Landau quantization and the thickness limit of topological insulator thin films of Sb2Te3

Double-sided van der Waals epitaxy of topological insulators across an atomically thin membrane

Atomically thin van der Waals (vdW) films provide a material platform for the epitaxial growth of quantum heterostructures. However, unlike the remote epitaxial growth of three-dimensional bulk crystals, the growth of two-dimensional material heterostructures across atomic layers has been limited due to the weak vdW interaction. Here we report the double-sided epitaxy of vdW layered materials through atomic membranes. We grow vdW topological insulators Sb2Te3 and Bi2Se3 by molecular-beam epitaxy on both surfaces of atomically thin graphene or hexagonal boron nitride, which serve as suspended two-dimensional vdW substrate layers. Both homo- and hetero-double-sided vdW topological insulator tunnel junctions are fabricated, with the atomically thin hexagonal boron nitride acting as a crystal-momentum-conserving tunnelling barrier with abrupt and epitaxial interfaces. By performing field-angle-dependent magneto-tunnelling spectroscopy on these devices, we reveal the energy-momentum-spin resonance of massless Dirac electrons tunnelling between helical Landau levels developed in the topological surface states at the interfaces.

2D Lateral Heterojunction Arrays with Tailored Interface Band Bending

Two-dimensional (2D) lateral heterojunction arrays, characterized by well-defined electronic interfaces, hold significant promise for advancing next-generation electronic devices. Despite this potential, the efficient synthesis of high-density lateral heterojunctions with tunable interfacial band alignment remains a challenging. Here, a novel strategy is reported for the fabrication of lateral heterojunction arrays between monolayer Si2Te2 grown on Sb2Te3 (ML-Si2Te2@Sb2Te3) and one-quintuple-layer Sb2Te3 grown on monolayer Si2Te2 (1QL-Sb2Te3@ML-Si2Te2) on a p-doped Sb2Te3 substrate. The site-specific formation of numerous periodically arranged 2D ML-Si2Te2@Sb2Te3/1QL-Sb2Te3@ML-Si2Te2 lateral heterojunctions is realized solely through three epitaxial growth steps of thick-Sb2Te3, ML-Si2Te2, and 1QL-Sb2Te3 films, sequentially. More importantly, the precisely engineering of the interfacial band alignment is realized, by manipulating the substrate's p-doping effect with lateral spatial dependency, on each ML-Si2Te2@Sb2Te3/1QL-Sb2Te3@ML-Si2Te2 junction. Atomically sharp interfaces of the junctions with continuous lattices are observed by scanning tunneling microscopy. Scanning tunneling spectroscopy measurements directly reveal the tailored type-II band bending at the interface. This reported strategy opens avenues for advancing lateral epitaxy technology, facilitating practical applications of 2D in-plane heterojunctions.

Topological minibands and interaction driven quantum anomalous Hall state in topological insulator based moiré heterostructures

The presence of topological flat minibands in moiré materials provides an opportunity to explore the interplay between topology and correlation. In this work, we study moiré minibands in topological insulator films with two hybridized surface states under a moiré superlattice potential created by two-dimensional insulating materials. We show the lowest conduction (highest valence) Kramers' pair of minibands can beZ 2 non-trivial when the minima (maxima) of moiré potential approximately form a hexagonal lattice with six-fold rotation symmetry. Coulomb interaction can drive the non-trivial Kramers' minibands into the quantum anomalous Hall state when they are half-filled, which is further stabilized by applying external gate voltages to break inversion. We propose the monolayer Sb2 on top of Sb2Te3 films as a candidate based on first principles calculations. Our work demonstrates the topological insulator based moiré heterostructure as a potential platform for studying interacting topological phases.

3D Quantum Anomalous Hall Effect in Magnetic Topological Insulator Trilayers of Hundred-Nanometer Thickness

Magnetic topological states refer to a class of exotic phases in magnetic materials with the non-trivial topological property determined by magnetic spin configurations. An example of such states is the quantum anomalous Hall (QAH) state, which is a zero magnetic field manifestation of the quantum Hall effect. Current research in this direction focuses on QAH insulators with a thickness of less than 10 nm. Here, molecular beam epitaxy (MBE) is employed to synthesize magnetic TI trilayers with a thickness of up to ≈106 nm. It is found that these samples exhibit well-quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field. By varying the magnetic dopants, gate voltages, temperature, and external magnetic fields, the properties of these thick QAH insulators are examined and the robustness of the 3D QAH effect is demonstrated. The realization of the well-quantized 3D QAH effect indicates that the nonchiral side surface states of the thick magnetic TI trilayers are gapped and thus do not affect the QAH quantization. The 3D QAH insulators of hundred-nanometer thickness provide a promising platform for the exploration of fundamental physics, including axion physics and image magnetic monopole, and the advancement of electronic and spintronic devices to circumvent Moore's law.

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.

Metavalent Bonding in Layered Phase-Change Memory Materials

Metavalent bonding (MVB) is characterized by the competition between electron delocalization as in metallic bonding and electron localization as in covalent or ionic bonding, serving as an essential ingredient in phase-change materials for advanced memory applications. The crystalline phase-change materials exhibits MVB, which stems from the highly aligned p orbitals and results in large dielectric constants. Breaking the alignment of these chemical bonds leads to a drastic reduction in dielectric constants. In this work, it is clarified how MVB develops across the so-called van der Waals-like gaps in layered Sb2 Te3 and Ge-Sb-Te alloys, where coupling of p orbitals is significantly reduced. A type of extended defect involving such gaps in thin films of trigonal Sb2 Te3 is identified by atomic imaging experiments and ab initio simulations. It is shown that this defect has an impact on the structural and optical properties, which is consistent with the presence of non-negligible electron sharing in the gaps. Furthermore, the degree of MVB across the gaps is tailored by applying uniaxial strain, which results in a large variation of dielectric function and reflectivity in the trigonal phase. At last, design strategies are provided for applications utilizing the trigonal phase.

Structural Defects and Ferromagnetic Signature of V-Doped Sb2Te3 Thin Films Grown on SrTiO3(001) Produced by RF-Magnetron Sputtering

Thin films of V-doped Sb₂Te₃ compounds were fabricated by co-deposition of Sb₂Te₃ and V using rf-magnetron sputtering onto SrTiO₃(001) substrates kept at 570 K. The microstructures of the films were characterized using transmission electron microscopy (TEM) and electron diffraction. The crystal structure of the sputtered film (Sb₃₈V₂Te₆₀) is the Bi₂Te₃-type structure with lattice parameters of a = 0.44 ± 0.03 nm and c = 3.02 ± 0.02 nm. A combination of cross-sectional and plan-view TEM observations revealed the preferential orientation of the c axis in the film's normal direction. A thin amorphous layer exists between the Sb₂Te₃ thin film and the SrTiO₃ substrate. The interfacial amorphous layer relaxes the strain between the thin film and the substrate, and hence, it should promote the growth of a low-index atomic plane with a low surface free energy (i.e., (0001) of the Sb₂Te₃). The onset of ferromagnetic order was detected at temperatures below 70 K. A remarkable increase in magnetization was detected in the film's normal direction, which corresponds to the magnetic easy axis (i.e., c axis of the Sb₂Te₃). V³⁺ ions substituting Sb sites should contribute to ferromagnetism at low temperatures.

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.

Berry-Phase Switch in Electrostatically Confined Topological Surface States

Here, we visualize the trapping of topological surface states in the circular n-p junctions on the top surface of the seven-quintuple-layer three dimensional (3D) topological insulator (TI) Sb_{2}Te_{3} epitaxial films. As shown by spatially dependent and field-dependent tunneling spectra, these trapped resonances show field-induced splittings between the degenerate time-reversal-symmetric states at zero magnetic field. These behaviors are attributed unambiguously to Berry-phase switch by comparing the experimental data with both numerical and semiclassical simulations. The successful electrostatic trapping of topological surface states in epitaxial films and the observation of Berry-phase switch provide a rich platform of exploiting new ideas for TI-based quantum devices.

Bulk band structure of Sb2Te3 determined by angle-resolved photoemission spectroscopy

The bulk band structure of the topological insulator Sb₂Te₃ is investigated by angle-resolved photoemission spectroscopy. Of particular interest is the dispersion of the uppermost valence band with respect to the topological surface state Dirac point. The valence band maximum has been calculated to be either near the Brillouin zone centre or in a low-symmetry position in the -M̄ azimuthal direction. In order to observe the full energy range of the valence band, the strongly p-doped crystals are counter-doped by surface alkali adsorption. The data show that the absolute valence band maximum is likely to be found at the bulk Γ point and predictions of a low-symmetry position with an energy higher than the surface Dirac point can be ruled out.

Topological Anderson Insulator in Cation-Disordered Cu2ZnSnS4

We present the first candidate for the realization of a disorder-induced Topological Anderson Insulator in a real material system. High-energy reactive mechanical alloying produces a polymorph of Cu₂ZnSnS₄ with high cation disorder. Density functional theory calculations show an inverted ordering of bands at the Brillouin zone center for this polymorph, which is in contrast to its ordered phase. Adiabatic continuity arguments establish that this disordered Cu₂ZnSnS₄ can be connected to the closely related Cu₂ZnSnSe₄, which was previously predicted to be a 3D topological insulator, while band structure calculations with a slab geometry reveal the presence of robust surface states. This evidence makes a strong case in favor of a novel topological phase. As such, the study opens up a window to understanding and potentially exploiting topological behavior in a rich class of easily-synthesized multinary, disordered compounds.

Superconductivity of topological insulator Sb2Te3-ySeyunder pressure

The crystal structures of Sb₂Te_3-ySe_y(y= 0.6 andy= 1.2) at 0-24 GPa were investigated by synchrotron x-ray diffraction. The stoichiometry of Sb₂Te_3-ySe_yused in this study was determined to be Sb₂Te_2.19(9)Se_0.7(2)fory= 0.6 and Sb₂Te_1.7(1)Se_1.3(3)fory= 1.2, on the basis of energy-dispersive x-ray spectroscopy. The sample of Sb₂Te_2.19(9)Se_0.7(2)showed a structural phase transition from a rhombohedral structure (space group No. 166,R3¯m) (phase I) to a monoclinic structure (space group No. 12,C2/m) (phase II), with increasing pressure up to ∼9 GPa. A new structural phase (phase II') emerged at 17.7 GPa, a monoclinic structure with the space groupC2/c(No. 15). Finally, a 9/10-fold monoclinic structure (space group No. 12,C2/m) (phase III) was observed at 21.8 GPa. In contrast, the sample of Sb₂Te_1.7(1)Se_1.3(3)provided only phase I (space group No. 166,R3¯m) and phase II (space group No. 12,C2/m), showing one structural phase transition from 0-19.5 GPa. These samples were not superconductors at ambient pressure, but superconductivity suddenly appeared with increasing pressure. Superconductivity with superconducting transition temperatures (T_c's) of 2 and 4 K was observed above 6 GPa in phase I of Sb₂Te_2.19(9)Se_0.7(2). In this sample, theT_cvalues of 6 and 9 K were observed in phase II and phase II' or III of Sb₂Te_2.19(9)Se_0.7(2), respectively. Superconductivity withT_c's of 4 and 5 K suddenly emerged in Sb₂Te_1.7(1)Se_1.3(3)at 13.6 GPa, which corresponds to phase II, and it evolved to 6.0 K under further increased pressure. AT_cvalue of 9 K was finally found above 15 GPa. The magnetic field dependence ofT_cin phase II of Sb₂Te_2.19(9)Se_0.7(2)and Sb₂Te_1.7(1)Se_1.3(3)followed ap-wave polar model, suggesting topologically nontrivial superconductivity.

Atom-surface van der Waals potentials of topological insulators and semimetals from scattering measurements

The phenomenology of resonant scattering has been known since the earliest experiments upon scattering of atomic beams from surfaces and is a means of obtaining experimental information about the fundamentals of weak adsorption systems in the van der Waals regime. We provide an overview of the experimental approach based on new experimental data for the He-Sb₂Te₃(111) system, followed by a comparative overview and perspective of recent results for topological semimetal and insulator surfaces. Moreover, we shortly discuss the perspectives of calculating helium-surface interaction potentials from ab initio calculations. Our perspective demonstrates that atom-surface scattering provides direct experimental information about the atom-surface interaction in the weak physisorption regime and can also be used to determine the lifetime and mean free path of the trapped atom. We further discuss the effects of elastic and inelastic scattering on the linewidth and lifetime of the trapped He atom with an outlook on future developments and applications.

Progress in Epitaxial Thin-Film Na3 Bi as a Topological Electronic Material

Trisodium bismuthide (Na₃ Bi) is the first experimentally verified topological Dirac semimetal, and is a 3D analogue of graphene hosting relativistic Dirac fermions. Its unconventional momentum-energy relationship is interesting from a fundamental perspective, yielding exciting physical properties such as chiral charge carriers, the chiral anomaly, and weak anti-localization. It also shows promise for realizing topological electronic devices such as topological transistors. Herein, an overview of the substantial progress achieved in the last few years on Na₃ Bi is presented, with a focus on technologically relevant large-area thin films synthesized via molecular beam epitaxy. Key theoretical aspects underpinning the unique electronic properties of Na₃ Bi are introduced. Next, the growth process on different substrates is reviewed. Spectroscopic and microscopic features are illustrated, and an analysis of semiclassical and quantum transport phenomena in different doping regimes is provided. The emergent properties arising from confinement in two dimensions, including thickness-dependent and electric-field-driven topological phase transitions, are addressed, with an outlook toward current challenges and expected future progress.

Materials Screening for Disorder-Controlled Chalcogenide Crystals for Phase-Change Memory Applications

Tailoring the degree of disorder in chalcogenide phase-change materials (PCMs) plays an essential role in nonvolatile memory devices and neuro-inspired computing. Upon rapid crystallization from the amorphous phase, the flagship Ge-Sb-Te PCMs form metastable rocksalt-like structures with an unconventionally high concentration of vacancies, which results in disordered crystals exhibiting Anderson-insulating transport behavior. Here, ab initio simulations and transport experiments are combined to extend these concepts to the parent compound of Ge-Sb-Te alloys, viz., binary Sb2 Te3 , in the metastable rocksalt-type modification. Then a systematic computational screening over a wide range of homologous, binary and ternary chalcogenides, elucidating the critical factors that affect the stability of the rocksalt structure is carried out. The findings vastly expand the family of disorder-controlled main-group chalcogenides toward many more compositions with a tunable bandgap size for demanding phase-change applications, as well as a varying strength of spin-orbit interaction for the exploration of potential topological Anderson insulators.

Polymorphism in Post-Dichalcogenide Two-Dimensional Materials

Two-dimensional (2D) materials exhibit a wide range of atomic structures, compositions, and associated versatility of properties. Furthermore, for a given composition, a variety of different crystal structures (i.e., polymorphs) can be observed. Polymorphism in 2D materials presents a fertile landscape for designing novel architectures and imparting new functionalities. The objective of this Review is to identify the polymorphs of emerging 2D materials, describe their polymorph-dependent properties, and outline methods used for polymorph control. Since traditional 2D materials (e.g., graphene, hexagonal boron nitride, and transition metal dichalcogenides) have already been studied extensively, the focus here is on polymorphism in post-dichalcogenide 2D materials including group III, IV, and V elemental 2D materials, layered group III, IV, and V metal chalcogenides, and 2D transition metal halides. In addition to providing a comprehensive survey of recent experimental and theoretical literature, this Review identifies the most promising opportunities for future research including how 2D polymorph engineering can provide a pathway to materials by design.

Magnetic plasmon resonances in nanostructured topological insulators for strongly enhanced light-MoS2 interactions

Magnetic resonances not only play crucial roles in artificial magnetic materials but also offer a promising way for light control and interaction with matter. Recently, magnetic resonance effects have attracted special attention in plasmonic systems for overcoming magnetic response saturation at high frequencies and realizing high-performance optical functionalities. As novel states of matter, topological insulators (TIs) present topologically protected conducting surfaces and insulating bulks in a broad optical range, providing new building blocks for plasmonics. However, until now, high-frequency (e.g. visible range) magnetic resonances and related applications have not been demonstrated in TI systems. Herein, we report for the first time, to our knowledge, a kind of visible range magnetic plasmon resonances (MPRs) in TI structures composed of nanofabricated Sb₂Te₃ nanogrooves. The experimental results show that the MPR response can be tailored by adjusting the nanogroove height, width, and pitch, which agrees well with the simulations and theoretical calculations. Moreover, we innovatively integrated monolayer MoS₂ onto a TI nanostructure and observed strongly reinforced light-MoS₂ interactions induced by a significant MPR-induced electric field enhancement, remarkable compared with TI-based electric plasmon resonances (EPRs). The MoS₂ photoluminescence can be flexibly tuned by controlling the incident light polarization. These results enrich TI optical physics and applications in highly efficient optical functionalities as well as artificial magnetic materials at high frequencies.

Highly Tunable Spin-Orbit Torque and Anisotropic Magnetoresistance in a Topological Insulator Thin Film Attached to Ferromagnetic Layer

We investigate spin-charge conversion phenomena in hybrid structures of topological insulator thin films and magnetic insulators. We find an anisotropic inverse spin-galvanic effect that yields a highly tunable spin-orbit torque. Concentrating on the quasiballistic limit, we also predict a giant anisotropic magnetoresistance at low dopings. These effects, which have no counterparts in thick topological insulators, depend on the simultaneous presence of the hybridization between the surface states and the in-plane magnetization. Both the inverse spin-galvanic effect and anisotropic magnetoresistance exhibit a strong dependence on the magnetization and the Fermi level position and can be used for spintronics and spin-orbit-torque-based applications at the nanoscale.

Stoichiometric Bi2Se3 topological insulator ultra-thin films obtained through a new fabrication process for optoelectronic applications

A new fabrication process is developed for growing Bi₂Se₃ topological insulators in the form of nanowires/nanobelts and ultra-thin films. It consists of two consecutive procedures: first Bi₂Se₃ nanowires/nanobelts are deposited by standard catalyst free vapour-solid deposition on different substrates positioned inside a quartz tube. Then, the Bi₂Se₃, stuck on the inner surface of the quartz tube, is re-evaporated and deposited in the form of ultra-thin films on new substrates at a temperature below 100 °C, which is of relevance for flexible electronic applications. The method is new, quick, very inexpensive, easy to control and allows obtaining films with different thickness down to one quintuple layer (QL) during the same procedure. The composition and the crystal structure of both the nanowires/nanobelts and the thin films are analysed by different optical, electronic and structural techniques. For the films, scanning tunnelling spectroscopy shows that the Fermi level is positioned in the middle of the energy bandgap as a consequence of the achieved correct stoichiometry. Ultra-thin films, with thickness in the range 1-10 QLs deposited on n-doped Si substrates, show good rectifying properties suitable for their use as photodetectors in the ultra violet-visible-near infrared wavelength range.

Electron-Hole Asymmetry of Surface States in Topological Insulator Sb2Te3 Thin Films Revealed by Magneto-Infrared Spectroscopy

When surface states (SSs) form in topological insulators (TIs), they inherit the properties of bulk bands, including the electron-hole (e-h) asymmetry but with much more profound impacts. Here via combining magneto-infrared spectroscopy with theoretical analysis, we show that e-h asymmetry significantly modifies the SS electronic structures when interplaying with the quantum confinement effect. Compared with the case without e-h asymmetry, the SSs now bear not only a band asymmetry, such as that in the bulk, but also a shift of the Dirac point relative to the bulk bands and a reduction of the hybridization gap of up to 70%. Our results signify the importance of e-h asymmetry in the band engineering of TIs in the thin-film limit.

Scanning tunneling spectroscopy studies of topological materials

Topological materials have become promising materials for next-generation devices by utilizing their exotic electronic states. Their exotic states caused by spin-orbital coupling usually locate on the surfaces or at the edges. Scanning tunneling spectroscopy (STS) is a powerful tool to reveal the local electronic structures of condensed matters. Therefore, STS provides us with an almost perfect method to access the exotic states of topological materials. In this topical review, we report the current investigations by several methods based on the STS technique for layered topological material from transition metal dichalcogenide Weyl semimetals (WTe₂ and MoTe₂) to two dimensional topological insulators (layered bismuth and silicene). The electronic characteristics of these layered topological materials are experimentally identified.

Single crystal growth and ferromagnetism of Cr-doped Sb4Te3

Here we report the single crystal growth, magnetic and transport properties of Cr-doped Sb₄Te₃, (Sb_1-x Cr _x )₄Te₃, with doping concentrations x  =  0.25%, 0.5%, 0.75%, and 1%. The samples with lower doping concentrations are paramagnetic, while ferromagnetism appears in higher doped samples with the highest Curie temperature of 7 K when x  =  1%. Anomalous Hall effect with clear hysteresis loop is observed in the samples with x  =  1%, indicating the intrinsic ferromagnetism in the system. Hall resistivity measurements show the dominant charge carriers are holes and the density of holes increases with the doping concentration. This work provides a possible single-crystalline platform for further experimental researches on the nontrivial band topology in Sb₄Te₃, and enriches the ferromagnetic members in the transition metal doped (Sb₂) _m -Sb₂Te₃ topological material series.

Studies on the origin of the interfacial superconductivity of Sb2Te3/Fe1+yTe heterostructures

The recent discovery of the interfacial superconductivity (SC) of the Bi2Te3/Fe1+yTe heterostructure has attracted extensive studies due to its potential as a novel platform for trapping and controlling Majorana fermions. Here we present studies of another topological insulator (TI)/Fe1+yTe heterostructure, Sb2Te3/Fe1+yTe, which also has an interfacial 2-dimensional SC. The results of transport measurements support that reduction of the excess Fe concentration of the Fe1+yTe layer not only increases the fluctuation of its antiferromagnetic (AFM) order but also enhances the quality of the SC of this heterostructure system. On the other hand, the interfacial SC of this heterostructure was found to have a wider-ranging TI-layer thickness dependence than that of the Bi2Te3/Fe1+yTe heterostructure, which is believed to be attributed to the much higher bulk conductivity of Sb2Te3 that enhances indirect coupling between its top and bottom topological surface states (TSSs). Our results provide evidence of the interplay among the AFM order, itinerant carries from the TSSs, and the induced interfacial SC of the TI/Fe1+yTe heterostructure system.

Coupling Topological Insulator SnSb2 Te4 Nanodots with Highly Doped Graphene for High-Rate Energy Storage

Topological insulators have spurred worldwide interest, but their advantageous properties have scarcely been explored in terms of electrochemical energy storage, and their high-rate capability and long-term cycling stability still remain a significant challenge to harvest. p-Type topological insulator SnSb₂ Te₄ nanodots anchoring on few-layered graphene (SnSb₂ Te₄ /G) are synthesized as a stable anode for high-rate lithium-ion batteries and potassium-ion batteries through a ball-milling method. These SnSb₂ Te₄ /G composite electrodes show ultralong cycle lifespan (478 mAh g^-1 at 1 A g^-1 after 1000 cycles) and excellent rate capability (remaining 373 mAh g^-1 even at 10 A g^-1 ) in Li-ion storage owing to the rapid ion transport accelerated by the PN heterojunction, virtual electron highways provided by the conductive topological surface state, and extraordinary pseudocapacitive contribution, whose excellent phase reversibility is confirmed by synchrotron in situ X-ray powder diffraction. Surprisingly, durable lifespan even at practical levels of mass loading (>10 mg cm^-2 ) for Li-ion storage and excellent K-ion storage performance are also observed. This work provides new insights for designing high-rate electrode materials by boosting conductive topological surfaces, atomic doping, and the interface interaction.

Quantum-Hall to Insulator Transition in Ultra-Low-Carrier-Density Topological Insulator Films and a Hidden Phase of the Zeroth Landau Level

A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it is challenging to probe the zeroth Landau level due to large electron-hole puddles smearing its energy landscape. Here, by developing ultra-low-carrier density topological insulator Sb₂ Te₃ films, an extreme quantum limit of the topological surface state is reached and a hidden phase at the zeroth Landau level is uncovered. First, an unexpected quantum-Hall-to-insulator-transition near the zeroth Landau level is discovered. Then, through a detailed scaling analysis, it is found that this quantum-Hall-to-insulator-transition belongs to a new universality class, implying that the insulating phase discovered here has a fundamentally different origin from those in nontopological systems.

Topological Phase Buried in a Chalcogenide Superlattice Monitored by Helicity-Dependent Kerr Measurement

Chalcogenide superlattices (SLs), formed by the alternate stacking of GeTe and Sb₂Te₃ layers, also referred to as interfacial phase-change memory (iPCM), are a leading candidate for spin-based memory device applications. Theoretically, the iPCM structure has been predicted to form a three-dimensional topological insulator or Dirac semimetal phase depending on the constituent layer thicknesses. Here, we experimentally investigate the topological insulating nature of chalcogenide SLs using a helicity-dependent time-resolved Kerr measurement. The helicity-dependent Kerr signal is observed to exhibit a four-cycle oscillation with π/2 periodicity, suggesting the existence of a Dirac-like cone in some chalcogenide SLs. Furthermore, we found that increasing the thickness of the GeTe layer dramatically changed the periodicity, indicating a phase transition from a Dirac semimetal into a trivial insulator. Our results demonstrate that thickness-tuned chalcogenide SLs can play an important role in the manipulation of topological states, which may open up new possibilities for spintronic devices based on chalcogenide SLs.

Topological Phase Transition with Nanoscale Inhomogeneity in (Bi1- xIn x)2Se3

Topological insulators are a class of band insulators with nontrivial topology, a result of band inversion due to the strong spin-orbit coupling. The transition between topological and normal insulator can be realized by tuning the spin-orbit coupling strength and has been observed experimentally. However, the impact of chemical disorders on the topological phase transition was not addressed in previous studies. Herein, we report a systematic scanning tunneling microscopy/spectroscopy and first-principles study of the topological phase transition in single crystals of In-doped Bi₂Se₃. Surprisingly, no band gap closure was observed across the transition. Furthermore, our spectroscopic-imaging results reveal that In defects are extremely effective "suppressors" of the band inversion, which leads to microscopic phase separation of topological-insulator-like and normal-insulator-like nano regions across the "transition". The observed topological electronic inhomogeneity demonstrates the significant impact of chemical disorders in topological materials, shedding new light on the fundamental understanding of topological phase transition.

A cascading nonlinear magneto-optical effect in topological insulators

Topological insulators (TIs) are characterized by possessing metallic (gapless) surface states and a finite band-gap state in the bulk. As the thickness of a TI layer decreases down to a few nanometers, hybridization between the top and bottom surfaces takes place due to quantum tunneling, consequently at a critical thickness a crossover from a 3D-TI to a 2D insulator occurs. Although such a crossover is generally accessible by scanning tunneling microscopy, or by angle-resolved photoemission spectroscopy, such measurements require clean surfaces. Here, we demonstrate that a cascading nonlinear magneto-optical effect induced via strong spin-orbit coupling can examine such crossovers. The helicity dependence of the time-resolved Kerr rotation exhibits a robust change in periodicity at a critical thickness, from which it is possible to predict the formation of a Dirac cone in a film several quintuple layers thick. This method enables prediction of a Dirac cone using a fundamental nonlinear optical effect that can be applied to a wide range of TIs and related 2D materials.

Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures

The "magnetoelectric effect" arises from the coupling between magnetic and electric properties in materials. The Z_{2} invariant of topological insulators (TIs) leads to a quantized version of this phenomenon, known as the topological magnetoelectric (TME) effect. This effect can be realized in a new topological phase called an "axion insulator" whose surface states are all gapped but the interior still obeys time reversal symmetry. We demonstrate such a phase using electrical transport measurements in a quantum anomalous Hall (QAH) sandwich heterostructure, in which two compositionally different magnetic TI layers are separated by an undoped TI layer. Magnetic force microscopy images of the same sample reveal sequential magnetization reversals of the top and bottom layers at different coercive fields, a consequence of the weak interlayer exchange coupling due to the spacer. When the magnetization is antiparallel, both the Hall resistance and Hall conductance show zero plateaus, accompanied by a large longitudinal resistance and vanishing longitudinal conductance, indicating the realization of an axion insulator state. Our findings thus show evidence for a phase of matter distinct from the established QAH state and provide a promising platform for the realization of the TME effect.

Tailoring the epitaxy of Sb2Te3 and GeTe thin films using surface passivation

Depending on the substrate surface termination the epitaxy of chalcogenide thin films can be drastically altered. While GeTe grows with many randomly oriented domains on H-terminated Si(111), the in-plane alignment is significantly improved on Sb-terminated Si(111).

Manipulation of dangling bonds of interfacial states coupled in GeTe-rich GeTe/Sb2Te3 superlattices

Superlattices consisting of stacked nano-sized GeTe and Sb2Te3 blocks have attracted considerable attention owing to their potential for an efficient non-melting switching mechanism, associated with complex bonding between blocks. Here, we propose possible atomic models for the superlattices, characterized by different interfacial bonding types. Based on interplanar distances extracted from ab initio calculations and electron diffraction measurements, we reveal possible intercalation of dangling bonds as the GeTe content in the superlattice increases. The dangling bonds were further confirmed by X-ray photoelectron spectroscopy, anisotropic temperature dependent resistivity measurements down to 2 K and magnetotransport analysis. Changes of partially coherent decoupled topological surfaces states upon dangling bonds varying contributed to the switching mechanism. Furthermore, the topological surface states controlled by changing the bonding between stacking blocks may be optimized for multi-functional applications.

Drive the Dirac electrons into Cooper pairs in SrxBi2Se3

Topological superconductors are a very interesting and frontier topic in condensed matter physics. Despite the tremendous efforts in exploring topological superconductivity, its presence is however still under heavy debate. The Dirac electrons have been proven to exist on the surface of a topological insulator. It remains unclear whether and how the Dirac electrons fall into Cooper pairing in an intrinsic superconductor with the topological surface states. Here we show the systematic study of scanning tunnelling microscope/spectroscopy on the possible topological superconductor Sr_xBi₂Se₃. We first demonstrate that only the intercalated Sr atoms can induce superconductivity. Then we show the full superconducting gaps without any in-gap density of states as expected theoretically for a bulk topological superconductor. Finally, we find that the surface Dirac electrons will simultaneously condense into the superconducting state within the superconducting gap. This vividly demonstrates how the surface Dirac electrons are driven into Cooper pairs.

Whether and how the Dirac electrons can be driven into superconducting state remains unclear. Here, Du et al. present systematic study to demonstrate the Dirac electrons condensing into Cooper pairs on the surface of a possible topological superconductor Sr_xBi₂Se₃.

Faraday Rotation Due to Surface States in the Topological Insulator (Bi1-xSbx)2Te3

Using magneto-infrared spectroscopy, we have explored the charge dynamics of (Bi,Sb)₂Te₃ thin films on InP substrates. From the magneto-transmission data we extracted three distinct cyclotron resonance (CR) energies that are all apparent in the broad band Faraday rotation (FR) spectra. This comprehensive FR-CR data set has allowed us to isolate the response of the bulk states from the intrinsic surface states associated with both the top and bottom surfaces of the film. The FR data uncovered that electron- and hole-type Dirac Fermions reside on opposite surfaces of our films, which paves the way for observing many exotic quantum phenomena in topological insulators.

Simultaneous observation of surface- and edge-states of a 2D topological insulator through scanning tunneling spectroscopy and differential conductance imaging

Gapless edge-states with a Dirac point below the Fermi energy and band-edges at the interior observed in 2D topological insulators.

Growth, characterization, and transport properties of ternary (Bi1-x Sb x )2Te3 topological insulator layers

Ternary (Bi_1-x Sb _x )₂Te₃ films with an Sb content between 0 and 100% were deposited on a Si(1 1 1) substrate by means of molecular beam epitaxy. X-ray diffraction measurements confirm single crystal growth in all cases. The Sb content is determined by x-ray photoelectron spectroscopy. Consistent values of the Sb content are obtained from Raman spectroscopy. Scanning Raman spectroscopy reveals that the (Bi_1-x Sb _x )₂Te₃ layers with an intermediate Sb content show spatial composition inhomogeneities. The observed spectra broadening in angular-resolved photoemission spectroscopy (ARPES) is also attributed to this phenomena. Upon increasing the Sb content from x  =  0 to 1 the ARPES measurements show a shift of the Fermi level from the conduction band to the valence band. This shift is also confirmed by corresponding magnetotransport measurements where the conductance changes from n- to p-type. In this transition region, an increase of the resistivity is found, indicating a location of the Fermi level within the band gap region. More detailed measurements in the transition region reveals that the transport takes place in two independent channels. By means of a gate electrode the transport can be changed from n- to p-type, thus allowing a tuning of the Fermi level within the topologically protected surface states.

Thickness Dependence of the Quantum Anomalous Hall Effect in Magnetic Topological Insulator Films

The evolution of the quantum anomalous Hall effect with the thickness of Cr-doped (Bi,Sb)2 Te3 magnetic topological insulator films is studied, revealing how the effect is caused by the interplay of the surface states, band-bending, and ferromagnetic exchange energy. Homogeneity in ferromagnetism is found to be the key to high-temperature quantum anomalous Hall material.

Band structure of a three-dimensional topological insulator quantum wire in the presence of a magnetic field

By means of a numerical diagonalization approach, we calculate the electronic structure of a three-dimensional topological insulator (3DTI) quantum wire (QW) in the presence of a magnetic field. The QW can be viewed as a 3DTI film with lateral surfaces, when its rectangular cross section has a large aspect ratio. Our calculation indicates that nonchiral edge states emerge because of the confined states at the lateral surfaces. These states completely cover the valence band region among the Landau levels, which reasonably account for the absence of the [Formula: see text] quantum Hall effect in the relevant experimental works. In an ultrathin 3DTI film, inversion between the electron-type and hole-type bands occurs, which leads to the so-called pseudo-spin Hall effect. In a 3DTI QW with a square cross section, a tilting magnetic field can establish well-defined Landau levels in all four surfaces. In such a case, the quantum Hall edge states are localized at the square corners, characterized by the linearly crossing one-dimensional band profile. And they can be shifted between the adjacent corners by simply rotating the magnetic field.

Electronic and magnetic properties of H-terminated graphene nanoribbons deposited on the topological insulator Sb2Te3

Magnetism in zigzag graphene nanoribbons (GNRs) has received enormous attention recently, due to the one-dimensional nature of this phenomenon, as well as its potential applications in the field of spintronics. In this work, we present a density functional theory (DFT) investigation of H-passivated GNRs on the (111) surface of the topological insulator Sb2Te3. We show that the chemical interaction between the GNR and the substrate is weak. As a result, the GNR-surface distance is large, of the order of 3.4 Angstrom, doping effects are almost negligible, and the mean-field magnetic properties of the GNR are preserved. Nevertheless, the presence of the substrate affects significantly the magnitude of the exchange coupling constants between the edges. Although our DFT calculations do not properly describe quantum fluctuations that destabilize the edge magnetism in free-standing GNRs, they provide important information about the stabilizing mechanisms which originate from the substrate-induced spin orbit coupling and the decoherence effects due to the surface states of Sb2Te3. We argue that, owing to these mechanisms, Sb2Te3 may be a suitable substrate to investigate experimentally the transition from "quantum" to "classical" magnetism in GNRs.

Electrical Detection of the Helical Spin Texture in a p-type Topological Insulator Sb2Te3

The surface states of 3D topological insulators (TIs) exhibit a helical spin texture with spin locked at right angles with momentum. The chirality of this spin texture is expected to invert crossing the Dirac point, a property that has been experimentally observed by optical probes. Here, we directly determine the chirality below the Dirac point by electrically detecting spin-momentum locking in surface states of a p-type TI, Sb2Te3. A current flowing in the Sb2Te3 surface states generates a net spin polarization due to spin-momentum locking, which is electrically detected as a voltage on an Fe/Al2O3 tunnel barrier detector. Measurements of this voltage as a function of current direction and detector magnetization indicate that hole spin-momentum locking follows the right-hand rule, opposite that of electron, providing direct confirmation that the chirality is indeed inverted below Dirac point. The spin signal is linear with current, and exhibits a temperature dependence consistent with the semiconducting nature of the TI film and freeze-out of bulk conduction below 100 K. Our results demonstrate that the chirality of the helical spin texture of TI surface states can be determined electrically, an enabling step in the electrical manipulation of spins in next generation TI-based quantum devices.

Dual nature of magnetic dopants and competing trends in topological insulators

Topological insulators interacting with magnetic impurities have been reported to host several unconventional effects. These phenomena are described within the framework of gapping Dirac quasiparticles due to broken time-reversal symmetry. However, the overwhelming majority of studies demonstrate the presence of a finite density of states near the Dirac point even once topological insulators become magnetic. Here, we map the response of topological states to magnetic impurities at the atomic scale. We demonstrate that magnetic order and gapless states can coexist. We show how this is the result of the delicate balance between two opposite trends, that is, gap opening and emergence of a Dirac node impurity band, both induced by the magnetic dopants. Our results evidence a more intricate and rich scenario with respect to the once generally assumed, showing how different electronic and magnetic states may be generated and controlled in this fascinating class of materials.

Magnetic impurities break time reversal symmetry in topological insulators, but there has been disagreement between theory and experiment. Here, the authors study the response of topological states to magnetic dopants at the atomic level and show that, contrary to what generally believed, magnetic order and gapless states can coexist.

Topological states and phase transitions in Sb2Te3-GeTe multilayers

Topological insulators (TIs) are bulk insulators with exotic 'topologically protected' surface conducting modes. It has recently been pointed out that when stacked together, interactions between surface modes can induce diverse phases including the TI, Dirac semimetal, and Weyl semimetal. However, currently a full experimental understanding of the conditions under which topological modes interact is lacking. Here, working with multilayers of the TI Sb2Te3 and the band insulator GeTe, we provide experimental evidence of multiple topological modes in a single Sb2Te3-GeTe-Sb2Te3 structure. Furthermore, we show that reducing the thickness of the GeTe layer induces a phase transition from a Dirac-like phase to a gapped phase. By comparing different multilayer structures we demonstrate that this transition occurs due to the hybridisation of states associated with different TI films. Our results demonstrate that the Sb2Te3-GeTe system offers strong potential towards manipulating topological states as well as towards controlledly inducing various topological phases.

Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators

The quantum anomalous Hall effect (QAHE), the last member of Hall family, was predicted to exhibit quantized Hall conductivity σ(yx) = e2/h without any external magnetic field. The QAHE shares a similar physical phenomenon with the integer quantum Hall effect (QHE), whereas its physical origin relies on the intrinsic topological inverted band structure and ferromagnetism. Since the QAHE does not require external energy input in the form of magnetic field, it is believed that this effect has unique potential for applications in future electronic devices with low-power consumption. More recently, the QAHE has been experimentally observed in thin films of the time-reversal symmetry breaking ferromagnetic (FM) topological insulators (TI), Cr- and V- doped (Bi,Sb)2Te3. In this topical review, we review the history of TI based QAHE, the route to the experimental observation of the QAHE in the above two systems, the current status of the research of the QAHE, and finally the prospects for future studies.

Experimental Realization of a Topological p-n Junction by Intrinsic Defect Grading

A Bi2Te3 single crystal is grown with the modified Bridgman technique. The crystal has a nominal composition with a Te content of 61 mol% resulting in the existence of two distinct regions, p- and n-doped, respectively; color-coded tunneling spectra are taken over 60 nm at the transition region.

Interface formation of two- and three-dimensionally bonded materials in the case of GeTe-Sb₂Te₃ superlattices

GeTe-Sb2Te3 superlattices are nanostructured phase-change materials which are under intense investigation for non-volatile memory applications. They show superior properties compared to their bulk counterparts and significant efforts exist to explain the atomistic nature of their functionality. The present work sheds new light on the interface formation between GeTe and Sb2Te3, contradicting previously proposed models in the literature. For this purpose [GeTe(1 nm)-Sb2Te3(3 nm)]15 superlattices were grown on passivated Si(111) at 230 °C using molecular beam epitaxy and they have been characterized particularly with cross-sectional HAADF scanning transmission electron microscopy. Contrary to the previously proposed models, it is found that the ground state of the film actually consists of van der Waals bonded layers (i.e. a van der Waals heterostructure) of Sb2Te3 and rhombohedral GeSbTe. Moreover, it is shown by annealing the film at 400 °C, which reconfigures the superlattice into bulk rhombohedral GeSbTe, that this van der Waals layer is thermodynamically favored. These results are explained in terms of the bonding dimensionality of GeTe and Sb2Te3 and the strong tendency of these materials to intermix. The findings debate the previously proposed switching mechanisms of superlattice phase-change materials and give new insights in their possible memory application.

Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials

It is well known that a nonvanishing Hall conductivity requires broken time-reversal symmetry. However, in this work, we demonstrate that Hall-like currents can occur in second-order response to external electric fields in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the driving frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. The nonlinear Hall coefficient is a rank-two pseudotensor, whose form is determined by point group symmetry. We discus optimal conditions to observe this effect and propose candidate two- and three-dimensional materials, including topological crystalline insulators, transition metal dichalcogenides, and Weyl semimetals.

Controlling the Spin Texture of Topological Insulators by Rational Design of Organic Molecules

We present a rational design approach to customize the spin texture of surface states of a topological insulator. This approach relies on the extreme multifunctionality of organic molecules that are used to functionalize the surface of the prototypical topological insulator (TI) Bi2Se3. For the rational design we use theoretical calculations to guide the choice and chemical synthesis of appropriate molecules that customize the spin texture of Bi2Se3. The theoretical predictions are then verified in angular-resolved photoemission experiments. We show that, by tuning the strength of molecule-TI interaction, the surface of the TI can be passivated, the Dirac point can energetically be shifted at will, and Rashba-split quantum-well interface states can be created. These tailored interface properties-passivation, spin-texture tuning, and creation of hybrid interface states-lay a solid foundation for interface-assisted molecular spintronics in spin-textured materials.

Ultrafast electron dynamics at the Dirac node of the topological insulator Sb2Te3

Topological insulators (TIs) are a new quantum state of matter. Their surfaces and interfaces act as a topological boundary to generate massless Dirac fermions with spin-helical textures. Investigation of fermion dynamics near the Dirac point (DP) is crucial for the future development of spintronic devices incorporating topological insulators. However, research so far has been unsatisfactory because of a substantial overlap with the bulk valence band and a lack of a completely unoccupied DP. Here, we explore the surface Dirac fermion dynamics in the TI Sb2Te3 by time- and angle-resolved photoemission spectroscopy (TrARPES). Sb2Te3 has an in-gap DP located completely above the Fermi energy (EF). The excited electrons in the upper Dirac cone stay longer than those below the DP to form an inverted population. This was attributed to a reduced density of states (DOS) near the DP.