Exchange-coupling-induced symmetry breaking in topological insulators

Controlling the spin current around the rectangular cavities in two-dimensional topological insulators

Controlling spin current in topological insulators (TIs) is a crucial requirement for applications in quantum computing and spintronics. Using the non-equilibrium Keldysh Green's function formalism, we demonstrate that such control can be established around rectangular cavities of two-dimensional TIs by breaking their time reversal symmetry via exchange magnetic fields and magnetic defects. In the presence of magnetic defects with xy symmetry or Ising symmetry, the density of states is localized, and the spin current forms a current loop around the rectangular cavity in TIs interfacing with two ferromagnetic stripes. We also observe that the spin direction of the traveling electrons is inverted under the reversal of bias and gate voltages. The change in the spin-polarized current around the cavities is predicted by varying the strength of Rashba spin-orbit coupling. This result allows for the creation and control of nearly fully spin-polarized currents with various spatial patterns around the cavities in TIs, and the design of tunable spin diodes for highly integrated spintronics.

Gate-tunable Intrinsic Anomalous Hall Effect in Epitaxial MnBi2Te4 Films

The anomalous Hall effect (AHE) is an important transport signature revealing topological properties of magnetic materials and their spin textures. Recently, MnBi2Te4 has been demonstrated to be an intrinsic magnetic topological insulator. However, the origin of its intriguing AHE behaviors remains elusive. Here, we demonstrate the Berry curvature-dominated intrinsic AHE in wafer-scale MnBi2Te4 films. By applying back-gate voltages, we observe an ambipolar conduction and n-p transition in ∼7-layer MnBi2Te4, where a quadratic relation between the AHE resistance and longitudinal resistance suggests its intrinsic AHE nature. In particular, for ∼3-layer MnBi2Te4, the AHE sign can be tuned from pristine negative to positive. First-principles calculations unveil that such an AHE reversal originated from the competing Berry curvature between oppositely polarized spin-minority-dominated surface states and spin-majority-dominated inner bands. Our results shed light on the underlying physical mechanism of the intrinsic AHE and provide new perspectives for the unconventional sign-tunable AHE.

Manipulating Topological Phases in Magnetic Topological Insulators

Magnetic topological insulators (MTIs) are a group of materials that feature topological band structures with concurrent magnetism, which can offer new opportunities for technological advancements in various applications, such as spintronics and quantum computing. The combination of topology and magnetism introduces a rich spectrum of topological phases in MTIs, which can be controllably manipulated by tuning material parameters such as doping profiles, interfacial proximity effect, or external conditions such as pressure and electric field. In this paper, we first review the mainstream MTI material platforms where the quantum anomalous Hall effect can be achieved, along with other exotic topological phases in MTIs. We then focus on highlighting recent developments in modulating topological properties in MTI with finite-size limit, pressure, electric field, and magnetic proximity effect. The manipulation of topological phases in MTIs provides an exciting avenue for advancing both fundamental research and practical applications. As this field continues to develop, further investigations into the interplay between topology and magnetism in MTIs will undoubtedly pave the way for innovative breakthroughs in the fundamental understanding of topological physics as well as practical applications.

Ubiquitous Superconducting Diode Effect in Superconductor Thin Films

The macroscopic coherence in superconductors supports dissipationless supercurrents that could play a central role in emerging quantum technologies. Accomplishing unequal supercurrents in the forward and backward directions would enable unprecedented functionalities. This nonreciprocity of critical supercurrents is called the superconducting (SC) diode effect. We demonstrate the strong SC diode effect in conventional SC thin films, such as niobium and vanadium, employing external magnetic fields as small as 1 Oe. Interfacing the SC layer with a ferromagnetic semiconductor EuS, we further accomplish the nonvolatile SC diode effect reaching a giant efficiency of 65%. By careful control experiments and theoretical modeling, we demonstrate that the critical supercurrent nonreciprocity in SC thin films could be easily accomplished with asymmetrical vortex edge and surface barriers and the universal Meissner screening current governing the critical currents. Our engineering of the SC diode effect in simple systems opens the door for novel technologies while revealing the ubiquity of the Meissner screening effect induced SC diode effect in superconducting films, and it should be eliminated with great care in the search for exotic superconducting states harboring finite-momentum Cooper pairing.

Spin transfer torques due to the bulk states of topological insulators

Spin torques at topological insulator (TI)/ferromagnet interfaces have received considerable attention in recent years with a view towards achieving full electrical manipulation of magnetic degrees of freedom. The most important question in this field concerns the relative contributions of bulk and surface states to the spin torque, a matter that remains incompletely understood. Whereas the surface state contribution has been extensively studied, the contribution due to the bulk states has received comparatively little attention. Here we study spin torques due to TI bulk states and show that: (i) there is no spin-orbit torque due to the bulk states on a homogeneous magnetisation, in contrast to the surface states, which give rise to a spin-orbit torque via the well-known Edelstein effect. (ii) The bulk states give rise to a spin transfer torque (STT) due to the inhomogeneity of the magnetisation in the vicinity of the interface. This spin transfer torque, which has not been considered in TIs in the past, is somewhat unconventional since it arises from the interplay of the bulk TI spin-orbit coupling and the gradient of the monotonically decaying magnetisation inside the TI. Whereas we consider an idealised model in which the magnetisation gradient is small and the spin transfer torque is correspondingly small, we argue that in real samples the spin transfer torque should be sizable and may provide the dominant contribution due to the bulk states. We show that an experimental smoking gun for identifying the bulk states is the fact that the field-like component of the spin transfer torque generates a spin density with the same size but opposite sign for in-plane and out-of-plane magnetisations. This distinguishes them from the surface states, which are expected to give a spin density of a similar size and the same sign for both an in-plane and out-of-plane magnetisations.

Topological properties of Xene tuned by perpendicular electric field and exchange field in the presence of Rashba spin-orbit coupling

Xene (X=Si, Ge, Sn) is a typical and promising two-dimensional topological insulator with many novel topological properties. Here, we investigate the topological properties of Xene tuned by a perpendicularly applied electric field, exchange field, and Rashba spin-orbit coupling (RSOC) using the tight-binding (TB) method. We show that in the presence of RSOC, the system can be converted from a quantum spin Hall (QSH) insulator into a conventional band insulator (BI) by a weak perpendicular electric field or into a quantum anomalous Hall (QAH) insulator by a weak exchange field. Additionally, a suitable combination of electric and exchange fields can give rise to a valley-polarized metallic (VPM) state. Furthermore, we explore the competition between the electric field and exchange field in tuning the topological states owing to the Rashba coupling effect. When the electric field is stronger than the exchange field, the system tends to be in a topologically trivial BI state; otherwise, it will be a QAH insulator. More intriguingly, for a fixed exchange field and RSOC, as the perpendicular electric field increase continuously from zero, the system undergoes multiphase (e.g. QSH-VPM-BI) transitions. This paves the way for designing multiphase transition devices through external single-field regulation.

Two-Dimensional Van Der Waals Topological Materials: Preparation, Properties, and Device Applications

Over the past decade, 2D van der Waals (vdW) topological materials (TMs), including topological insulators and topological semimetals, which combine atomically flat 2D layers and topologically nontrivial band structures, have attracted increasing attention in condensed-matter physics and materials science. These easily cleavable and integrated TMs provide the ideal platform for exploring topological physics in the 2D limit, where new physical phenomena may emerge, and represent a potential to control and investigate exotic properties and device applications in nanoscale topological phases. However, multifaced efforts are still necessary, which is the prerequisite for the practical application of 2D vdW TMs. Herein, this review focuses on the preparation, properties, and device applications of 2D vdW TMs. First, three common preparation strategies for 2D vdW TMs are summarized, including single crystal exfoliation, chemical vapor deposition, and molecular beam epitaxy. Second, the origin and regulation of various properties of 2D vdW TMs are introduced, involving electronic properties, transport properties, optoelectronic properties, thermoelectricity, ferroelectricity, and magnetism. Third, some device applications of 2D vdW TMs are presented, including field-effect transistors, memories, spintronic devices, and photodetectors. Finally, some significant challenges and opportunities for the practical application of 2D vdW TMs in 2D topological electronics are briefly addressed.

Two-dimensional antiferromagnetic nodal-line semimetal and quantum anomalous Hall state in the van der Waals heterostructure germanene/Mn2S2

Materials with interactions between the topology and magnetism are triggering increasing interest. We constructed a two-dimensional (2D) van der Waals heterostructure germanene/Mn₂S₂, where the germanene is a quantum spin Hall insulator and Mn₂S₂provides antiferromagnetic (AFM) interactions. In this structure, a 2D AFM nodal-line semimetal (NLSM) phase is expected without the spin-orbit coupling (SOC), which is of a high density of states around the Fermi level. The band touching rings originate from the intersection between different spin components ofporbitals of germanene. This result provides a possible 2D realization of NLSMs, which are usually realized in three-dimensional systems. When the SOC is present, a quantum anomalous Hall (QAH) state emerges with the annihilation of the band-touching rings. The nontrivial topology is determined by calculating the Chern number and Wannier charge centers. This provides an alternative platform to realize QAH states. These results could also provide the possibility of further understanding the topological states in NLSM and electronic applications.

Gate-Tunable Anomalous Hall Effect in Stacked van der Waals Ferromagnetic Insulator-Topological Insulator Heterostructures

The search of novel topological states, such as the quantum anomalous Hall insulator and chiral Majorana fermions, has motivated different schemes to introduce magnetism into topological insulators. A promising scheme is using the magnetic proximity effect (MPE), where a ferromagnetic insulator magnetizes the topological insulator. Most of these heterostructures are synthesized by growth techniques which prevent mixing many of the available ferromagnetic and topological insulators due to difference in growth conditions. Here, we demonstrate that MPE can be obtained in heterostructures stacked via the dry transfer of flakes of van der Waals ferromagnetic and topological insulators (Cr₂Ge₂Te₆/BiSbTeSe₂), as evidenced in the observation of an anomalous Hall effect (AHE). Furthermore, devices made from these heterostructures allow modulation of the AHE when controlling the carrier density via electrostatic gating. These results show that simple mechanical transfer of magnetic van der Waals materials provides another possible avenue to magnetize topological insulators by MPE.

Gate-Tunable Anomalous Hall Effect in a 3D Topological Insulator/2D Magnet van der Waals Heterostructure

We demonstrate advantages of samples made by mechanical stacking of exfoliated van der Waals materials for controlling the topological surface state of a three-dimensional topological insulator (TI) via interaction with an adjacent magnet layer. We assemble bilayers with pristine interfaces using exfoliated flakes of the TI BiSbTeSe₂ and the magnet Cr₂Ge₂Te₆, thereby avoiding problems caused by interdiffusion that can affect interfaces made by top-down deposition methods. The samples exhibit an anomalous Hall effect (AHE) with abrupt hysteretic switching. For the first time in samples composed of a TI and a separate ferromagnetic layer, we demonstrate that the amplitude of the AHE can be tuned via gate voltage with a strong peak near the Dirac point. This is the signature expected for the AHE due to Berry curvature associated with an exchange gap induced by interaction between the topological surface state and an out-of-plane-oriented magnet.

Anomalous transverse resistance in the topological superconductor β-Bi2Pd

A supercurrent flowing in a superconductor meets no resistance. Yet an electric field may still be established within the superconductor in the presence of dissipative processes, such as vortex motion. Here we report the observation of a transverse voltage drop in superconducting β-Bi₂Pd thin films. Unlike the Hall effect in general or in other superconductors, the sign of the observed transverse voltage does not depend on the external magnetic field. Instead, it is dictated by the broken inversion symmetry on the film interfaces. This anomalous transverse voltage, or transverse resistance, is indicative of a chirality that likely resonates with the topological surface states reported in β-Bi₂Pd.

Centrosymmetric β-Bi₂Pd is a candidate topological superconductor. Here, the authors observe a transverse voltage in β-Bi₂Pd thin films and propose that this voltage is a result of chiral topological surface states.

Topological Surface State Annihilation and Creation in SnTe/Crx(BiSb)2-xTe3 Heterostructures

Topological surface states are a new class of electronic states with novel properties, including the potential for annihilation between surface states from two topological insulators at a common interface. Here, we report the annihilation and creation of topological surface states in the SnTe/Cr_x(BiSb)_2-xTe₃ (CBST) heterostructures as evidenced by magneto-transport, polarized neutron reflectometry, and first-principles calculations. Our results show that topological surface states are induced in the otherwise topologically trivial two-quintuple-layers thick CBST when interfaced with SnTe, as a result of the surface state annihilation at the SnTe/CBST interface. Moreover, we unveiled systematic changes in the transport behaviors of the heterostructures with respect to changing Fermi level and thickness. Our observation of surface state creation and annihilation demonstrates a promising way of designing and engineering topological surface states for dissipationless electronics.

Emergent Multifunctional Magnetic Proximity in van der Waals Layered Heterostructures

Proximity effect, which is the coupling between distinct order parameters across interfaces of heterostructures, has attracted immense interest owing to the customizable multifunctionalities of diverse 3D materials. This facilitates various physical phenomena, such as spin order, charge transfer, spin torque, spin density wave, spin current, skyrmions, and Majorana fermions. These exotic physics play important roles for future spintronic applications. Nevertheless, several fundamental challenges remain for effective applications: unavoidable disorder and lattice mismatch limits in the growth process, short characteristic length of proximity, magnetic fluctuation in ultrathin films, and relatively weak spin-orbit coupling (SOC). Meanwhile, the extensive library of atomically thin, 2D van der Waals (vdW) layered materials, with unique characteristics such as strong SOC, magnetic anisotropy, and ultraclean surfaces, offers many opportunities to tailor versatile and more effective functionalities through proximity effects. Here, this paper focuses on magnetic proximity, i.e., proximitized magnetism and reviews the engineering of magnetism-related functionalities in 2D vdW layered heterostructures for next-generation electronic and spintronic devices. The essential factors of magnetism and interfacial engineering induced by magnetic layers are studied. The current limitations and future challenges associated with magnetic proximity-related physics phenomena in 2D heterostructures are further discussed.

Magnetoelectric effects in Josephson junctions

The review is devoted to the fundamental aspects and characteristic features of the magnetoelectric effects, reported in the literature on Josephson junctions (JJs). The main focus of the review is on the manifestations of the direct and inverse magnetoelectric effects in various types of Josephson systems. They provide a coupling of the magnetization in superconductor/ferromagnet/superconductor JJs to the Josephson current. The direct magnetoelectric effect is a driving force of spin torques acting on the ferromagnet inside the JJ. Therefore it is of key importance for the electrical control of the magnetization. The inverse magnetoelectric effect accounts for the back action of the magnetization dynamics on the Josephson subsystem, in particular, making the JJ to be in the resistive state in the presence of the magnetization dynamics of any origin. The perspectives of the coupling of the magnetization in JJs with ferromagnetic interlayers to the Josephson current via the magnetoelectric effects are discussed.

Proximity-Induced Magnetism in a Topological Insulator/Half-Metallic Ferromagnetic Thin Film Heterostructure

Topological insulator (TI) Bi2Se3 thin films were prepared on half-metallic ferromagnetic La0.7Sr0.3MnO3 thin film by magnetron sputtering, forming a TI/FM heterostructure. The conductivity of Bi2Se3was modified by La0.7Sr0.3MnO3 at high- and low-temperature regions via different mechanisms, which could be explained by the short-range interactions and long-range interaction between ferromagnetic insulator and Bi2Se3 due to the proximity effect. Magnetic and transport measurements prove that the ferromagnetic phase and extra magnetic moment are induced in Bi2Se3 films. The weak anti-localized (WAL) effect was suppressed in Bi2Se3 films, accounting for the magnetism of La0.7Sr0.3MnO3 layers. This work clarifies the special behavior in Bi2Se3/La0.7Sr0.3MnO3 heterojunctions, which provides an effective way to study the magnetic proximity effect of the ferromagnetic phase in topological insulators.

Interior and Edge Magnetization in Thin Exfoliated CrGeTe3 Films

CrGeTe₃ (CGT) is a semiconducting vdW ferromagnet shown to possess magnetism down to a two-layer thick sample. Although CGT is one of the leading candidates for spintronics devices, a comprehensive analysis of CGT thickness dependent magnetization is currently lacking. In this work, we employ scanning SQUID-on-tip (SOT) microscopy to resolve the magnetic properties of exfoliated CGT flakes at 4.2 K. Combining transport measurements of CGT/NbSe₂ samples with SOT images, we present the magnetic texture and hysteretic magnetism of CGT, thereby matching the global behavior of CGT to the domain structure extracted from local SOT magnetic imaging. Using this method, we provide a thickness dependent magnetization state diagram of bare CGT films. No zero-field magnetic memory was found for films thicker than 10 nm, and hard ferromagnetism was found below that critical thickness. Using scanning SOT microscopy, we identify a unique edge magnetism, contrasting the results attained in the CGT interior.

Understanding Signatures of Emergent Magnetism in Topological Insulator/Ferrite Bilayers

Magnetic insulator-topological insulator heterostructures have been studied in search of chiral edge states via proximity induced magnetism in the topological insulator, but these states have been elusive. We identified MgAl_{0.5}Fe_{1.5}O_{4}/Bi_{2}Se_{3} bilayers for a possible magnetic proximity effect. Electrical transport and polarized neutron reflectometry suggest a proximity effect, but structural data indicate a disordered interface as the origin of the magnetic response. Our results provide a strategy via correlation of microstructure with magnetic data to confirm a magnetic proximity effect.

Progress and prospects in magnetic topological materials

Magnetic topological materials represent a class of compounds with properties that are strongly influenced by the topology of their electronic wavefunctions coupled with the magnetic spin configuration. Such materials can support chiral electronic channels of perfect conduction, and can be used for an array of applications, from information storage and control to dissipationless spin and charge transport. Here we review the theoretical and experimental progress achieved in the field of magnetic topological materials, beginning with the theoretical prediction of the quantum anomalous Hall effect without Landau levels, and leading to the recent discoveries of magnetic Weyl semimetals and antiferromagnetic topological insulators. We outline recent theoretical progress that has resulted in the tabulation of, for the first time, all magnetic symmetry group representations and topology. We describe several experiments realizing Chern insulators, Weyl and Dirac magnetic semimetals, and an array of axionic and higher-order topological phases of matter, and we survey future perspectives.

Enormous Berry-Curvature-Based Anomalous Hall Effect in Topological Insulator (Bi,Sb)2Te3 on Ferrimagnetic Europium Iron Garnet beyond 400 K

To realize the quantum anomalous Hall effect (QAHE) at elevated temperatures, the approach of magnetic proximity effect (MPE) was adopted to break the time-reversal symmetry in the topological insulator (Bi_0.3Sb_0.7)₂Te₃ (BST) based heterostructures with a ferrimagnetic insulator europium iron garnet (EuIG) of perpendicular magnetic anisotropy. Here we demonstrate large anomalous Hall resistance (R_AHE) exceeding 8 Ω (ρ_AHE of 3.2 μΩ·cm) at 300 K and sustaining to 400 K in 35 BST/EuIG samples, surpassing the past record of 0.28 Ω (ρ_AHE of 0.14 μΩ·cm) at 300 K. The large R_AHE is attributed to an atomically abrupt, Fe-rich interface between BST and EuIG. Importantly, the gate dependence of the AHE loops shows no sign change with varying chemical potential. This observation is supported by our first-principles calculations via applying a gradient Zeeman field plus a contact potential on BST. Our calculations further demonstrate that the AHE in this heterostructure is attributed to the intrinsic Berry curvature. Furthermore, for gate-biased 4 nm BST on EuIG, a pronounced topological Hall effect-like (THE-like) feature coexisting with AHE is observed at the negative top-gate voltage up to 15 K. Interface tuning with theoretical calculations has realized topologically distinct phenomena in tailored magnetic TI-based heterostructures.

Electronic properties and interface contact of graphene/CrSiTe3 van der Waals heterostructures

Electronic properties and interface contact of Graphene-based heterostructure Graphene/CrSiTe3 (Gr/CrSiTe3) is modulated by tuning the interfacial distance, along with appling an external electric field. Our first-principles calculations show that the...

Magnetic Topological Insulator Heterostructures: A Review

Topological insulators (TIs) provide intriguing prospects for the future of spintronics due to their large spin-orbit coupling and dissipationless, counter-propagating conduction channels in the surface state. The combination of topological properties and magnetic order can lead to new quantum states including the quantum anomalous Hall effect that was first experimentally realized in Cr-doped (Bi,Sb)₂ Te₃ films. Since magnetic doping can introduce detrimental effects, requiring very low operational temperatures, alternative approaches are explored. Proximity coupling to magnetically ordered systems is an obvious option, with the prospect to raise the temperature for observing the various quantum effects. Here, an overview of proximity coupling and interfacial effects in TI heterostructures is presented, which provides a versatile materials platform for tuning the magnetic and topological properties of these exciting materials. An introduction is first given to the heterostructure growth by molecular beam epitaxy and suitable structural, electronic, and magnetic characterization techniques. Going beyond transition-metal-doped and undoped TI heterostructures, examples of heterostructures are discussed, including rare-earth-doped TIs, magnetic insulators, and antiferromagnets, which lead to exotic phenomena such as skyrmions and exchange bias. Finally, an outlook on novel heterostructures such as intrinsic magnetic TIs and systems including 2D materials is given.

Quantum anomalous Hall effect in Cr2Ge2Te6/Bi2Se3/Cr2Ge2Te6heterostructures

Currently, quantum anomalous Hall (QAH) effect can only be observed at very low temperatures, which severely hinders its utilization from spintronics to quantum computation. Finding or predicting new systems supporting QAH effect at high temperatures remains essential and challenging. This work presents first-principles studies on the proximity effect between Bi₂Se₃slabs and Cr₂Ge₂Te₆(CGT) layers, reporting that Chern insulators are available in CGT/Bi₂Se₃/CGT heterostructures. If the sandwiched Bi₂Se₃slab is 4 quintuple layers (QLs) or thicker, the Chern insulating state is robust against the interfacial stacking manner. If the Bi₂Se₃slab is only 2 or 3 QLs, the CrBi- and CrH-aligned heterostructures are also Chern insulators, while the CrSe-aligned ones are trivial. The Chern insulators support the Hall conductivityσ_xy=e²/hand have energy gaps ranging from 3 to 20 meV, implying QAH effect at higher temperatures. An effective model Hamiltonian is introduced to understand the topological phase of the heterostructures.

Insight into the Temperature Evolution of Electronic Structure and Mechanism of Exchange Interaction in EuS

Discovered in 1962, the divalent ferromagnetic semiconductor EuS (T_C = 16.5 K, E_g = 1.65 eV) has remained constantly relevant to the engineering of novel magnetically active interfaces, heterostructures, and multilayer sequences and to combination with topological materials. Because detailed information on the electronic structure of EuS and, in particular, its evolution across T_C is not well-represented in the literature but is essential for the development of new functional systems, the present work aims at filling this gap. Our angle-resolved photoemission measurements complemented with first-principles calculations demonstrate how the electronic structure of EuS evolves across a paramagnetic-ferromagnetic transition. Our results emphasize the importance of the strong Eu 4f-S 3p mixing for exchange-magnetic splittings of the sulfur-derived bands as well as coupling between f and d orbitals of neighboring Eu atoms to derive the value of T_C accurately. The 4f-3p mixing facilitates the coupling between 4f and 5d orbitals of neighboring Eu atoms, which mainly governs the exchange interaction in EuS.

Recent Progress in Proximity Coupling of Magnetism to Topological Insulators

Inducing long-range magnetic order in 3D topological insulators can gap the Dirac-like metallic surface states, leading to exotic new phases such as the quantum anomalous Hall effect or the axion insulator state. These magnetic topological phases can host robust, dissipationless charge and spin currents or unique magnetoelectric behavior, which can be exploited in low-energy electronics and spintronics applications. Although several different strategies have been successfully implemented to realize these states, to date these phenomena have been confined to temperatures below a few Kelvin. This review focuses on one strategy: inducing magnetic order in topological insulators by proximity of magnetic materials, which has the capability for room temperature operation, unlocking the potential of magnetic topological phases for applications. The unique advantages of this strategy, the important physical mechanisms facilitating magnetic proximity effect, and the recent progress to achieve, understand, and harness proximity-coupled magnetic order in topological insulators are discussed. Some emerging new phenomena and applications enabled by proximity coupling of magnetism and topological materials, such as skyrmions and the topological Hall effect, are also highlighted, and the authors conclude with an outlook on remaining challenges and opportunities in the field.

Evolution of Topological Surface States Following Sb Layer Adsorption on Bi2Se3

Thin antimony layers adsorbed on bismuth selenide (Bi2Se3) present an exciting topological insulator system. Much recent effort has been made to understand the synthesis and electronic properties of the heterostructure, particularly the migration of the topological surface states under adsorption. However, the intertwinement of the topological surface states of the pristine Bi2Se3 substrate with the Sb adlayer remains unclear. In this theoretical work, we apply density functional theory (DFT) to model heterostructures of single and double atomic layers of Sb on a bismuth selenide substrate. We thereby discuss established and alternative structural models, as well as the hybridization of topological surface states with the Sb states. Concerning the geometry, we reveal the possibility of structures with inverted Sb layers which are energetically close to the established ones. The formation energy differences are below 10 meV/atom. Concerning the hybridization, we trace the band structure evolution as a function of the adlayer-substrate distance. By following changes in the connection between the Kramers pairs, we extract a series of topological phase transitions. This allows us to explain the origin of the complex band structure, and ultimately complete our knowledge about this peculiar system.

Topological Hall Effect in a Topological Insulator Interfaced with a Magnetic Insulator

A topological insulator (TI) interfaced with a magnetic insulator (MI) may host an anomalous Hall effect (AHE), a quantum AHE, and a topological Hall effect (THE). Recent studies, however, suggest that coexisting magnetic phases in TI/MI heterostructures may result in an AHE-associated response that resembles a THE but in fact is not. This Letter reports a genuine THE in a TI/MI structure that has only one magnetic phase. The structure shows a THE in the temperature range of T = 2-3 K and an AHE at T = 80-300 K. Over T = 3-80 K, the two effects coexist but show opposite temperature dependencies. Control measurements, calculations, and simulations together suggest that the observed THE originates from skyrmions, rather than the coexistence of two AHE responses. The skyrmions are formed due to a Dzyaloshinskii-Moriya interaction (DMI) at the interface; the DMI strength estimated is substantially higher than that in heavy metal-based systems.

Recent Advances in Two-Dimensional Spintronics

Spintronics is the most promising technology to develop alternative multi-functional, high-speed, low-energy electronic devices. Due to their unusual physical characteristics, emerging two-dimensional (2D) materials provide a new platform for exploring novel spintronic devices. Recently, 2D spintronics has made great progress in both theoretical and experimental researches. Here, the progress of 2D spintronics has been reviewed. In the last, the current challenges and future opportunities have been pointed out in this field.

Absence of Magnetic Proximity Effect at the Interface of Bi_{2}Se_{3} and (Bi,Sb)_{2}Te_{3} with EuS

We performed x-ray magnetic circular dichroism (XMCD) measurements on heterostructures comprising topological insulators (TIs) of the (Bi,Sb)_{2}(Se,Te)_{3} family and the magnetic insulator EuS. XMCD measurements allow us to investigate element-selective magnetic proximity effects at the very TI/EuS interface. A systematic analysis reveals that there is neither significant induced magnetism within the TI nor an enhancement of the Eu magnetic moment at such interface. The induced magnetic moments in Bi, Sb, Te, and Se sites are lower than the estimated detection limit of the XMCD measurements of ∼10^{-3}  μ_{B}/at.

Topologization of β-antimonene on Bi2Se3 via proximity effects

Topological surface states usually emerge at the boundary between a topological and a conventional insulator. Their precise physical character and spatial localization depend on the complex interplay between the chemical, structural and electronic properties of the two insulators in contact. Using a lattice-matched heterointerface of single and double bilayers of β-antimonene and bismuth selenide, we perform a comprehensive experimental and theoretical study of the chiral surface states by means of microscopy and spectroscopic measurements complemented by first-principles calculations. We demonstrate that, although β-antimonene is a trivial insulator in its free-standing form, it inherits the unique symmetry-protected spin texture from the substrate via a proximity effect that induces outward migration of the topological state. This "topologization" of β-antimonene is found to be driven by the hybridization of the bands from either side of the interface.

Exchange Bias in Magnetic Topological Insulator Superlattices

Magnetic doping and proximity coupling can open a band gap in a topological insulator (TI) and give rise to dissipationless quantum conduction phenomena. Here, by combining these two approaches, we demonstrate a novel TI superlattice structure that is alternately doped with transition and rare earth elements. An unexpected exchange bias effect is unambiguously confirmed in the superlattice with a large exchange bias field using magneto-transport and magneto-optical techniques. Further, the Curie temperature of the Cr-doped layers in the superlattice is found to increase by 60 K compared to a Cr-doped single-layer film. This result is supported by density-functional-theory calculations, which indicate the presence of antiferromagnetic ordering in Dy:Bi2Te3 induced by proximity coupling to Cr:Sb2Te3 at the interface. This work provides a new pathway to realizing the quantum anomalous Hall effect at elevated temperatures and axion insulator state at zero magnetic field by interface engineering in TI heterostructures.

Changes of Magnetism in a Magnetic Insulator due to Proximity to a Topological Insulator

We report the modification of magnetism in a magnetic insulator Y_{3}Fe_{5}O_{12} thin film by topological surface states (TSS) in an adjacent topological insulator Bi_{2}Se_{3} thin film. Ferromagnetic resonance measurements show that the TSS in Bi_{2}Se_{3} produces a perpendicular magnetic anisotropy, results in a decrease in the gyromagnetic ratio, and enhances the damping in Y_{3}Fe_{5}O_{12}. Such TSS-induced changes become more pronounced as the temperature decreases from 300 to 50 K. These results suggest a completely new approach for control of magnetism in magnetic thin films.

High-Temperature Anomalous Hall Effect in a Transition Metal Dichalcogenide Ferromagnetic Insulator Heterostructure

Integration of transition metal dichalcogenides (TMDs) on ferromagnetic materials (FM) may yield fascinating physics and promise for electronics and spintronic applications. In this work, high-temperature anomalous Hall effect (AHE) in the TMD ZrTe₂ thin film using a heterostructure approach by depositing it on a ferrimagnetic insulator YIG (Y₃Fe₅O₁₂, yttrium iron garnet) is demonstrated. In this heterostructure, significant anomalous Hall effect can be observed at temperatures up to at least 400 K, which is a record high temperature for the observation of AHE in TMDs, and the large R_AHE is more than 1 order of magnitude larger than those previously reported values in topological insulators or TMD-based heterostructures. A complicated interface with additional ZrO₂ and amorphous YIG layers is actually observed between ZrTe₂ and YIG. The magnetization of interfacial reaction-induced ZrO₂ and YIG is believed to play a crucial role in the induced high-temperature AHE in the ZrTe₂. These results present a promising system for the spintronic device applications, and it may shed light on the designing approach to introduce magnetism to TMDs at room temperature.

Magnetic proximity and nonreciprocal current switching in a monolayer WTe2 helical edge

The integration of diverse electronic phenomena, such as magnetism and nontrivial topology, into a single system is normally studied either by seeking materials that contain both ingredients, or by layered growth of contrasting materials^1-9. The ability to simply stack very different two-dimensional van der Waals materials in intimate contact permits a different approach^10,11. Here we use this approach to couple the helical edges states in a two-dimensional topological insulator, monolayer WTe₂ (refs. ^12-16), to a two-dimensional layered antiferromagnet, CrI₃ (ref. ¹⁷). We find that the edge conductance is sensitive to the magnetization state of the CrI₃, and the coupling can be understood in terms of an exchange field from the nearest and next-nearest CrI₃ layers that produces a gap in the helical edge. We also find that the nonlinear edge conductance depends on the magnetization of the nearest CrI₃ layer relative to the current direction. At low temperatures this produces an extraordinarily large nonreciprocal current that is switched by changing the antiferromagnetic state of the CrI₃.

Signature of a pair of Majorana zero modes in superconducting gold surface states

Under certain conditions, a fermion in a superconductor can separate in space into two parts known as Majorana zero modes, which are immune to decoherence from local noise sources and are attractive building blocks for quantum computers. Promising experimental progress has been made to demonstrate Majorana zero modes in materials with strong spin-orbit coupling proximity coupled to superconductors. Here we report signatures of Majorana zero modes in a material platform utilizing the surface states of gold. Using scanning tunneling microscope to probe EuS islands grown on top of gold nanowires, we observe two well-separated zero-bias tunneling conductance peaks aligned along the direction of the applied magnetic field, as expected for a pair of Majorana zero modes. This platform has the advantage of having a robust energy scale and the possibility of realizing complex designs using lithographic methods.

Two-dimensional ferromagnetic superlattices

Mechanically exfoliated two-dimensional ferromagnetic materials (2D FMs) possess long-range ferromagnetic order and topologically nontrivial skyrmions in few layers. However, because of the dimensionality effect, such few-layer systems usually exhibit much lower Curie temperature (T_C) compared to their bulk counterparts. It is therefore of great interest to explore effective approaches to enhance their T_C, particularly in wafer-scale for practical applications. Here, we report an interfacial proximity-induced high-T_C 2D FM Fe₃GeTe₂ (FGT) via A-type antiferromagnetic material CrSb (CS) which strongly couples to FGT. A superlattice structure of (FGT/CS)_n, where n stands for the period of FGT/CS heterostructure, has been successfully produced with sharp interfaces by molecular-beam epitaxy on 2-inch wafers. By performing elemental specific X-ray magnetic circular dichroism (XMCD) measurements, we have unequivocally discovered that T_C of 4-layer Fe₃GeTe₂ can be significantly enhanced from 140 K to 230 K because of the interfacial ferromagnetic coupling. Meanwhile, an inverse proximity effect occurs in the FGT/CS interface, driving the interfacial antiferromagnetic CrSb into a ferrimagnetic state as evidenced by double-switching behavior in hysteresis loops and the XMCD spectra. Density functional theory calculations show that the Fe-Te/Cr-Sb interface is strongly FM coupled and doping of the spin-polarized electrons by the interfacial Cr layer gives rise to the T_C enhancement of the Fe₃GeTe₂ films, in accordance with our XMCD measurements. Strikingly, by introducing rich Fe in a 4-layer FGT/CS superlattice, T_C can be further enhanced to near room temperature. Our results provide a feasible approach for enhancing the magnetic order of few-layer 2D FMs in wafer-scale and render opportunities for realizing realistic ultra-thin spintronic devices.

Fluctuation-Induced Torque on a Topological Insulator out of Thermal Equilibrium

Topological insulators with the time reversal symmetry broken exhibit strong magnetoelectric and magneto-optic effects. While these effects are well understood in or near equilibrium, nonequilibrium physics is richer yet less explored. We consider a topological insulator thin film, weakly coupled to a ferromagnet, out of thermal equilibrium with a cold environment (quantum electrodynamics vacuum). We show that the heat flow to the environment is strongly circularly polarized, thus carrying away angular momentum and exerting a purely fluctuation-driven torque on the topological insulator film. Utilizing the Keldysh framework, we investigate the universal nonequilibrium response of the TI to the temperature difference with the environment. Finally, we argue that experimental observation of this effect is within reach.

Chiral spin ordering of electron gas in solids with broken time reversal symmetry

In this work we manifest that an electrostatic disorder in conducting systems with broken time reversal symmetry universally leads to a chiral ordering of the electron gas giving rise to skyrmion-like textures in spatial distribution of the electron spin density. We describe a microscopic mechanism underlying the formation of the equilibrium chiral spin textures in two-dimensional systems with spin-orbit interaction and exchange spin splitting. We have obtained analytical expressions for spin-density response functions and have analyzed both local and non-local spin response to electrostatic perturbations for systems with parabolic-like and Dirac electron spectra. With the proposed theory we come up with a concept of controlling spin chirality by electrical means.

Large Anomalous Hall Effect in Topological Insulators with Proximitized Ferromagnetic Insulators

We report a proximity-driven large anomalous Hall effect in all-telluride heterostructures consisting of the ferromagnetic insulator Cr_{2}Ge_{2}Te_{6} and topological insulator (Bi,Sb)_{2}Te_{3}. Despite small magnetization in the (Bi,Sb)_{2}Te_{3} layer, the anomalous Hall conductivity reaches a large value of 0.2e^{2}/h in accord with a ferromagnetic response of the Cr_{2}Ge_{2}Te_{6}. The results show that the exchange coupling between the surface state of the topological insulator and the proximitized Cr_{2}Ge_{2}Te_{6} layer is effective and strong enough to open the sizable exchange gap in the surface state.

Superconductivity in the Surface State of Noble Metal Gold and its Fermi Level Tuning by EuS Dielectric

The induced superconductivity (SC) in a robust and scalable quantum material with strong Rashba spin-orbit coupling is particularly attractive for generating topological superconductivity and Majorana bound states (MBS). Gold (111) thin film has been proposed as a promising candidate because of the large Rashba energy, the predicted topological nature, and the possibility for large-scale MBS device fabrications. We experimentally demonstrate two important steps towards achieving such a goal. We successfully show induced SC in the Shockley surface state (SS) of ultrathin Au(111) layers grown over epitaxial vanadium films, which is easily achievable on a wafer scale. The emergence of SC in the SS, which is physically separated from a bulk superconductor, is attained by indirect quasiparticle scattering processes instead of by conventional interfacial Andreev reflections. We further show the ability to tune the SS Fermi level (E_{F}) by interfacing SS with a high-κ dielectric ferromagnetic insulator EuS. The shift of E_{F} from ∼550 to ∼34  mV in superconducting SS is an important step towards realizing MBS in this robust system.

Observation of Interfacial Antiferromagnetic Coupling between Magnetic Topological Insulator and Antiferromagnetic Insulator

Inducing magnetic orders in a topological insulator (TI) to break its time reversal symmetry has been predicted to reveal many exotic topological quantum phenomena. The manipulation of magnetic orders in a TI layer can play a key role in harnessing these quantum phenomena toward technological applications. Here we fabricated a thin magnetic TI film on an antiferromagnetic (AFM) insulator Cr₂O₃ layer and found that the magnetic moments of the magnetic TI layer and the surface spins of the Cr₂O₃ layers favor interfacial AFM coupling. Field cooling studies show a crossover from negative to positive exchange bias clarifying the competition between the interfacial AFM coupling energy and the Zeeman energy in the AFM insulator layer. The interfacial exchange coupling also enhances the Curie temperature of the magnetic TI layer. The unique interfacial AFM alignment in magnetic TI on AFM insulator heterostructures opens a new route toward manipulating the interplay between topological states and magnetic orders in spin-engineered heterostructures, facilitating the exploration of proof-of-concept TI-based spintronic and electronic devices with multifunctionality and low power consumption.

Band structure engineering in 3D topological insulators

The discovery of novel topological phases has revolutionized the way we think about electronic matter. Topologically protected states have been demonstrated for many materials, however, creating materials that exhibit desired properties often remains a challenge. For example, one of the key challenges in three dimensional topological insulators has been the realization of insulating bulk, such that the unique properties of surface states could be fully employed in electron transport applications. Further challenges are in creating materials that simultaneously exhibit states protected by various symmetries on their different surfaces, inducing magnetic exchange coupling into the topological materials, as well as potentially creating non-trivial transient electronic states. This review presents theoretical concepts and a selection of experimental results from the point view of a spectroscopist, and as such might be useful for physicists who want to get familiar with the key concepts in a self-contained form with formalism reduced to readily understandable concepts.

Magnetizing topological surface states of Bi2Se3 with a CrI3 monolayer

To magnetize surfaces of topological insulators without damaging their topological feature is a crucial step for the realization of the quantum anomalous Hall effect (QAHE) and remains as a challenging task. Through density functional calculations, we found that adsorption of a semiconducting two-dimensional van der Waals (2D-vdW) ferromagnetic CrI₃ monolayer can create a sizable spin splitting at the Dirac point of the topological surface states of Bi₂Se₃ films. Furthermore, general rules that connect different quantum and topological parameters are established through model analyses. This work provides a useful guideline for the realization of QAHE at high temperatures in heterostructures of 2D-vdW magnetic monolayers and topological insulators.

Axion Insulator State in a Ferromagnet/Topological Insulator/Antiferromagnet Heterostructure

We propose the use of ferromagnetic insulator MnBi₂Se₄/Bi₂Se₃/antiferromagnetic insulator Mn₂Bi₂Se₅ heterostructures for the realization of the axion insulator state. Importantly, the axion insulator state in such heterostructures only depends on the magnetization of the ferromagnetic insulator and, hence, can be observed in a wide range of external magnetic fields. Using density functional calculations and model Hamiltonian simulations, we find that the top and bottom surfaces have opposite half-quantum Hall conductances, [Formula: see text] and [Formula: see text], with a sizable global spin gap of 5.1 meV opened for the topological surface states of Bi₂Se₃. Our work provides a new strategy for the search of axion insulators by using van der Waals antiferromagnetic insulators along with three-dimensional topological insulators.

New Universal Type of Interface in the Magnetic Insulator/Topological Insulator Heterostructures

Magnetic proximity effect at the interface between magnetic and topological insulators (MIs and TIs) is considered to have great potential in spintronics as, in principle, it allows realizing the quantum anomalous Hall and topological magneto-electric effects (QAHE and TME). Although an out-of-plane magnetization induced in a TI by the proximity effect was successfully probed in experiments, first-principles calculations reveal that a strong electrostatic potential mismatch at abrupt MI/TI interfaces creates harmful trivial states rendering both the QAHE and TME unfeasible in practice. Here on the basis of recent progress in formation of planar self-assembled single layer MI/TI heterostructure (T. Hirahara et al. Nano Lett. 2017 , 17 , 3493 - 3500 ), we propose a conceptually new type of the MI/TI interfaces by means of density functional theory calculations. By considering MnSe/Bi₂Se₃, MnTe/Bi₂Te₃, and EuS/Bi₂Se₃ we demonstrate that, instead of a sharp MI/TI interface clearly separating the two subsystems, it is energetically far more favorable to form a built-in interface via insertion of the MI film inside the TI's surface quintuple layer (e.g., Se-Bi-Se-[MnSe]-Bi-Se) where it forms a bulk-like MI structure. This results in a smooth MI-to-TI connection that yields the interface electronic structure essentially free of trivial states. Our findings open a new direction in studies of the MI/TI interfaces and restore their potential for the QAHE and TME observation.

Proximity-induced magnetism and an anomalous Hall effect in Bi2Se3/LaCoO3: a topological insulator/ferromagnetic insulator thin film heterostructure

Inducing magnetism in a topological insulator (TI) by exchange coupling with a ferromagnetic insulator (FMI) will break the time-reversal symmetry of topological surface states, offering possibilities to realize several predicted novel magneto-electric effects. Seeking suitable FMI materials is crucial for the coupling of heterojunctions, and yet is challenging as well and only a few kinds have been explored. In this report, we introduce epitaxial LaCoO3 thin films on a SrTiO3 substrate, which is an insulating ferromagnet with a Curie temperature of TC ∼ 85 K, to be combined with TIs for proximity coupling. Thin films of the prototype topological insulator, Bi2Se3, are successfully grown onto the (001) surface of LaCoO3/SrTiO3, forming a high-quality TI/FMI heterostructure with a sharp interface. The magnetic and transport measurements manifest the emergence of a ferromagnetic phase in Bi2Se3 films, with additional induced moments and a suppressed weak antilocalization effect, while preserving the carrier mobility of the intrinsic Bi2Se3 films at the same time. Moreover, a signal of an anomalous Hall effect is observed and persists up to temperatures above 100 K, paving the way towards spintronic device applications.

Proximity-Induced Magnetic Order in a Transferred Topological Insulator Thin Film on a Magnetic Insulator

Breaking the time reversal symmetry (TRS) in a topological insulator (TI) by introducing a magnetic order gives rise to exotic quantum phenomena. One of the promising routes to inducing a magnetic order in a TI is utilizing magnetic proximity effect between a TI and a strong magnetic insulator (MI). In this article, we demonstrate a TI/MI heterostructure prepared through transferring a molecular beam epitaxy (MBE)-grown Bi₂Se₃ film onto a yttrium iron garnet (YIG) substrate via wet transfer. The transferred Bi₂Se₃ exhibits excellent quality over a large scale. Moreover, through wet transfer we are able to engineer the interface and perform a comparative study to probe the proximity coupling between Bi₂Se₃ and YIG under different interface conditions. A detailed investigation of both the anomalous Hall effect and quantum corrections to the conductivity in magnetotransport measurements reveals an induced magnetic order as well as TRS breaking in the transferred Bi₂Se₃ film on YIG. In contrast, a thin layer of AlO _x at the interface obstructs the proximity coupling and preserves the TRS, indicating the critical role of the interface in mediating magnetic proximity effect.

Non-Dirac Chern insulators with large band gaps and spin-polarized edge states

Based on first-principles calculations and k·p models, we demonstrate that PbC/MnSe heterostructures are a non-Dirac type of Chern insulator with very large band gaps (244 meV) and exotically half-metallic edge states, providing the possibilities of realizing very robust, completely spin polarized, and dissipationless spintronic devices from the heterostructures. The achieved extraordinarily large nontrivial band gap can be ascribed to the contribution of the non-Dirac type electrons (composed of px and py) and the very strong atomic spin-orbit coupling (SOC) interaction of the heavy Pb element in the system. Surprisingly, the band structures are found to be sensitive to the different exchange and correlation functionals adopted in the first-principles calculations. Chern insulators with various mechanisms are acquired from them. These discoveries show that the predicted nontrivial topology in PbC/MnSe heterostructures is robust and can be observed in experiments at high temperatures. The system has great potential to have attractive applications in future spintronics.

Relativistic quantum chaos-An emergent interdisciplinary field

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Real-Space Observation of Skyrmionium in a Ferromagnet-Magnetic Topological Insulator Heterostructure

The combination of topological insulators, that is, bulk insulators with gapless, topologically protected surface states, with magnetic order is a love-hate relationship that can unlock new quantum states and exotic physical phenomena, such as the quantum anomalous Hall effect and axion electrodynamics. Moreover, the unusual coupling between topological insulators and ferromagnets can also result in the formation of topological spin textures in the ferromagnetic layer. Skyrmions are topologically protected magnetization swirls that are promising candidates for spintronics memory carriers. Here, we report on the observation of skyrmionium in thin ferromagnetic films coupled to a magnetic topological insulator. The occurrence of skyrmionium, which appears as a soliton composed of two skyrmions with opposite winding numbers, is tied to the ferromagnetic state of the topological insulator. Our work presents a new combination of two important classes of topological materials and may open the door to new topologically inspired information-storage concepts in the future.