Quantum Hall Research Articles

Selective and quasi-continuous switching of ferroelectric Chern insulator devices for neuromorphic computing.

Quantum materials exhibit dissipationless topological edge state transport with quantized Hall conductance, offering notable potential for fault-tolerant computing technologies. However, the development of topological edge state-based computing devices remains a challenge. Here we report the selective and quasi-continuous ferroelectric switching of topological Chern insulator devices, showcasing a proof-of-concept demonstration in noise-immune neuromorphic computing. We fabricate this ferroelectric Chern insulator device by encapsulating magic-angle twisted bilayer graphene with doubly aligned h-BN layers and observe the coexistence of the interfacial ferroelectricity and the topological Chern insulating states. The observed ferroelectricity exhibits an anisotropic dependence on the in-plane magnetic field. By tuning the amplitude of the gate voltage pulses, we achieve ferroelectric switching between any pair of Chern insulating states in the presence of a finite magnetic field, resulting in 1,280 ferroelectric states with distinguishable Hall resistance levels on a single device. Furthermore, we demonstrate deterministic switching between two arbitrary levels among the record-high number of ferroelectric states. This unique switching capability enables the implementation of a convolutional neural network resistant to external noise, utilizing the quantized Hall conductance levels of the Chern insulator device as weights. Our study provides a promising avenue towards the development of topological quantum neuromorphic computing, where functionality and performance can be drastically enhanced by topological quantum materials.

Semiclassical perspective on Landau levels and Hall conductivity in an anisotropic cubic Dirac semimetal and the peculiar case of star-shaped classical orbits

We study an anisotropic cubic Dirac semimetal subjected to a constant magnetic field. In the case of an isotropic dispersion in the x−y plane, with parameters vx=vy, it is possible to find exact Landau levels, indexed by the quantum number n, using the typical ladder operator approach. Interestingly, we find that the lowest energy level (the zero-energy state in the case of kz=0) has a degeneracy that is 3 times that of other states. This degeneracy manifests in the Hall conductivity as a step at a zero chemical potential 3/2 the size of other steps. Moreover, as n→∞, we find energies En∝n3/2, which means the nth step as a function of the chemical potential roughly occurs at a value μ∝n3/2. We propose that these exciting features could be used to experimentally identify cubic Dirac semimetals. Subsequently, we analyze the anisotropic case vy=λvx, with λ≠1. First, we consider a perturbative treatment around λ≈1 and find that energies En∝n3/2 still hold as n→∞. To gain further insight into the Landau level structure for a maximum anisotropy, we turn to a semiclassical treatment that reveals interesting star-shaped orbits in phase space that close at infinity. This property is a manifestation of weakly localized states. Despite being infinite in length, these orbits enclose a finite phase space volume and permit finding a simple semiclassical formula for the energy, which has the same form as above. Our findings suggest that both isotropic and anisotropic cubic Dirac semimetals should leave similar experimental imprints. Published by the American Physical Society 2024

Highly Efficient Spin Current Transport Properties in Spintronic Devices Based on Topological Insulator

AbstractRecently, topological insulators (TIs) have regained extensive attention in spintronics due to their potential applications in new‐generation spintronic devices, following the discovery of the quantum Hall effect and quantum anomalous Hall effect, which introduce the topological concept. In this review, the exotic spin transport phenomena are explored in TIs. The review offers a concise overview of the fundamental principles of TIs, followed by an exploration of diverse fabrication methods for TI materials. Characterization techniques of the topological surface states are also presented. The review delves into the intriguing spin current transport phenomena, focusing on spin‐to‐charge and charge‐to‐spin conversions in TI/ferromagnet bilayers, respectively. The review culminates summarizing key insights and project future directions for research on spin transport phenomena in TIs, emphasizing practical implications.

Experimental investigation of intrinsic mechanism dominated anomalous Hall effect in hexagonal alloys Fe3-xMnxGe (x = 0.05, 0.1, 0.5)

Iron alloys are among the most fundamental and extensively studied alloys, particularly in recent years with the advancements in spintronics. The anomalous Hall effect based on intrinsic Berry curvature has sparked a significant research interest in magnetic materials. In this experimental study, we quantitatively elucidated the AHE mechanism in Fe3-xMnxGe (x = 0.05, 0.1, 0.5) alloy using the Tian-Ye-Jin model. It is found that the intrinsic mechanism associated with the band structure dominates the anomalous Hall effect of alloys, akin to the parent compound Fe3Ge. In addition, the total and separated intrinsic anomalous Hall conductivity decrease with the increase of doping level. The percentage of anomalous Hall conductivity in total anomalous Hall conductivity increases with increasing temperature and decreasing doping level. The percentage of intrinsic contribution was significantly higher than extrinsic contribution, confirming the intrinsic mechanism dominated anomalous Hall effect. This study provides a reference for tailoring transverse transport properties through doping.

Interactions Enable Thouless Pumping in a Nonsliding Lattice

A topological “Thouless” pump represents the quantized motion of particles in response to a slow, cyclic modulation of external control parameters. The Thouless pump, like the quantum Hall effect, is of fundamental interest in physics, because it links physically measurable quantities, such as particle currents, to geometric properties of the experimental system, which can be robust against perturbations and, thus, technologically useful. So far, experiments probing the interplay between topology and interparticle interactions have remained relatively scarce. Here, we observe a Thouless-type charge pump in which the particle current and its directionality inherently rely on the presence of strong interactions. Experimentally, we utilize a two-component Fermi gas in a dynamical superlattice which does not exhibit a sliding motion and remains trivial in the single-particle regime. However, when tuning interparticle interactions from zero to positive values, the system undergoes a transition from being stationary to drifting in one direction, consistent with quantized pumping in the first cycle. Remarkably, the topology of the interacting pump trajectory cannot be adiabatically connected to a noninteracting limit, highlighted by the fact that only one atom is transferred per cycle. Our experiments suggest that Thouless charge pumps are promising platforms to gain insights into interaction-driven topological transitions and topological quantum matter. Published by the American Physical Society 2024

Extended Berry Curvature Tail in Ferromagnetic Weyl Semimetals NiMnSb and PtMnSb.

Heusler compounds belong to a large family of materials and exhibit numerous physical phenomena with promising applications, particularly ferromagnetic Weyl semimetals for their use in spintronics and memory devices. Here, anomalous Hall transport is reported in the room-temperature ferromagnets NiMnSb (half-metal with a Curie temperature (TC) of 660 K) and PtMnSb (pseudo half-metal with a TC of 560 K). They exhibit 4 µB/f.u. magnetic moments and non-trivial topological states. Moreover, NiMnSb and PtMnSb are the first half-Heusler ferromagnets to be reported as Weyl semimetals, and they exhibit anomalous Hall conductivity (AHC) due to the extended tail of the Berry curvature in these systems. The experimentally measured AHC values at 2 K are 1.8×102Ω-1cm-1 for NiMnSb and 2.2×103Ω-1 cm-1 for PtMnSb. The comparatively large value between them can be explained in terms of the spin-orbit coupling strength. The combined approach of using ab initio calculations and a simple model shows that the Weyl nodes located far from the Fermi energy act as the driving mechanism for the intrinsic AHC. This contribution of topological features at higher energies can be generalized.

First principles prediction of novel quantum topological insulator state in two-dimensional XMg2Bi2 (X=Eu/Yb)

Topological insulator (TIs), a novel quantum state of materials, has a lot of significance in the development of low-power electronic equipments as the conducting edge states display exceptional endurance against back-scattering. The absence of suitable materials with high fabrication feasibility and significant nontrivial bandgap, is now the biggest hurdle in their potential applications in devices. Here, we illustrate using first principles density functional calculations that the quintuplet layers of EuMg2Bi2 and YbMg2Bi2 crystals are potential two-dimensional TIs with a sizeable nontrivial gaps of 72 meV and 147 meV respectively. Dynamical stability of these quintuplet layers of EuMg2Bi2 and YbMg2Bi2 is confirmed by our phonon calculations. The weakly coupled layered structure of parent compounds makes it possible for simple exfoliation from a three-dimensional structure. We observed gapless edge states inside the bulk band gap in both the systems which indicate their TI nature. Further, we observed the anomalous and spin Hall conductivities to be quantized in two dimensional EuMg2Bi2 and YbMg2Bi2 respectively. Our findings predict two viable candidate materials as two dimensional quantum TIs which can be explored by future experimental investigations and possible applications of quantized spin and anomalous Hall conductance in spintronics.

Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect

A delicate tension complicates the relationship between the topological magnetoelectric effect (TME) in three-dimensional (3D) Z2 topological insulators (TIs) and time-reversal symmetry (TRS). TRS underlies a particular Z2 topological classification of the electronic ground state of crystalline band insulators and the associated quantization of the magnetoelectric response coefficient calculated using bulk linear-response theory but, according to standard symmetry arguments, simultaneously forbids a nonzero magnetoelectric coefficient in any physical finite-size system. This contrast between theories of magnetoelectric response in formal bulk models and in real finite-sized materials originates from the distinct approaches required to introduce notions of (electronic) polarization and orbital magnetization in these fundamentally different environments. In this work we argue for a modified interpretation of the bulk linear-response calculations in nonmagnetic Z2 TIs that is more plainly consistent with TRS and use this interpretation to discuss the effect's observation—still absent over a decade after its prediction. Our analysis is reinforced by microscopic bulk and thin-film calculations carried out using a simplified but still realistic effective model for the well established V2VI3 [V=(Sb,Bi) and VI=(Se,Te)] family of nonmagnetic Z2 TIs. When a uniform dc magnetic field is included in this model, the anomalous n=0 Landau levels (LLs) play the central role, both in thin films and in bulk. In the former case, only the n=0 LL eigenfunctions can support a dipole moment, which vanishes if there are no magnetic surface dopants and is quantized in the thick-film limit if magnetic dopants at the top and bottom surfaces have opposite orientation. In the latter case, the Hamiltonian projected into the n=0 LL subspace is a one-dimensional Su-Schrieffer-Heeger model with ground-state polarization that is quantized in accordance with the bulk linear-response coefficient calculated for (a lattice regularization of) the starting 3D model. Motivated by analytical results, we conjecture a type of microscopic bulk-boundary correspondence: a bulk insulator with (generalized) TRS supports a magnetoelectric coefficient that is purely itinerant (which is generically related to the geometry of the ground state) if and only if magnetic surface dopants are required for the TME to manifest in finite samples thereof. We conclude that in nonmagnetic Z2 TIs the TME is activated by magnetic surface dopants, that the charge-density response to a uniform dc magnetic field is localized at the surface and specified by the configuration of those dopants, and that the TME is qualitatively less robust against disorder than the integer quantum Hall effect. Published by the American Physical Society 2024

Singular Hall Response from a Correlated Ferromagnetic Flat Nodal-Line Semimetal.

Topological quantum phases are largely understood in weakly correlated systems, which have identified various quantum phenomena, such as the spin Hall effect, protected transport of helical fermions, and topological superconductivity. Robust ferromagnetic order in correlated topological materials particularly attracts attention, as it can provide a versatile platform for novel quantum devices. Here, a singular Hall response arising from a unique band structure of flat topological nodal lines in combination with electron correlation in a van der Waals ferromagnetic semimetal, Fe3GaTe2, with a high Curie temperature of Tc = 347 K is reported. High anomalous Hall conductivity violating the conventional scaling, resistivity upturn at low temperature, and a large Sommerfeld coefficient are observed in Fe3GaTe2, which implies heavy fermion features in this ferromagnetic topological material. The scanning tunneling microscopy, circular dichroism in angle-resolved photoemission spectroscopy, and theoretical calculations support the original electronic features of the material. Thus, low-dimensional Fe3GaTe2 with electronic correlation, topology, and room-temperature ferromagnetic order appears to be a promising candidate for robust quantum devices.

The Impact of a Strong Electromagnetic Wave on the Quantum Hall Effect in Cylindrical Quantum Wires

The impact of strong electromagnetic waves Hall effect is studied theoretically in a Cylindrical Quantum Wire (CQW) with infinitely high potential inside the wire and elsewhere subjected to a dc electric field , a magnetic field and a laser radiation . By using the quantum kinetic equation method for electrons interacting with Acoustic Phonon (AP) at low temperatures, we obtain analytical expressions for the conductivity tensor and the Hall Coefficient (HC), which are different from in comparison to those obtained for a rectangular quantum wire (RQW) or two-dimensional (2D) electron systems. Numerical calculations are also applied for GaAs/GaAsAl CQW to show the nonlinear dependence of the HC on the electromagnetic wave (EMW) frequency, and the radius, the length characteristic parameters of CQW. Wave function and energy spectrum in a CQW are dissiminar to those in Quantum Wires (QWs). Therefore, all numerical results are different from those in the case of QWs. The most important result is that the HC reaches saturation as the radius, the length of CQW or the EMW frequency increases.

Controlling the orbital Hall effect in gapped bilayer graphene in the terahertz regime

We study the orbital Hall effect (OHE) in the AC regime using bilayer graphene (BLG) as a prototypical material platform. While the unbiased BLG has gapless electronic spectra, applying a perpendicular electric field creates an energy band gap that can be continuously tuned from zero to high values. By exploiting this flexibility, we demonstrate the ability to control the behavior of AC orbital Hall conductivity. Particularly, we demonstrate that the orbital Hall conductivity at the neutrality point changes its signal at a critical frequency, the value of which is proportional to the perpendicular electric field. For BLG with narrow band gaps, the active frequency region for the AC OHE may extend to a few terahertz, which is experimentally accessible with current technologies. We also consider the introduction of a perpendicular magnetic field in the weak-coupling regime using first-order perturbation theory to illustrate how the breaking of time-reversal symmetry enables the emergence of the AC charge Hall effect in the charge-doped situation and modifies the AC orbital Hall conductivity. Our calculations suggest that BLG with narrow band gaps is a practical candidate for investigating time-dependent orbital angular momentum transport. Published by the American Physical Society 2024

Observation of a spontaneous anomalous Hall response in the Mn5Si3 d-wave altermagnet candidate

Phases with spontaneous time-reversal (T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{T}}}}}}}}$$\\end{document}) symmetry breaking are sought after for their anomalous physical properties, low-dissipation electronic and spin responses, and information-technology applications. Recently predicted altermagnetic phase features an unconventional and attractive combination of a strong T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{T}}}}}}}}$$\\end{document}-symmetry breaking in the electronic structure and a zero or only weak-relativistic magnetization. In this work, we experimentally observe the anomalous Hall effect, a prominent representative of the T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{T}}}}}}}}$$\\end{document}-symmetry breaking responses, in the absence of an external magnetic field in epitaxial thin-film Mn5Si3 with a vanishingly small net magnetic moment. By symmetry analysis and first-principles calculations we demonstrate that the unconventional d-wave altermagnetic phase is consistent with the experimental structural and magnetic characterization of the Mn5Si3 epilayers, and that the theoretical anomalous Hall conductivity generated by the phase is sizable, in agreement with experiment. An analogy with unconventional d-wave superconductivity suggests that our identification of a candidate of unconventional d-wave altermagnetism points towards a new chapter of research and applications of magnetic phases.

Quantum Hall effect in InAsSb quantum wells at elevated temperatures

We have characterized the electronic properties of a high-mobility two-dimensional electron system in modulation doped InAsSb quantum wells and compare them to InSb quantum wells grown in a similar fashion. Using temperature-dependent Shubnikov-de Haas experiments as well as FIR transmission, we find an effective mass of m*≈0.022me, which is lower than in the investigated InSb quantum well, but due to a rather strong confinement still higher than in the corresponding bulk compound. The effective g-factor was determined to be g*≈24.1. These results are also corroborated by k·p band structure calculations. When spin polarizing the electrons in a tilted magnetic field, the g-factor is significantly enhanced by electron-electron interactions, reaching a value as large as g*=60 at a spin polarization P=0.75. Finally, we show that due to the low effective mass, the quantum Hall effect in our particular sample can be observed up to a temperature of 60 K. Published by the American Physical Society 2024

Height profile variations of ionospheric conductivity: A case study in Addis Ababa, Ethiopia

Ionospheric conductivity is the ability to conduct ionospheric current and is impacted by a variety of current system flows in height profiles, which increase ionosphere conductivity. In this study, we have analyzed the height profiles of the ionospheric conductivity daily and monthly variations in Addis Ababa, Ethiopia, during a very low solar activity phase in the year 2020. The daily height profile variations of ionospheric conductivity in Addis Ababa with geographic latitude 9o N and longitude 39o E are estimated at midnight (00:00 UT), morning (09:00 UT), mid-day (12:00 UT), and early nighttime (18:00 UT). The monthly variations of ionospheric conductivity (parallel, Pedersen, and Hall conductivity) are also presented for all months, with the highest ionospheric variability occurring after noon (14.00 UT). At midnight (00:00 UT) and early nighttime (18:00 UT), the ionospheric conductivity shows more fluctuation than in the morning (09:00 UT) and midday (12:00 UT) in diurnal variation. The monthly variations of ionospheric conductivity (parallel, Pedersen, and Hall conductivity) in the daytime at 14:00 UT increase steeply to reach their peak values and keep the sharpness of their variability.

Simulating 4D quantum Hall effect with two bosons in a 1D quasicrystal

Recent advances promote the study of topological systems with additional synthetic dimensions. In this work, we propose a method to realize the four-dimensional (4D) quantum hall effect by using two strongly interacting bosons. The 1D lattice of the Aubry-André-Harper (AAH) model with two hard-core bosons can be mapped to a synthetic 4D space. The energy spectrum of this system is similar to that of one particle evolving in a 2D AAH model mimicking the 4D quantum hall effect. The energy spectrum contains bulk, edge, and corner states, which can be interpreted as the summation of two independent single-particle spectra in the 1D Aubry-André-Harper (AAH) model. Our results pave the way to realizing higher-dimension physics such as topology and localization by using many particles.

Does high-latitude ionospheric electrodynamics exhibit hemispheric mirror symmetry?

Abstract. Ionospheric electrodynamics is a problem of mechanical stress balance mediated by electromagnetic forces. Joule heating (the total rate of frictional heating of thermospheric gases and ionospheric plasma) and ionospheric Hall and Pedersen conductances comprise three of the most basic descriptors of this problem. More than half a century after identification of their central role in ionospheric electrodynamics, several important questions about these quantities, including the degree to which they exhibit hemispheric symmetry under reversal of the sign of dipole tilt and the sign of the y component of the interplanetary magnetic field (so-called “mirror symmetry”), remain unanswered. While global estimates of these key parameters can be obtained by combining existing empirical models, one often encounters some frustrating sources of uncertainty: the measurements from which such models are derived, usually magnetic field and electric field or ion drift measurements, are typically measured separately and do not necessarily align. The models to be combined moreover often use different input parameters, different assumptions about hemispheric symmetry, and/or different coordinate systems. We eliminate these sources of uncertainty in model predictions of electromagnetic work J⋅E (in general not equal to Joule heating ηJ2) and ionospheric conductances by combining two new empirical models of the high-latitude ionospheric electric potential and ionospheric currents that are derived in a mutually consistent fashion: these models do not assume any form of symmetry between the two hemispheres; are based on Apex magnetic coordinates (denoted Apex), spherical harmonics, and the same model input parameters; and are derived exclusively from convection and magnetic field measurements made by the Swarm and CHAMP satellites. The model source code is open source and publicly available. Comparison of high-latitude distributions of electromagnetic work in each hemisphere as functions of dipole tilt and interplanetary magnetic field clock angle indicates that the typical assumption of mirror symmetry is largely justified. Model predictions of ionospheric Hall and Pedersen conductances exhibit a degree of symmetry, but clearly asymmetric responses to dipole tilt and solar wind driving conditions are also identified. The distinction between electromagnetic work and Joule heating allows us to identify where and under what conditions the assumption that the neutral wind corotates with the Earth is not likely to be physically consistent with predicted Hall and Pedersen conductances.

Topological Quantum Transport Characteristic by Three‐band Correlation Mechanism in 2D SnSe

AbstractUnderstanding electron quantum transport and their coupling interactions in 2D matrix is crucial for manipulating and designing more efficient energy conversion devices, especially in the context of spin transport. Here, we systematically calculate the electronic dispersion properties which the synergistic interaction of the three‐band accounted for the topological transport of edge correlated electrons. The helical state protected by the topology appears at the boundary, accompanied by the upward movement (∼0.2 eV) of the helical point caused by the excitation and the loop channel, which the weak braiding effect reveal local strongly correlated interactions between the boundary electrons. In addition, we also introduce spin Hall conductance and Z2 topological invariants to describe the election dispersion of the topological transport. This provides more possibilities for the realization of topological quantum computing application.

Tailoring the quantum anomalous layer Hall effect in multiferroic bilayers through sliding

Layer Hall effect (LHE), initially discovered in the magnetic topological insulator MnBi2Te4 film, expands the Hall effect family and opens a promising avenue for layertronics applications. In this study, we present an innovative ferroelectric bilayer model to attain a tunable quantum anomalous layer Hall effect (QALHE). This model comprises two ferromagnetic orbital-active Dirac monolayers stacked antiferromagnetically, accompanied by out-of-plane electric polarization. The interplay between the layer-locked Berry curvature monopoles and the intrinsic out-of-plane electric polarization leads to layer-polarized near-quantized anomalous Hall conductance. Using first-principles calculations, we have identified a promising material for this model, namely FeS bilayer. Our calculations demonstrate that the intrinsic out-of-plane electric polarization in the Bernal-stacked FeS bilayer can induce QALHE by regulating the layer-locked Berry curvature of FeS monolayers. Importantly, the intrinsic electric field can be reversed through interlayer sliding. The discovery of ferroelectrically modulated QALHE paves the way for the integrability and non-volatility of layertronics, offering exciting prospects for future applications.

Intrinsic Anomalous Hall Conductivity of Strained Fe: A Combination Approach

In this study, the effect of elastic biaxial strain on electronic structure and the anomalous Hall conductivity (AHC) of α‐Fe has been systematically studied by using the combination of a first principles calculation with the tight binding method through the Wannier function. It is found that applying strain in cubic structure of α‐Fe results in the reduction of crystal symmetry and gives the modification on the bands near Fermi level, which causes a significant change in the AHC of strained systems. The AHC of strained α‐Fe is found to be sensitive with applying strain, which shows the large enhancement of AHC at +2% tensile strain with AHC value is up to 929 Ω−1 cm−1 (increases more than 30%) compared with the unstrained one, while slightly reduces when applying compressive strain. The modification of AHC is found to be related to the change of Berry curvature contributed from the spin orbit coupling (SOC) induced energy gap near Fermi level. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Quantum spin Hall insulating phase in two-dimensional MA2Z4 materials: SrTl2Te4 and BaTl2Te4

With the recent synthesis of two-dimensional (2D) MoSi2N4, the 2D material family with the general formula MA2Z4 has become increasingly popular. However, their topological properties have yet to be explored. Using first-principles calculations, we examine the electronic and topological properties of monolayer MA2Z4 (M = Ca, Sr, or Ba; A = In or Tl; Z = S, Se, or Te) compounds. Our study reveals the quantum spin Hall phase in SrTl2Te4 and BaTl2Te4 with a nontrivial topological bandgap of 97 and 28 meV, respectively, under a hybrid functional approach with the inclusion of spin–orbit coupling. Remarkably, the Z2 topological invariant and the presence of gapless edge states further confirmed their nontrivial topological phase. In addition, we demonstrate the quantized spin Hall conductivity in SrTl2Te4, which stems from the non-zero Berry curvature. The topological phase transition is driven by SOC due to the band inversion between the Te-px+py and Tl-s orbitals around Γ. Interestingly, the nontrivial topological properties are robust against strain and preserved under an applied electric field. Finally, our research identifies that the emergent MA2Z4 monolayers have interesting topological properties and have great potential for experimental realization of future topological applications.