Axion Insulator Research Articles

Incommensurate magnetic order in an axion insulator candidate EuIn2As2 investigated by NMR measurement

Magnetic topological insulators exhibit unique electronic states due to the interplay between the electronic topology and the spin structure. The antiferromagnetic metal EuIn2As2 is a prominent candidate material in which exotic topological phases, including an axion insulating state, are theoretically predicted depending on the magnetic structure of the Eu2+ moments. Here, we report experimental results of the nuclear magnetic resonance (NMR) measurements of all the nuclei in EuIn2As2 to investigate the coupling between the magnetic moments in the Eu ions and the conduction electrons in In2As2 layers and the magnetic structure. The 75As and 115In NMR spectra observed at zero external magnetic fields reveal the appearance of internal fields of 4.9 and 3.6 T, respectively, at the lowest temperature, suggesting a strong coupling between the conduction electrons in the In2As2 layer and the ordered magnetic moments in the Eu ions. The 75As NMR spectra under in-plane external magnetic fields show broad distributions of the internal fields produced by an incommensurate fan-like spin structure which turns into a forced ferromagnetic state above 0.7 T. We propose a spin reorientation process that an incommensurate helical state at zero external magnetic field quickly changes into a fan state by applying a slight magnetic field.

Topotaxial mutual-exchange growth of magnetic Zintl Eu3In2As4 nanowires with axion insulator classification.

Due to quasi-one-dimensional confinement, nanowires possess unique electronic properties, which can promote specific device architectures. However, nanowire growth presents paramount challenges, limiting the accessible crystal structures and elemental compositions. Here we demonstrate solid-state topotactic exchange that converts wurtzite InAs nanowires into Zintl Eu3In2As4. Molecular-beam-epitaxy-based in situ evaporation of Eu and As onto InAs nanowires results in the mutual exchange of Eu from the shell and In from the core. Therefore, a single-phase Eu3In2As4 shell grows, which gradually consumes the InAs core. The mutual exchange is supported by the substructure of the As matrix, which is similar across the wurtzite InAs and Zintl Eu3In2As4 and therefore is topotactic. The Eu3In2As4 nanowires undergo an antiferromagnetic transition at a Néel temperature of ~6.5 K. Ab initio calculations confirm the antiferromagnetic ground state and classify Eu3In2As4 as a C2T axion insulator, hosting both chiral hinge modes and unpinned Dirac surface states. The topotactic mutual-exchange nanowire growth will, thus, enable the exploration of intricate magneto-topological states in Eu3In2As4 and potentially in other exotic compounds.

Tutorial 2.0: computing topological invariants in 3D photonic crystals

The field of topological photonics has been on the rise due to its versatility in manufacturing and its applications as topological lasers or unidirectional waveguides. Contrary to 1D or 2D photonic crystals, the transversal and vectorial nature of light in 3D precludes using standard methods for diagnosing topology. This tutorial describes the problems that emerge in computing topological invariants in 3D photonic crystals and the diverse strategies for overcoming them. Firstly, we introduce the fundamentals of light propagation in 3D periodic media and expose the complications of directly implementing the usual topological diagnosis tools. Secondly, we describe the properties of electromagnetic Wilson loops and how they can be used to diagnose topology and compute topological invariants in 3D photonic crystals. Finally, we apply the previously described methods to several examples of 3D photonic crystals showing different topological phases, such as Weyl nodes and walls, 3D photonic Chern insulators, and photonic axion insulators.

Axion topology in photonic crystal domain walls

Axion insulators are 3D magnetic topological insulators supporting hinge states and quantized magnetoelectric effects, recently proposed for detecting dark-matter axionic particles via their axionic excitations. Beyond theoretical interest, obtaining a photonic counterpart of axion insulators offers potential for advancing magnetically-tunable photonic devices and axion haloscopes based on axion-photon conversion. This work proposes an axionic 3D phase within a photonic setup. By building inversion-symmetric domain-walls in gyrotropic photonic crystals, we bind chiral modes on inversion-related hinges, ultimately leading to the realization of an axionic channel of light. These states propagate embedded in a 3D structure, thus protected from radiation in the continuum. Employing a small external gyromagnetic bias, we transition across different axionic mode configurations, enabling effective topological switching of chiral photonic fibers. While demonstrating the possibility of realizing axion photonic crystals within state-of-the-art gyrotropic setups, we propose a general scheme for rendering axion topology at domain walls of Weyl semimetals.

Multimodal Approach Reveals the Symmetry-Breaking Pathway to the Broken Helix in EuIn2As2

Understanding and manipulating emergent phases, which are themes at the forefront of quantum-materials research, rely on identifying their underlying symmetries. This general principle has been particularly prominent in materials with coupled electronic and magnetic degrees of freedom, in which magnetic order influences the electronic band structure and can lead to exotic topological effects. However, identifying symmetry of a magnetically ordered phase can pose a challenge, particularly in the presence of small domains. Here we introduce a multimodal approach for determining magnetic structures, which combines symmetry-sensitive optical probes, scattering, and group-theoretical analysis. We apply it to EuIn2As2, a material that has received attention as a candidate axion insulator. While first-principles calculations predict this state on the assumption of a simple collinear antiferromagnetic structure, subsequent neutron-scattering measurements reveal a much more intricate magnetic ground state characterized by two coexisting magnetic wave vectors reached by successive thermal phase transitions. The proposed high- and low-temperature phases are a spin helix and a state with interpenetrating helical and Néel antiferromagnetic order termed a “broken helix,” respectively. Employing a multimodal approach, we identify the magnetic structure associated with these two phases of EuIn2As2. We find that the higher-temperature phase is characterized by a variation of the magnetic moment amplitude from layer to layer, with the moment vanishing entirely in every third Eu layer. The lower-temperature structure is similar to the broken helix, with one important difference: Because of local strain, the relative orientation of the magnetic structure and the lattice is not fixed. Consequently, the symmetry required to protect the axion phase is not generically protected in EuIn2As2, but we show that it can be restored if the magnetic structure is tuned with uniaxial strain. Finally, we present a spin Hamiltonian that identifies the spin interactions that account for the complex magnetic order in EuIn2As2. Our work highlights the importance of a multimodal approach in determining the symmetry of complex order parameters. Published by the American Physical Society 2024

Search for an antiferromagnetic Weyl semimetal in (MnTe) m (Sb2Te3) n and (MnTe) m (Bi2Te3) n superlattices

The interaction between topology and magnetism can lead to novel topological materials including Chern insulators, axion insulators, and Dirac and Weyl semimetals. In this work, a family of van der Waals layered materials using MnTe and Sb2Te3 or Bi2Te3 superlattices as building blocks are systematically examined in a search for antiferromagnetic Weyl semimetals, preferably with a simple node structure. The approach is based on controlling the strength of the exchange interaction as a function of layer composition to induce the phase transition between the topological and the normal insulators. Our calculations, utilizing a combination of first-principles density functional theory and tight-binding analyses based on maximally localized Wannier functions, clearly indicate a promising candidate for a type-I magnetic Weyl semimetal. This centrosymmetric material, Mn10Sb8Te22 (or (MnTe) m (Sb2Te3) n with m = 10 and n = 4), shows ferromagnetic intralayer and antiferromagnetic interlayer interactions in the antiferromagnetic ground state. The obtained electronic bandstructure also exhibits a single pair of Weyl points in the spin-split bands consistent with a Weyl semimetal. The presence of Weyl nodes is further verified with Berry curvature, Wannier charge center, and surface state (i.e. Fermi arc) calculations. Other combinations of the MnSbTe-family materials are found to be antiferromagnetic topological or normal insulators on either side of the Mn:Sb ratio, respectively, illustrating the topological phase transition as anticipated. A similar investigation in the homologous (MnTe) m (Bi2Te3) n system produces mostly nontrivial antiferromagnetic insulators due to the strong spin–orbit coupling. When realized, the antiferromagnetic Weyl semimetals in the simplest form (i.e. a single pair of Weyl nodes) are expected to provide a promising candidate for low-power spintronic applications.

Unconventional Spectral Gaps Induced by Charge Density Waves in the Weyl Semimetal (TaSe4)2I.

Coupling Weyl quasiparticles and charge density waves (CDWs) can lead to fascinating band renormalization and many-body effects beyond band folding and Peierls gaps. For the quasi-one-dimensional chiral compound (TaSe4)2I with an incommensurate CDW transition at TC = 263 K, photoemission mappings thus far are intriguing due to suppressed emission near the Fermi level. Models for this unconventional behavior include axion insulator phases, correlation pseudogaps, polaron subbands, bipolaron bound states, etc. Our photoemission measurements show sharp quasiparticle bands crossing the Fermi level at T > TC, but for T < TC, these bands retain their dispersions with no Peierls or axion gaps at the Weyl points. Instead, occupied band edges recede from the Fermi level, opening a spectral gap. Our results confirm localization of quasiparticles (holes created by photoemission) is the key physics, which suppresses spectral weights over an energy window governed by incommensurate modulation and inherent phase defects of CDW.

Even-Odd Layer-Dependent Exchange Bias Effect in MnBi2Te4 Chern Insulator Devices.

Magnetic topological materials with coexisting magnetism and nontrivial band structures exhibit many novel quantum phenomena, including the quantum anomalous Hall effect, the axion insulator state, and the Weyl semimetal phase. As a stoichiometric layered antiferromagnetic topological insulator, thin films of MnBi2Te4 show fascinating even-odd layer-dependent physics. In this work, we fabricate a series of thin-flake MnBi2Te4 devices using stencil masks and observe the Chern insulator state at high magnetic fields. Upon magnetic field training, a large exchange bias effect is observed in odd but not in even septuple layer (SL) devices. Through theoretical calculations, we attribute the even-odd layer-dependent exchange bias effect to the contrasting surface and bulk magnetic properties of MnBi2Te4 devices. Our findings reveal the microscopic magnetic configuration of MnBi2Te4 thin flakes and highlight the challenges in replicating the zero magnetic field quantum anomalous Hall effect in odd SL MnBi2Te4 devices.

High spin axion insulator

Axion insulators possess a quantized axion field θ = π protected by combined lattice and time-reversal symmetry, holding great potential for device applications in layertronics and quantum computing. Here, we propose a high-spin axion insulator (HSAI) defined in large spin-s representation, which maintains the same inherent symmetry but possesses a notable axion field θ = (s + 1/2)2π. Such distinct axion field is confirmed independently by the direct calculation of the axion term using hybrid Wannier functions, layer-resolved Chern numbers, as well as the topological magneto-electric effect. We show that the guaranteed gapless quasi-particle excitation is absent at the boundary of the HSAI despite its integer surface Chern number, hinting an unusual quantum anomaly violating the conventional bulk-boundary correspondence. Furthermore, we ascertain that the axion field θ can be precisely tuned through an external magnetic field, enabling the manipulation of bonded transport properties. The HSAI proposed here can be experimentally verified in ultra-cold atoms by the quantized non-reciprocal conductance or topological magnetoelectric response. Our work enriches the understanding of axion insulators in condensed matter physics, paving the way for future device applications.

Chemical Rules for Stacked Kagome and Honeycomb Topological Semimetals.

The chemical rules for predicting and understanding topological states in stacked kagome and honeycomb lattices are studied in both analytical and numerical ways. Starting with a minimal five-band tight-binding model, all the topological states are sorted into five groups, which are determined by the interlayer and intralayer hopping parameters. Combined with the model, an algorithm is designed to obtain a series of experimentally synthesized topological semimetals with kagome and honeycomb layers, i.e., IAMX family (IA = Alkali metal element, M = Rare earth metal element, X = Carbon group element), in the inorganic crystal structure database. A follow-up high-throughput calculation shows that IAMX family materials are all nodal-line semimetals and they will be Weyl semimetals after taking spin-orbit coupling into consideration. To have further insights into the topology of the IAMX family, a detailed chemical rule analysis is carried out on the high-throughput calculations, including the lattice constants of the structure, intralayer and interlayer couplings, bond strengths, electronegativity, and so on, which are consistent with the tight-binding model. This study provides a way to discover and modulate topological properties in stacked kagome and honeycomb crystals and offers candidates for studying topology-related properties like topological superconductors and axioninsulators.

Magnetotransport of Sm2Ir2O7 across the pressure-induced quantum-critical phase boundary

Rare-earth pyrochlore iridates host two interlocking magnetic sublattices of corner-sharing tetrahedra and can harbour a unique combination of frustrated moments, exotic excitations and highly correlated electrons. They are also the first systems predicted to display both topological Weyl semimetal and axion insulator phases. We have measured the transport and magnetotransport properties of single-crystal Sm2Ir2O7 up to and beyond the pressure-induced quantum critical point for all-in-all-out (AIAO) Ir order at pc = 63 kbar previously identified by resonant X-ray scattering and close to which Weyl semimetallic behavior has been previously predicted. Our findings overturn the accepted expectation that the suppression of AIAO order should lead to metallic conduction persisting down to zero temperature. Instead, the resistivity-minimum temperature, which tracks the decrease in the AIAO ordering temperature for pressures up to 30 kbar, begins to increase under further application of pressure, pointing to the presence of a second as-yet unidentified mechanism leading to non-metallic behavior. The magnetotransport does track the suppression of Ir magnetism, however, with a strong hysteresis observed only within the AIAO phase boundary, similar to that found for Ho2Ir2O7 and attributed to plastic deformation of Ir domains. Around pc we find the emergence of a new type of electronic phase, characterized by a negative magnetoresistance with small hysteresis at the lowest temperatures, and hysteresis-free positive magnetoresistance above approximately 5 K. The temperature dependence of our low-temperature transport data are found to be best described by a model consistent with a Weyl semimetal across the entire pressure range.

Chirality manipulation of ultrafast phase switches in a correlated CDW-Weyl semimetal

Light engineering of correlated states in topological materials provides a new avenue of achieving exotic topological phases inaccessible by conventional tuning methods. Here we demonstrate a light control of correlation gaps in a model charge-density-wave (CDW) and polaron insulator (TaSe4)2I recently predicted to be an axion insulator. Our ultrafast terahertz photocurrent spectroscopy reveals a two-step, non-thermal melting of polarons and electronic CDW gap via the fluence dependence of a longitudinal circular photogalvanic current. This helicity-dependent photocurrent reveals continuous ultrafast phase switches from the polaronic state to the CDW (axion) phase, and finally to a hidden Weyl phase as the pump fluence increases. Additional distinctive attributes aligning with the light-induced switches include: the mode-selective coupling of coherent phonons to the polaron and CDW modulation, and the emergence of a non-thermal chiral photocurrent above the pump threshold of CDW-related phonons. The demonstrated ultrafast chirality control of correlated topological states here holds large potentials for realizing axion electrodynamics and advancing quantum-computing applications.

ARPES investigation of the electronic structure and its evolution in magnetic topological insulator MnBi2+2nTe4+3n family.

In the past 5 years, there has been significant research interest in the intrinsic magnetic topological insulator family compounds MnBi2+2nTe4+3n (where n=0, 1, 2 …). In particular, exfoliated thin films of MnBi2Te4 have led to numerous experimental breakthroughs, such as the quantum anomalous Hall effect, axion insulator phase and high-Chern number quantum Hall effect without Landau levels. However, despite extensive efforts, the energy gap of the topological surface states due to exchange magnetic coupling, which is a key feature of the characteristic band structure of the system, remains experimentally elusive. The electronic structure measured by using angle-resolved photoemission (ARPES) shows significant deviation from ab initio prediction and scanning tunneling spectroscopy measurements, making it challenging to understand the transport results based on the electronic structure. This paper reviews the measurements of the band structure of MnBi2+2nTe4+3n magnetic topological insulators using ARPES, focusing on the evolution of their electronic structures with temperature, surface and bulk doping and film thickness. The aim of the review is to construct a unified picture of the electronic structure of MnBi2+2nTe4+3n compounds and explore possible control of their topological properties.

Recent progress of MnBi2Te4 epitaxial thin films as a platform for realising the quantum anomalous Hall effect.

Since the first realisation of the quantum anomalous Hall effect (QAHE) in a dilute magnetic-doped topological insulator thin film in 2013, the quantisation temperature has been limited to less than 1 K due to magnetic disorder in dilute magnetic systems. With magnetic moments ordered into the crystal lattice, the intrinsic magnetic topological insulator MnBi2Te4 has the potential to eliminate or significantly reduce magnetic disorder and improve the quantisation temperature. Surprisingly, to date, the QAHE has yet to be observed in molecular beam epitaxy (MBE)-grown MnBi2Te4 thin films at zero magnetic field, and what leads to the difficulty in quantisation is still an active research area. Although bulk MnBi2Te4 and exfoliated flakes have been well studied, revealing both the QAHE and axion insulator phases, experimental progress on MBE thin films has been slower. Understanding how the breakdown of the QAHE occurs in MnBi2Te4 thin films and finding solutions that will enable mass-produced millimetre-size QAHE devices operating at elevated temperatures are required. In this mini-review, we will summarise recent studies on the electronic and magnetic properties of MBE MnBi2Te4 thin films and discuss mechanisms that could explain the failure of the QAHE from the aspects of defects, electronic structure, magnetic order, and consequences of their delicate interplay. Finally, we propose several strategies for realising the QAHE at elevated temperatures in MnBi2Te4 thin films.

Phase Separation Prevents the Synthesis of VBi2Te4 by Molecular Beam Epitaxy.

Intrinsic magnetic topological insulators (IMTIs) have a non-trivial band topology in combination with magnetic order. This potentially leads to fascinating states of matter, such as quantum anomalous Hall (QAH) insulators and axion insulators. One of the theoretically predicted IMTIs is VBi2Te4, but experimental evidence of this material is lacking so far. Here, we report on our attempts to synthesise VBi2Te4 by molecular beam epitaxy (MBE). X-ray diffraction reveals that in the thermodynamic phase space reachable by MBE, there is no region where VBi2Te4 is stably synthesised. Moreover, scanning transmission electron microscopy shows a clear phase separation to Bi2Te3 and VTe2 instead of the formation of VBi2Te4. We suggest the phase instability to be due to either the large lattice mismatch between VTe2 and Bi2Te3 or the unfavourable valence state of vanadium.

Dissipative edge transport in disordered axion insulator films

Dissipative edge transport in disordered axion insulator films

Axion insulator state in hundred-nanometer-thick magnetic topological insulator sandwich heterostructures

An axion insulator is a three-dimensional (3D) topological insulator (TI), in which the bulk maintains the time-reversal symmetry or inversion symmetry but the surface states are gapped by surface magnetization. The axion insulator state has been observed in molecular beam epitaxy (MBE)-grown magnetically doped TI sandwiches and exfoliated intrinsic magnetic TI MnBi2Te4 flakes with an even number layer. All these samples have a thickness of ~ 10 nm, near the 2D-to-3D boundary. The coupling between the top and bottom surface states in thin samples may hinder the observation of quantized topological magnetoelectric response. Here, we employ MBE to synthesize magnetic TI sandwich heterostructures and find that the axion insulator state persists in a 3D sample with a thickness of ~ 106 nm. Our transport results show that the axion insulator state starts to emerge when the thickness of the middle undoped TI layer is greater than ~ 3 nm. The 3D hundred-nanometer-thick axion insulator provides a promising platform for the exploration of the topological magnetoelectric effect and other emergent magnetic topological states, such as the high-order TI phase.

Recent progress in MnBi2nTe3n+1 intrinsic magnetic topological insulators: crystal growth, magnetism and chemical disorder.

The search for magnetic topological materials has been at the forefront of condensed matter research for their potential to host exotic states such as axion insulators, magnetic Weyl semimetals, Chern insulators, etc. To date, the MnBi2nTe3n+1 family is the only group of materials showcasing van der Waals-layered structures, intrinsic magnetism and non-trivial band topology without trivial bands at the Fermi level. The interplay between magnetism and band topology in this family has led to the proposal of various topological phenomena, including the quantum anomalous Hall effect, quantum spin Hall effect and quantum magnetoelectric effect. Among these, the quantum anomalous Hall effect has been experimentally observed at record-high temperatures, highlighting the unprecedented potential of this family of materials in fundamental science and technological innovation. In this paper, we provide a comprehensive review of the research progress in this intrinsic magnetic topological insulator family, with a focus on single-crystal growth, characterization of chemical disorder, manipulation of magnetism through chemical substitution and external pressure, and important questions that remain to be conclusively answered.

Growth and characterization of Bi(110)/CrTe2 heterostructures: Exploring interplay between magnetism and topology

The interplay between topology and magnetism is vital for realizing exotic quantum phenomena, significant examples including quantum anomalous Hall effect, axion insulators, and high-order topological states. These states host great potential for future applications in high-speed and low-consumption electronic devices. Despite being extensively investigated, practical platforms are still scarce. In this work, with molecular beam epitaxy (MBE), we provide the first experimental report on high-quality Bi(110)/CrTe2 magnetic heterostructure. By employing in-situ high-resolution scanning tunneling microscopy, we are able to examine the interaction between magnetism and topology. There is a potential edge state at an energy level above the Fermi level, but no edge states observed near the Fermi level The absence of high-order topological corner states near E F highlights the importance of lattice matching and interface engineering in designing high-order topological states. Our study provides key insights into the interplay between two-dimensional magnetic and topological materials and offers an important dimension for engineering magnetic topological states.

Gate-electric-field and magnetic-field control of versatile topological phases in a semi-magnetic topological insulator

Surface states of a topological insulator demonstrate interesting quantum phenomena, such as the quantum anomalous Hall (QAH) effect and the quantum magnetoelectric effect. Fermi energy tuning plays a role in inducing phase transitions and developing future device functions. Here, we report on controlling the topological phases in a dual-gate field-effect transistor of a semi-magnetic topological insulator heterostructure. The heterostructure consists of magnetized one-surface and non-magnetic other-surface. By tuning the Fermi energy to the energy gap of the magnetized surface, the Hall conductivity σxy becomes close to the half-integer quantized Hall conductivity e2/2h, exemplifying parity anomaly. The dual-gate control enables the band structure alignment to the two quantum Hall states with σxy = e2/h and 0 under a strong magnetic field. These states are topologically equivalent to the QAH and axion insulator states, respectively. Precise and independent control of the band alignment of the top and bottom surfaces successively induces various topological phase transitions among the QAH, axion insulator, and parity anomaly states in magnetic topological insulators.