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The combination of magnetism and topology in magnetic topological insulators (MTIs) has led to unprecedented advancements of time reversal symmetry-breaking topological quantum physics in the past decade. Compared with the uniform films, the MTI heterostructures provide a better framework to manipulate the spin-orbit coupling and spin properties. In this review, we summarize the fundamental mechanisms related to the physical orders host in (Bi,Sb)2(Te,Se)3-based hybrid systems. Besides, we provide an assessment on the general strategies to enhance the magnetic coupling and spin-orbit torque strength through different structural engineering approaches and effective interfacial interactions. Finally, we offer an outlook of MTI heterostructures-based spintronics applications, particularly in view of their feasibility to achieve room-temperature operation., 33 pages, 11 figures

Atomic termination plays a key role in activating the proximity effect of antiferromagnet., This work reports the ferromagnetism of topological insulator, (Bi,Sb)2Te3 (BST), with a Curie temperature of approximately 120 K induced by magnetic proximity effect (MPE) of an antiferromagnetic CrSe. The MPE was shown to be highly dependent on the stacking order of the heterostructure, as well as the interface symmetry: Growing CrSe on top of BST results in induced ferromagnetism, while growing BST on CrSe yielded no evidence of an MPE. Cr-termination in the former case leads to double-exchange interactions between Cr3+ surface states and Cr2+ bulk states. This Cr3+-Cr2+ exchange stabilizes the ferromagnetic order localized at the interface and magnetically polarizes the BST Sb band. In contrast, Se-termination at the CrSe/BST interface yields no detectable MPE. These results directly confirm the MPE in BST films and provide critical insights into the sensitivity of the surface state.

Integration of a quantum anomalous Hall insulator with a magnetically ordered material provides an additional degree of freedom through which the resulting exotic quantum states can be controlled. Here, an experimental observation is reported of the quantum anomalous Hall effect in a magnetically-doped topological insulator grown on the antiferromagnetic insulator Cr2 O3 . The exchange coupling between the two materials is investigated using field-cooling-dependent magnetometry and polarized neutron reflectometry. Both techniques reveal strong interfacial interaction between the antiferromagnetic order of the Cr2 O3 and the magnetic topological insulator, manifested as an exchange bias when the sample is field-cooled under an out-of-plane magnetic field, and an exchange spring-like magnetic depth profile when the system is magnetized within the film plane. These results identify antiferromagnetic insulators as suitable candidates for the manipulation of magnetic and topological order in topological insulator films.

Topological superconductor is described by a full pairing gap in the bulk with nonzero topological number and gapless surface states consisting of Majorana fermion that is a hypothetical particle of its own. Here, being its own means that a Majorana fermion should be an equal superposition of an electron and a hole state. The emergence of Majorana fermions is the most prominent characteristic of topological superconductors. In particle physics, it is still unclear if there are some elementary particles that are Majorana fermions, but importantly, they are likely to exist as quasiparticle excitations in certain condensed matter systems. It has drawn much attention in the content of Majorana fermions recently in particular the condensed matter physics area, since these Majorana states are ideal platform for non-Abelian statistics studies and can be used to fabricate as topological qubit, thus having great potential application in fault-tolerant topological quantum computation. A general introduction to the remarkable properties of Majorana fermions in condensed matter systems will be introduced following the story from Dirac equation to Majorana equation. Then this review elaborates a variety of routes to topological superconductivity in the realm of condensed mater physics, from Majorana modes in zero dimension to one dimension, that is, Majorana bound state and Majorana edge state. These Majorana states are localized states and propagating states respectively, but still obey non-Abelian statistics and remain their topological properties. Specifically, one-dimensional tight-binding model of a p-wave superconductor and a magnetic Fe chain with superconducting pairing are representative platforms for hosting Majorana bound states at the wires ends. Some emergent topological material systems, such as topological insulator, quantum spin Hall insulator, and quantum anomalous Hall insulator are two-dimensional material systems that can not only accommodate Majorana bound states but also Majorana edge states. Different material systems, from one-dimension quantum wire to two-dimension material system, from hybridized system to intrinsic system, will also be discussed specifically. Relevant theoretical studies and experimental results that show possible signatures of topological superconductivity and Majorana states are summarized as well. Particularly, experimental signatures of these Majorana states, such as zero-bias conductance peaks in tunneling spectra due to Majorana bound states, quantization of conductance in magneto-electric transport measurements due to chiral Majorana edge states, and some unconventional superconductivities in intrinsic topological superconductors will be briefly reviewed. Insights about methods to perspectives to realize topological quantum computation is provided at the end, emphasizing the braiding using different Majorana states. The goal of this review is to provide a general introduction to the subject for either experimentalists or theorists who are new to this field, focusing on the aspects and current progresses which are most important for understanding these basic physics.

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 ...

We investigate the hydrostatic pressure dependence of interfacial superconductivity occurring at the atomically sharp interface between two non-superconducting materials: the topological insulator (TI) Bi2Te3 and the parent compound Fe1+yTe of the chalcogenide iron-based superconductors. Under pressure, a significant increase in the superconducting transition temperature Tc is observed. We interpret our data in the context of a pressure-induced enhanced coupling of the Fe1+yTe interfacial layer with the Bi2Te3 surface state, which modifies the electronic properties of the interface layer in a way that superconductivity emerges and becomes further enhanced under pressure. This demonstrates the important role of the TI in the interfacial superconducting mechanism.

The low occurring temperature of quantum anomalous Hall effect is a result of weak ferromagnetism and trivial band involvement., Quantum anomalous Hall effect has been observed in magnetically doped topological insulators. However, full quantization, up until now, is limited within the sub–1 K temperature regime, although the material’s magnetic ordering temperature can go beyond 100 K. Here, we study the temperature limiting factors of the effect in Cr-doped (BiSb)2Te3 systems using both transport and magneto-optical methods. By deliberate control of the thin-film thickness and doping profile, we revealed that the low occurring temperature of quantum anomalous Hall effect in current material system is a combined result of weak ferromagnetism and trivial band involvement. Our findings may provide important insights into the search for high-temperature quantum anomalous Hall insulator and other topologically related phenomena.

Topological insulators are emergent states of quantum matter that are gapped in the bulk with time-reversal symmetry-preserved gapless edge/surface states, adiabatically distinct from conventional materials. By proximity to various magnets and superconductors, topological insulators show novel physics at the interfaces, which give rise to two new areas named topological spintronics and topological quantum computation. Effects in the former such as the spin torques, spin-charge conversion, topological antiferromagnetic spintronics, and skyrmions realized in topological systems will be addressed. In the latter, a superconducting pairing gap leads to a state that supports Majorana fermions states, which may provide a new path for realizing topological quantum computation. Various signatures of Majorana zero modes/edge mode in topological superconductors will be discussed. The review ends by outlooks and potential applications of topological insulators. Topological superconductors that are fabricated using topological insulators with superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

Geometric Hall effect is induced by the emergent gauge field experienced by the carriers adiabatically passing through certain real-space topological spin textures, which is a probe to non-trivial spin textures, such as magnetic skyrmions. We report experimental indications of spin-texture topological charges induced in heterostructures of a topological insulator (Bi,Sb)2Te3 coupled to an antiferromagnet MnTe. Through a seeding effect, the pinned spins at the interface leads to a tunable modification of the averaged real-space topological charge. This effect experimentally manifests as a modification of the field-dependent geometric Hall effect when the system is field-cooled along different directions. This heterostructure represents a platform for manipulating magnetic topological transitions using antiferromagnetic order., Spin-polarized carriers could show an extra Hall component when moving through certain real-space topological spin textures. Here, He et al. report an exchange bias experienced by the topological spin textures living at the interface between a topological insulator and an adjacent antiferromagnet, suggesting a chiral spin texture is induced.

Magnetic topological insulators such as Cr-doped (Bi,Sb)2Te3 provide a platform for the realization of versatile time-reversal symmetry-breaking physics. By constructing heterostructures with N\'eel order in an antiferromagnetic CrSb and magnetic topological order in Cr-doped (Bi,Sb)2Te3, we realize emergent interfacial magnetic phenomena which can be tailored through artificial structural engineering. Through deliberate geometrical design of heterostructures and superlattices, we demonstrate the use of antiferromagnetic exchange coupling in manipulating the magnetic properties of the topological surface massive Dirac fermions. This work provides a new framework on integrating topological insulators with antiferromagnetic materials and unveils new avenues towards dissipationless topological antiferromagnetic spintronics., Comment: 25 pages, 4 figures

Heavy metals and topological insulators are promising materials for converting charge current into spin current for efficient manipulation of magnetization states in magnetic devices [1]–[5]. One of the most important parameters is the charge-to-spin conversion (CS) efficiency. Improving CS efficiency is critical for reducing write current of the emerging nonvolatile memory technology, spin-orbit torque MRAM (SOT-MRAM) [2], which provides comparable speed with SRAM but with a much higher memory capacity. Here, we measure CS efficiency in various topological insulators (TIs) using second-harmonic method (2eo-method) and obtain a record-high value 8.33±0.65 for insulating (BiSb)2 Te3 at room temperature. We first establish the consistency of CS efficiency obtained between spin-torque ferromagnetic resonance (ST-FMR) and 2eo-method. Then, we systematically investigate the CS efficiency in a bilayer consisting of a metallic Bi2Se3 and a CoFeB thin film using 2eo-method. By tuning the Fermi level of TI layer into bulk band gap using (BiSb)2 Te3, we improve the CS efficiency by an order of magnitude.

The Bi2Te3/FeTe heterostructure intersects several phenomena and key classes of materials in condensed matter physics: topological insulators, superconductivity, magnetism, and the physics of interfaces. While neither the topological insulator (Bi2Te3) nor the iron chalcogenide (FeTe) are themselves superconductors, superconductivity forms in a thin 7nm interfacial layer between the two. The restricted dimensionality and the extraordinarily conductive normal state, possibly sourced by the topologically protected surface states, have led to the observation of novel phenomena such as the Likharev vortex explosion and transitions in behavior resulting from the interplay between current induced depairing and the Berezinski-Kosterlitz-Thouless regime. Bi2Te3/FeTe also displays the anomalous oscillatory magnetoresistance phenomenon, which we had previously observed in cuprates.

Recently, a logarithmic decrease of conductivity has been observed in topological insulators at low temperatures, implying a tendency of localization of surface electrons. Here, we report quantum transport experiments on the topological insulator Bi2Te3 thin films with arrayed antidot nanostructures. With increasing density of the antidots, a systematic decrease is observed in the slope of the logarithmic temperature-dependent conductivity curves, indicating the electron-electron interaction can be tuned by the antidots. Meanwhile, the weak anti-localization effect revealed in magnetoconductivity exhibits an enhanced dominance of electron-electron interaction among decoherence mechanisms. The observation can be understood from an antidot-induced reduction of the effective dielectric constant, which controls the interactions between the surface electrons. Our results clarify the indispensable role of the electron-electron interaction in the localization of surface electrons and indicate the localization of surface electrons in an interacting topological insulator., 27 pages, article+supplemental materials, published in ACS Nano

A propagating Majorana mode Although Majorana fermions remain elusive as elementary particles, their solid-state analogs have been observed in hybrid semiconductor-superconductor nanowires. In a nanowire setting, the Majorana states are localized at the ends of the wire. He et al. built a two-dimensional heterostructure in which a one-dimensional Majorana mode is predicted to run along the sample edge (see the Perspective by Pribiag). The heterostructure consisted of a quantum anomalous Hall insulator (QAHI) bar contacted by a superconductor. The authors used an external magnetic field as a “knob” to tune into a regime where a Majorana mode was propagating along the edge of the QAHI bar covered by the superconductor. A signature of this propagation—half-quantized conductance—was then observed in transport experiments. Science , this issue p. 294 ; see also p. 252

In the interfacial superconductor Bi2Te3/Fe1+yTe, two dimensional superconductivity occurs in direct vicinity to the surface state of a topological insulator. If this state were to become involved in superconductivity, under certain conditions a topological superconducting state could be formed, which is of high interest due to the possibility of creating Majorana fermionic states. We report directional point-contact spectroscopy data on the novel Bi2Te3/Fe1+yTe interfacial superconductor for a Bi2Te3 thickness of 9 quintuple layers, bonded by van der Waals epitaxy to a Fe1+yTe film at an atomically sharp interface. Our data show highly unconventional superconductivity, which appears as complex as in the cuprate high temperature superconductors. A very large superconducting twin-gap structure is replaced by a pseudogap above ~12 K which persists up to 40 K. While the larger gap shows unconventional order parameter symmetry and is attributed to a thin FeTe layer in proximity to the interface, the smaller gap is associated with superconductivity induced via the proximity effect in the topological insulator Bi2Te3.

Ferromagnetism in topological insulators (TIs) opens a topologically non-trivial exchange band gap, providing an exciting platform to manipulate the topological order through an external magnetic field. Here, we experimentally show that the surface of an antiferromagnetic thin film can independently control the topological order of the top and the bottom surface states of a TI thin film through proximity couplings. During the magnetization reversal in a field scan, two intermediate spin configurations stem from unsynchronized magnetic switchings of the top and the bottom AFM/TI interfaces. These magnetic configurations are shown to result in new topological phases with non-zero Chern numbers for each surface, introducing two counter-propagating chiral edge modes inside the exchange gap. This change in the number of transport channels, as the result of the topological transitions, induces antisymmetric magneto-resistance spikes during the magnetization reversal. With the high Neel ordering temperature provided by the antiferromagnetic layers, the signature of the induced topological transition persists in transport measurements up to a temperature of around 90 K, a factor of three over the Curie temperature in a typical magnetically doped TI thin film.

Superconductivity at the interface of a heterostructure confined to nanometer-sized scale offers unique opportunities to study the exotic physics of two-dimensional superconductivity. The realization of superconductivity at the interface between a topological insulator and an iron-chalcogenide compound is highly attractive for exploring several recent theoretical predictions involving these two new classes of materials. Here, we report transport measurements on a Bi2Te3/FeTe heterostructure fabricated via van der Waals epitaxy, which demonstrate superconductivity at the interface induced by the Bi2Te3 epilayer with thickness even down to one quintuple layer. The two-dimensional nature of the observed superconductivity with the highest transition temperature around 12 K was verified by the existence of a Berezinsky-Kosterlitz-Thouless transition and the diverging ratio of in-plane to out-plane upper critical field on approaching the superconducting transition temperature. With the combination of interface superconductivity and Dirac surface states of Bi2Te3, the heterostructure studied in this work provides a novel platform for realizing Majorana fermions., 24 pages, 5 figures and supplementary information