin degeneracy and paves the way for graphene-based spintronic devices. An estimate suggests that a Rashba type pseudospin–spin coupling of the order of 5 meV can be achieved in tens nanometer samples.

Observing movement of Dirac cones from single-photon dynamics

Graphene with honeycomb structure, being critically important in understanding physics of matter, exhibits exceptionally unusual half-integer quantum Hall effect and unconventional electronic spectrum with quantum relativistic phenomena. Particularly, graphene-like structure can be used for realizing topological insulator which inspires an intrinsic topological protection mechanism with strong immunity for maintaining coherence of quantum information. These various peculiar physics arise from the unique properties of Dirac cones which show high hole degeneracy, massless charge carriers and linear intersection of bands. Experimental observation of Dirac cones conventionally focuses on the energy-momentum space with bulk measurement. Recently, the wave function and band structure have been mapped into the real-space in photonic system, and made flexible control possible. Here, we demonstrate a direct observation of the movement of Dirac cones from single-photon dynamics in photonic graphene under different biaxial strains. Sharing the same spirit of wave-particle nature in quantum mechanics, we identify the movement of Dirac cones by dynamically detecting the edge modes and extracting the diffusing distance of the packets with accumulation and statistics on individual single-particle registrations. Our results of observing movement of Dirac cones from single-photon dynamics, together with the method of direct observation in real space by mapping the band structure defined in momentum space, pave the way to understand a variety of artificial structures in quantum regime.

Magnetoconductivity in quasiperiodic graphene superlattices

The magnetoconductivity in Fibonacci graphene superlattices is investigated in a perpendicular magnetic field B. It was shown that the B-dependence of the diffusive conductivity exhibits a complicated oscillatory behavior whose characteristics cannot be associated with Weiss oscillations, but rather with Shubnikov-de Haas ones. The absense of Weiss oscillations is attributed to the existence of two incommensurate periods in Fibonacci superlattices. It was also found that the quasiperiodicity of the structure leads to a renormalization of the Fermi velocity v_{F} of graphene. Our calculations revealed that, for weak B, the dc Hall conductivity sigma _{yx} exhibits well defined and robust plateaux, where it takes the unexpected values pm 4e^{2}/hslash left( 2N+1right) , indicating that the half-integer quantum Hall effect does not occur in the considered structure. It was finally shown that sigma _{yx} displays self-similarity for magnetic fields related by tau ^{2} and tau ^{4}, where tau is the golden mean.

Graphene: an exotic condensed matter and its impact on technology

Graphene is a (2 + 1)-dimensional quantum electrodynamic system. The carriers have a vanishing mass and a relativistic velocity of 106 m/s, obeying charge-conjugate parity time symmetry. Graphene exhibits the Klein paradox, due to which, through spatial confinement, a bandgap can be opened in zigzag graphene nanoribbons for logic applications. The high Debye temperature of 2800 K ensures that phonons are frozen out and lattice scattering is suppressed at 300 K. The perfect crystallinity ensures that defect/impurity scattering is suppressed. The two together give very high electrical conductivity and electric mobility. This permits a current density of 108 A/cm2, about 100 times greater than that in copper. Single-layer graphene has a thermal conductivity of 3000–5000 (W/m)/K at 300 K, but graphite has K = 2000 (W/m)/K. This may open up few-layer graphene applications in thermal management of nanoelectronics. The half-integer quantum Hall effect and non-zero Berry phase have been verified in the laboratory. These magneto-transport properties are a result of the exceptional topology of the graphene band structure. Ballistic transport observable up to 300 K makes graphene an ideal replacement for silicon (Si) electronics. The optical response of graphene is determined by the fine-structure constant over a wide band of the visible spectrum, and hence, it is ideal for high-speed optical modulators. This paper describes a commercially significant process for synthesizing large-area fold-free and defect-free graphene.

Intrinsic axion insulating behavior in antiferromagnetic MnBi6Te10

A striking feature of time reversal symmetry (TRS) protected topological insulators (TIs) is that they are characterized by a half integer quantum Hall effect on the boundary when the surface states are gapped by time reversal breaking perturbations. While time reversal symmetry (TRS) protected TIs have become increasingly under control, magnetic analogs are still largely unexplored territories with novel rich structures. In particular, topological magnetic insulators can also host a quantized axion term in the presence of lattice symmetries. Since these symmetries are naturally broken on the boundary, the surface states can develop a gap without external manipulation. In this work, we combine theoretical analysis, density functional calculations and experimental evidence to reveal intrinsic axion insulating behavior in MnBi6Te10. The quantized axion term arises from the simplest possible mechanism in the antiferromagnetic regime where it is protected by inversion symmetry and a fractional translation symmetry. The anticipated gapping of the Dirac surface state at the edge is subsequently experimentally established using Angle Resolved Spectroscopy. As a result, this system provides the magnetic analogue of the simplest TRS protected TI with a single, gapped Dirac cone at the surface.

Distinct Topological Surface States on the Two Terminations of MnBi4Te7

The recent discovered intrinsic magnetic topological insulator MnBi2Te4 have been met with unusual success in hosting emergent phenomena such as the quantum anomalous Hall effect and the axion insulator states. However, the surface-bulk correspondence of the Mn-Bi-Te family, composed by the superlattice-like MnBi2Te4/(Bi2Te3)n (n = 0, 1, 2, 3 ...) layered structure, remains intriguing but elusive. Here, by using scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES) techniques, we unambiguously assign the two distinct surface states of MnBi4Te7 (n = 1) to the quintuple-layer (QL) Bi2Te3 termination and the septuple-layer (SL) MnBi2Te4 termination, respectively. A comparison of the experimental observations with theoretical calculations reveals the diverging topological behaviors, especially the hybridization effect between magnetic and nonmagnetic layers, on the two terminations: a gap on the QL termination originating from the topological surface states of the QL hybridizing with the bands of the beneath SL, and a gapless Dirac-cone band structure on the SL termination with time-reversal symmetry. The quasi-particle interference patterns further confirm the topological nature of the surface states for both terminations, continuing far above the Fermi energy. The QL termination carries a spin-helical Dirac state with hexagonal warping, while at the SL termination, a strongly canted helical state from the surface lies between a pair of Rashba-split states from its neighboring layer. Our work elucidates an unprecedented hybridization effect between the building blocks of the topological surface states, and also reveals the termination-dependent time-reversal symmetry breaking in a magnetic topological insulator, rendering an ideal platform to realize the half-integer quantum Hall effect and relevant quantum phenomena.

Pfaffian paired states for half-integer fractional quantum Hall effect

In this review, the physics of Pfaffian paired states, in the context of fractional quantum Hall effect, is discussed using field-theoretical approaches. The Pfaffian states are prime examples of topological ([Formula: see text]-wave) Cooper pairing and are characterized by non-Abelian statistics of their quasiparticles. Here we focus on conditions for their realization and competition among them at half-integer filling factors. Using the Dirac composite fermion description, in the presence of a mass term, we study the influence of Landau level mixing in selecting a particular Pfaffian state. While Pfaffian and anti-Pfaffian are selected when Landau level mixing is not strong, and can be taken into account perturbatively, the particle–hole (PH) Pfaffian state requires non-perturbative inclusion of at least two Landau levels. Our findings, for small Landau level mixing, are in accordance with numerical investigations in the literature, and call for a non-perturbative approach in the search for PH Pfaffian correlations. We demonstrated that a method based on the Chern–Simons field-theoretical approach can be used to generate characteristic interaction pseudo-potentials for Pfaffian paired states.

Anomalous magneto-transport properties of bilayer phosphorene

The magneto-transport properties of phosphorene are investigated by employing the generalized tight-binding model to calculate the energy bands. For bilayer phosphorene, a composite magnetic and electric field is shown to induce a feature-rich Landau level (LL) spectrum which includes two subgroups of low-lying LLs. The two subgroups possess distinct features in level spacings, quantum numbers, as well as field dependencies. These together lead to anomalous quantum Hall (QH) conductivities which include a well-shape, staircase and composite quantum structures with steps having varying heights and widths. The Fermi energy-magnetic field-Hall conductivity (EF−Bz−σxy) and Fermi energy-electric field-Hall conductivity (EF−Ez−σxy) phase diagrams clearly exhibit oscillatory behaviors and cross-over from integer to half-integer QH effect. The predicted results should be verifiable by magneto-transport measurements in a dual-gated system.

Quantum Hall Effect in Trilayer Graphene

Graphene is a two-dimensional sheet of carbon atoms with properties that are superior to other materials. Due to these superior properties, a lot of research is being done with this material. One of those properties is the Quantum Hall Effect (QHE). Monolayer graphene shows very interesting behaviour in the presence of a high magneticfield (up to 30T) and at very low temperature (~0.2K). Its unconventional Landau Level (LL) spectrum of massless Diracfermions leads to a new type of quantum Hall effect, known as half-integer quantum Hall effect or anomalous QHE. We expect uniqueresults can also be seen in trilayer graphene (TLG).In this work, we study the integer quantum Hall effect in trilayer graphene theoretically.

Bulk quantum Hall effect of spin-valley coupled Dirac fermions in the polar antiferromagnet BaMnSb2

Unconventional features of relativistic Dirac/Weyl quasiparticles in topological materials are most evidently manifested in the two-dimensional quantum Hall effect (QHE), whose variety is further enriched by their spin and/or valley polarization. Although its extension to three dimensions has been long sought and inspired theoretical proposals, material candidates have been lacking. Here, we have discovered valley-contrasting spin-polarized Dirac fermions in a multilayer form in the bulk antiferromagnet ${\mathrm{BaMnSb}}_{2}$, where out-of-plane Zeeman-type spin splitting is induced by in-plane inversion symmetry breaking and spin-orbit coupling in the distorted Sb square net. Furthermore, we have observed well-defined quantized Hall plateaus together with vanishing interlayer conductivity at low temperatures as a hallmark of the half-integer QHE in a bulk form. The Hall conductance of each layer is found to be nearly quantized to $2(N+1/2){e}^{2}/h$, with $N$ being the Landau index, which is consistent with two spin-polarized Dirac valleys protected by the strong spin-valley coupling.

Gapless Surface Dirac Cone in Antiferromagnetic Topological Insulator MnBi2Te4

The recent discovered antiferromagnetic topological insulators in Mn-Bi-Te family with intrinsic magnetic ordering have rapidly drawn broad interest since its cleaved surface state is believed to be gapped, hosting the unprecedented axion states with half-integer quantum Hall effect. Here, however, we show unambiguously by using high-resolution angle-resolved photoemission spectroscopy that a gapless Dirac cone at the (0001) surface of MnBi$_2$Te$_4$ exists between the bulk band gap. Such unexpected surface state remains unchanged across the bulk N\'eel temperature, and is even robust against severe surface degradation, indicating additional topological protection. Through symmetry analysis and $\textit{ab}$-$\textit{initio}$ calculations we consider different types of surface reconstruction of the magnetic moments as possible origins giving rise to such linear dispersion. Our results reveal that the intrinsic magnetic topological insulator hosts a rich platform to realize various topological phases such as topological crystalline insulator and time-reversal-preserved topological insulator, by tuning the magnetic configurations.

Tunable Coupling between Surface States of a Three-Dimensional Topological Insulator in the Quantum Hall Regime

The paired top and bottom Dirac surface states, each associated with a half-integer quantum Hall (QH) effect, and a resultant integer QH conductance (νe^{2}/h), are hallmarks of a three-dimensional topological insulator (TI). In a dual-gated system, chemical potentials of the paired surface states are controlled through separate gates. In this work, we establish tunable capacitive coupling between the surface states of a bulk-insulating TI BiSbTeSe_{2} and study the effect of this coupling on QH plateaus and Landau level (LL) fan diagram via dual-gate control. We observe nonlinear QH transitions at low charge density in strongly coupled surface states, which are related to the charge-density-dependent coupling strength. A splitting of the N=0 LL at the charge neutrality point for thin devices (but thicker than the 2D limit) indicates intersurface hybridization possibly beyond single-particle effects. By applying capacitor charging models to the surface states, we explore their chemical potential as a function of charge density and extract the fundamental electronic quantity of LL energy gaps from dual-gated transport measurements. These studies are essential for the realization of exotic quantum effects such as topological exciton condensation.

Topological Semimetals in Square-Net Materials

Many materials crystallize in structure types that feature a square net of atoms. While these compounds can exhibit many different properties, some members of this family are topological materials. Within the square-net-based topological materials, the observed properties are rich, ranging, for example, from nodal-line semimetals to a bulk half-integer quantum Hall effect. Hence, the potential for guided design of topological properties is enormous. Here we provide an overview of the crystallographic and electronic properties of these phases and show how they are linked, with the goal of understanding which square-net materials can be topological, and predict additional examples. We close the review by discussing the experimentally observed electronic properties in this family.

Giant Valley-Isospin Conductance Oscillations in Ballistic Graphene.

At high magnetic fields the conductance of graphene is governed by the half-integer quantum Hall effect. By local electrostatic gating a p-n junction perpendicular to the graphene edges can be formed, along which quantum Hall channels copropagate. It has been predicted by Tworzidło and co-workers that if only the lowest Landau level is filled on both sides of the junction, the conductance is determined by the valley (isospin) polarization at the edges and by the width of the flake. This effect remained hidden so far due to scattering between the channels copropagating along the p-n interface (equilibration). Here we investigate p-n junctions in encapsulated graphene with a movable p-n interface with which we are able to probe the edge-configuration of graphene flakes. We observe large quantum conductance oscillations on the order of e2/h which solely depend on the p-n junction position providing the first signature of isospin-defined conductance. Our experiments are underlined by quantum transport calculations.

Theory of the Half-integer Quantum Hall Effect in Graphene

The unusual quantum Hall effect (QHE) in graphene is described in terms of the composite (c-) bosons, which move with a linear dispersion relation. The “electron” (wave packet) moves easier in the direction [1 1 0 c-axis] ≡ [1 1 0] of the honeycomb lattice than perpendicular to it, while the “hole” moves easier in [0 0 1]. Since “electrons” and “holes” move in different channels, the particle densities can be high especially when the Fermi surface has “necks”. The strong QHE arises from the phonon exchange attraction in the neighborhood of the “neck” surfaces. The plateau observed for the Hall conductivity and the accompanied resistivity drop is due to the superconducting energy gap caused by the Bose-Einstein condensation of the c-bosons, each forming from a pair of one-electron–two-fluxons c-fermions by phonon-exchange attraction. The half-integer quantization rule for the Hall conductivity: (1/2)(2P−1)(4e 2/h), P=1,2,..., is derived.