Landau quantization of topological surface states in Bi2Se3

Time resolution of terahertz scanning tunneling microscopy measurements inside a superconducting magnet using a hollow waveguide

A terahertz scanning tunneling microscope (THz-STM) is an STM that allows us to perform time-resolved measurements of tunneling currents with high temporal resolution, in addition to the high spatial resolution of STMs. In such a device, it is necessary to guide the THz beam to the STM tip, which can be difficult if there are tight space restrictions due to experimental requirements, such as ultra-high vacuum and high magnetic fields. We aim to develop a THz-STM that allows us to measure tunneling currents in high magnetic fields at cryogenic temperatures with a time resolution on the order of picoseconds. In this paper, we placed a specially designed chamber containing a homemade STM head inside a superconducting magnet and performed time-resolved measurements of the tunneling current between the Pt-Ir tip and a highly oriented pyrolytic graphite (HOPG) sample. To introduce the THz pulse into the STM chamber, we used a narrow pipe as a waveguide and evaluated a time resolution of better than 1 ps, which suggests that the realization of a THz-STM for multi-extreme conditions with picosecond time resolution is possible.

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.

Quantum States Induced by Strong Interface Coupling in a 2D VSe2/Bi2Se3 Heterostructure

We have successfully fabricated single-layer (SL) 1T-VSe2/Bi2Se3 heterostructures using molecular beam epitaxy (MBE), which exhibits uniform moiré patterns on the heterostructure surface. Scanning tunneling microscopy/spectroscopy (STM/STS) reveals a notable quantum state near the Fermi energy, robust across the entire moiré lattice. This quantum state peak shifts slightly across different domain ranges, suggesting an elastic strain dependence in SL VSe2, confirmed by geometric phase analysis (GPA) simulations. Density functional theory (DFT) calculations indicate that the enhanced quantum state results from charge redistribution between the substrate and the epifilm with the orbitals of Se atoms in the deformed VSe2 playing a dominant role.

Growth optimization and crossover of transport mechanisms in Bi2Se3thin films

We report the growth, structural characterization, and transport studies of Bi2Se3thin film on single crystalline silicon (Si), Si/SiO2, quartz, and glass substrates by thermal evaporation method. Our results show that 300 °C is the optimum substrate temperature to obtain thec-axis (001) oriented Bi2Se3films on all the substrates. The film grown on the Si substrate has the minimum crystalline disorder. The energy-dispersive x-ray spectroscopy results show that film on Si substrate is bismuth deficient, the film on Si/SiO2substrate is selenium deficient, and the film on quartz substrate is near perfect stoichiometric providing a way to tune the electronic properties of Bi2Se3films through substrate selection. The film grown on quartz shows the highest mobility (2.7 × 104cm2V-1s-1) which drops to 150 cm2V-1s-1for Si, 60 cm2V-1s-1for Si/SiO2, and 0.9 cm2V-1s-1for glass substrate. Carrier concentration is n-type for Bi2Se3films on Si (∼1018cm-3), quartz (∼1018cm-3) and Si/SiO2(∼1019cm-3) substrate with a clear indication of frozen out effect around 50 K for Si/SiO2and Si substrate. Longitudinal resistivity of Bi2Se3film on Si/SiO2substrate shows different behavior in three different temperature regions: temperature dependent resistivity region due to electron-phonon scattering, a nearly temperature independent resistivity region due to electron-phonon and electron-ion scattering, and a quantum coherent transport region.

Tuning Multiple Landau Quantization in Transition-Metal Dichalcogenide with Strain

Landau quantization associated with the quantized cyclotron motion of electrons under magnetic field provides the effective way to investigate topologically protected quantum states with entangled degrees of freedom and multiple quantum numbers. Here we report the cascade of Landau quantization in a strained type-II Dirac semimetal NiTe₂ with spectroscopic-imaging scanning tunneling microscopy. The uniform-height surfaces exhibit single-sequence Landau levels (LLs) at a magnetic field originating from the quantization of topological surface state (TSS) across the Fermi level. Strikingly, we reveal the multiple sequence of LLs in the strained surface regions where the rotation symmetry is broken. First-principles calculations demonstrate that the multiple LLs attest to the remarkable lifting of the valley degeneracy of TSS by the in-plane uniaxial or shear strains. Our findings pave a pathway to tune multiple degrees of freedom and quantum numbers of TMDs via strain engineering for practical applications such as high-frequency rectifiers, Josephson diode and valleytronics.

Effect of Cu Intercalation Layer on the Enhancement of Spin-to-Charge Conversion in Py/Cu/Bi2Se3

The spin-to-charge conversion in Permalloy (Py)/Cu/Bi₂Se₃ is tunable by changing the Cu layer thickness. The conversion rate was studied using the spin pumping technique. The inverse Edelstein effect (IEE) length λ_IEE is found to increase up to ~2.7 nm when a 7 nm Cu layer is introduced. Interestingly, the maximized λ_IEE is obtained when the effective spin-mixing conductance (and thus J_s) is decreased due to Cu insertion. The monotonic increase in λ_IEE with decreasing J_s suggests that the IEE relaxation time (τ) is enhanced due to the additional tunnelling barrier (Cu layer) that limits the interfacial transmission rate. The results demonstrate the importance of interface engineering in the magnetic heterostructure of Py/topological insulators (TIs), the key factor in optimizing spin-to-charge conversion efficiency.

Evidence of a room-temperature quantum spin Hall edge state in a higher-order topological insulator

Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics^1,2. The quantum spin Hall phase^3-6 is a topological quantum phase that features a two-dimensional insulating bulk and a helical edge state. Here we use vector magnetic field and variable temperature based scanning tunnelling microscopy to provide micro-spectroscopic evidence for a room-temperature quantum spin Hall edge state on the surface of the higher-order topological insulator Bi₄Br₄. We find that the atomically resolved lattice exhibits a large insulating gap of over 200 meV, and an atomically sharp monolayer step edge hosts an in-gap gapless state, suggesting topological bulk-boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent in the underlying band topology. We further identify the geometrical hybridization of such edge states, which not only supports the Z₂ topology of the quantum spin Hall state but also visualizes the building blocks of the higher-order topological insulator phase. Our results further encourage the exploration of high-temperature transport quantization of the putative topological phase reported here.

Nearly Ideal Two-Dimensional Electron Gas Hosted by Multiple Quantized Kronig-Penney States Observed in Few-Layer InSe

A theoretical ideal two-dimensional electron gas (2DEG) was characterized by a flat density of states independent of energy. Compared with conventional two-dimensional free-electron systems in semiconductor heterojunctions and noble metal surfaces, we report here the achievement of ideal 2DEG with multiple quantized states in few-layer InSe films. The multiple quantum well states (QWSs) in few-layer InSe films are found, and the number of QWSs is strictly equal to the number of atomic layers. The multiple stair-like DOS as well as multiple bands with parabolic dispersion both characterize ideal 2DEG features in these QWSs. Density functional theory calculations and numerical simulations based on quasi-bounded square potential wells described as the Kronig-Penney model provide a consistent explanation of 2DEG in the QWSs. Our work demonstrates that 2D van der Waals materials are ideal systems for realizing 2DEG hosted by multiple quantized Kronig-Penney states, and the semiconducting nature of the material provides a better chance for construction of high-performance electronic devices utilizing these states, for example, superlattice devices with negative differential resistance.

Electronic Quantum Materials Simulated with Artificial Model Lattices

The band structure and electronic properties of a material are defined by the sort of elements, the atomic registry in the crystal, the dimensions, the presence of spin–orbit coupling, and the electronic interactions. In natural crystals, the interplay of these factors is difficult to unravel, since it is usually not possible to vary one of these factors in an independent way, keeping the others constant. In other words, a complete understanding of complex electronic materials remains challenging to date. The geometry of two- and one-dimensional crystals can be mimicked in artificial lattices. Moreover, geometries that do not exist in nature can be created for the sake of further insight. Such engineered artificial lattices can be better controlled and fine-tuned than natural crystals. This makes it easier to vary the lattice geometry, dimensions, spin–orbit coupling, and interactions independently from each other. Thus, engineering and characterization of artificial lattices can provide unique insights. In this Review, we focus on artificial lattices that are built atom-by-atom on atomically flat metals, using atomic manipulation in a scanning tunneling microscope. Cryogenic scanning tunneling microscopy allows for consecutive creation, microscopic characterization, and band-structure analysis by tunneling spectroscopy, amounting in the analogue quantum simulation of a given lattice type. We first review the physical elements of this method. We then discuss the creation and characterization of artificial atoms and molecules. For the lattices, we review works on honeycomb and Lieb lattices and lattices that result in crystalline topological insulators, such as the Kekulé and “breathing” kagome lattice. Geometric but nonperiodic structures such as electronic quasi-crystals and fractals are discussed as well. Finally, we consider the option to transfer the knowledge gained back to real materials, engineered by geometric patterning of semiconductor quantum wells.

Fabrication and Characterization of a Self-Powered n-Bi2Se3/p-Si Nanowire Bulk Heterojunction Broadband Photodetector

In the present study, vacuum evaporation method is used to deposit Bi2Se3 film onto Si nanowires (NWs) to form bulk heterojunction for the first time. Its photodetector is self-powered, its detection wavelength ranges from 390 nm to 1700 nm and its responsivity reaches its highest value of 84.3 mA/W at 390 nm. In comparison to other Bi2Se3/Si photodetectors previously reported, its infrared detection length is the second longest and its response speed is the third fastest. Before the fabrication of the photodetector, we optimized the growth parameter of the Bi2Se3 film and the best Bi2Se3 film with atomic steps could finally be achieved. The electrical property measurement conducted by the physical property measurement system (PPMS) showed that the grown Bi2Se3 film was n-type conductive and had unique topological insulator properties, such as a metallic state, weak anti-localization (WAL) and linear magnetic resistance (LMR). Subsequently, we fabricated Si NWs by the metal-assisted chemical etching (MACE) method. The interspace between Si NWs and the height of Si NWs could be tuned by Ag deposition and chemical etching times, respectively. Finally, Si NWs fabricated with the Ag deposition time of 60 s and the etching time of 10 min was covered by the best Bi2Se3 film to be processed for the photodetector. The primary n-Bi2Se3/p-Si NWs photodetector that we fabricated can work in a self-powered mode and it has a broadband detection range and fast response speed, which indicates that it can serve as a promising silicon-based near- and mid-infrared photodetector.

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.

Searching for Band-Dispersive and Defect-Tolerant Semiconductors from Element Substitution in Topological Materials

Topological insulators and semimetal materials composed of heavy elements usually have inverted and dispersive band structures. It is interesting to notice that if lighter elements with reduced spin-orbit coupling are substituted for the heavy elements, the topological materials can be mutated into semiconductors with variable band gaps; for example, topological HgTe and Bi₂Se₃ can be mutated into CdTe and Sb₂Se₃, which are excellent optoelectronic semiconductors because the element substitution opens the band gap and meanwhile inherits the large band dispersion and high carrier mobility. Recently, many topological materials have been reported, and their databases have been built. Here, we demonstrate that these new topological materials can be used as the starting points to search for semiconductors with high carrier mobility and defect tolerance through element substitution. We take three recently discovered topological materials, Na₃Bi, Pb₂Bi₂Te₅, and EuCd₂Sb₂, as the benchmark systems to show the general validity of this strategy and find that the derived Na₃P, Na₃As, Sn₂Sb₂S₅, and CaZn₂N₂ are all band-dispersive and defect-tolerant semiconductors with potential optoelectronic applications. For Na₃P, Na₃As, and Na₃Sb, the new P3̅c1 structure derived from the topological Na₃Bi is found unexpectedly to be their ground-state structure, more stable than their well-known structures reported in the literature. This study not only gains new insights into the physical properties of these semiconductors but also proposes an effective strategy for the search of band-dispersive and defect-tolerant semiconductors that can be generalized to other topological materials.

Super-Resonant Transport of Topological Surface States Subjected to In-Plane Magnetic Fields

Magnetic oscillations of Dirac surface states of topological insulators are typically expected to be associated with the formation of Landau levels or the Aharonov-Bohm effect. We instead study the conductance of Dirac surface states subjected to an in-plane magnetic field in the presence of a barrier potential. Strikingly, we find that, in the case of large barrier potentials, the surface states exhibit pronounced oscillations in the conductance when varying the magnetic field, in the absence of Landau levels or the Aharonov-Bohm effect. These novel magnetic oscillations are attributed to the emergence of super-resonant transport by tuning the magnetic field, in which many propagating modes cross the barrier with perfect transmission. In the case of small and moderate barrier potentials, we identify a positive magnetoconductance due to the increase of the Fermi surface by tilting the surface Dirac cone. Moreover, we show that for weak magnetic fields, the conductance displays a shifted sinusoidal dependence on the field direction with period π and phase shift determined by the tilting direction with respect to the field direction. Our predictions can be applied to various topological insulators, such as HgTe and Bi_{2}Se_{3}, and provide important insights into exploring and understanding exotic magnetotransport properties of topological surface states.

Imaging current distribution in a topological insulator Bi2Se3 in the presence of competing surface and bulk contributions to conductivity

Two-dimensional (2D) topological surface states in a three-dimensional topological insulator (TI) should produce uniform 2D surface current distribution. However, our transport current imaging studies on Bi₂Se₃ thin film reveal non-uniform current sheet flow at 15 K with strong edge current flow. This is consistent with other imaging studies on thin films of Bi₂Se₃. In contrast to strong edge current flow in thin films, in single crystal of Bi₂Se₃ at 15 K our current imaging studies show the presence of 3.6 nm thick uniform 2D sheet current flow. Above 70 K, this uniform 2D sheet current sheet begins to disintegrate into a spatially non-uniform flow. The flow becomes patchy with regions having high and low current density. The area fraction of the patches with high current density rapidly decreases at temperatures above 70 K, with a temperature dependence of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1/\left| {T - 70} \right|^{0.35}$$\end{document}1/T-700.35. The temperature scale of 70 K coincides with the onset of bulk conductivity in the crystal due to electron doping by selenium vacancy clusters in Bi₂Se₃. Thus our results show a temperature dependent competition between surface and bulk conductivity produces a temperature dependent variation in uniformity of current flow in the topological insulator.

Bulk spin conductivity of three-dimensional topological insulators

We study the spin conductivity of the bulk states of three-dimensional topological insulators within Kubo formalism. Spin Hall effect is the generation of the spin current that is perpendicular to the applied voltage. In the case of a three-dimensional topological insulator, applied voltage along x direction generates transverse spin currents along y and z directions with comparable values. We found that finite non-universal value of the spin conductivity exists in the gapped region due to the inversion of bands. Contribution to the spin conductivity from the vertex corrections enhances the spin conductivity from the filled states. These findings explain large spin conductivity that has been observed in topological insulators.

Hofstadter Topology: Noncrystalline Topological Materials at High Flux

The Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding ∼10^{4}  T magnetic fields to a trivial band structure. In this Letter, we show that when a magnetic field is added to an initially topological band structure, a wealth of possible phases emerges. Remarkably, we find topological phases that cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with a nonzero Chern number or mirror Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with a nontrivial Kane-Mele invariant can be classified as a 3D topological insulator (TI) or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of twofold rotation and time reversal and show that there exists a higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group that exists at rational values of the flux. The advent of Moiré lattices renders our work relevant experimentally. Due to the enlarged Moiré unit cell, it is possible for laboratory-strength fields to reach one flux per plaquette and allow access to our proposed Hofstadter topological phase.

Severe Dirac Mass Gap Suppression in Sb2Te3-Based Quantum Anomalous Hall Materials

The quantum anomalous Hall (QAH) effect appears in ferromagnetic topological insulators (FMTIs) when a Dirac mass gap opens in the spectrum of the topological surface states (SSs). Unaccountably, although the mean mass gap can exceed 28 meV (or ∼320 K), the QAH effect is frequently only detectable at temperatures below 1 K. Using atomic-resolution Landau level spectroscopic imaging, we compare the electronic structure of the archetypal FMTI Cr_0.08(Bi_0.1Sb_0.9)_1.92Te₃ to that of its nonmagnetic parent (Bi_0.1Sb_0.9)₂Te₃, to explore the cause. In (Bi_0.1Sb_0.9)₂Te₃, we find spatially random variations of the Dirac energy. Statistically equivalent Dirac energy variations are detected in Cr_0.08(Bi_0.1Sb_0.9)_1.92Te₃ with concurrent but uncorrelated Dirac mass gap disorder. These two classes of SS electronic disorder conspire to drastically suppress the minimum mass gap to below 100 μeV for nanoscale regions separated by <1 μm. This fundamentally limits the fully quantized anomalous Hall effect in Sb₂Te₃-based FMTI materials to very low temperatures.

Gate-Tunable Surface States in Topological Insulator β-Ag2Te with High Mobility

Stimulated by novel properties in topological insulators, experimentally realizing quantum phases of matter and employing control over their properties have become a central goal in condensed matter physics. β-silver telluride (Ag₂Te) is predicted to be a new type narrow-gap topological insulator. While enormous efforts have been plunged into the topological nature in silver chalcogenides, sophisticated research on low-dimensional nanostructures remains unexplored. Here, we report the record-high bulk carrier mobility of 298 600 cm²/(V s) in high-quality Ag₂Te nanoplates and the coexistence of the surface and bulk state from systematic Shubnikov-de Haas oscillations measurements. By tuning the correlation between the top and bottom surfaces, we can effectively enhance the contribution of the surface to the total conductance up to 87% at 130 V. These results are instrumental to the high-mobility physics study and even suitable to explore exotic topological phenomena in this material system.

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.

Electronic States and Magnetic Response of MnBi2Te4 by Scanning Tunneling Microscopy and Spectroscopy

Exotic quantum phenomena have been demonstrated in recently discovered intrinsic magnetic topological insulator MnBi₂Te₄. At its two-dimensional limit, the quantum anomalous Hall effect and axion insulator state were observed in odd and even layers of MnBi₂Te₄, respectively. Here, we employ low-temperature scanning tunneling microscopy to study the electronic properties of MnBi₂Te₄. The quasiparticle interference patterns indicate that the electronic structures on the topmost layer of MnBi₂Te₄ are different from those of the expected out-of-plane A-type antiferromagnetic phase. The topological surface states may be embedded in deeper layers beneath the topmost surface. Such novel electronic structure is presumably related to the modification of crystalline structure during sample cleaving and reorientation of the magnetic moment of Mn atoms near the surface. Mn dopants substituted at the Bi site on the second atomic layer are observed. The electronic structures fluctuate at atomic scale on the surface, which can affect the magnetism of MnBi₂Te₄.

Landau Levels of Topologically-Protected Surface States Probed by Dual-Gated Quantum Capacitance

Spectroscopy of discrete Landau levels (LLs) in bulk-insulating three-dimensional topological insulators (3D TIs) in perpendicular magnetic field characterizes the Dirac nature of their surface states. Despite a number of studies demonstrating the quantum Hall effect (QHE) of topological surface states, quantitative evaluation of the LL energies, which serve as fundamental electronic quantities for study of the quantum states, is still limited. In this work, we explore the density of states of LLs by measuring quantum capacitance (C_Q) in a truly bulk insulating 3D TI via a van der Waals heterostructure configuration. By applying dual-gate voltages, we access the individual surface states' LLs and extract their chemical potentials to quantify the LL spacings of each surface. We evaluate the LLs' energies at two distinguished QH states, namely, dissipationless (ν = ±1) and dissipative (ν = 0) states in the 3D TI.

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.

Influence of an Anomalous Temperature Dependence of the Phase Coherence Length on the Conductivity of Magnetic Topological Insulators

Magnetotransport constitutes a useful probe to understand the interplay between electronic band topology and magnetism in spintronic devices. A recent theory of Lu and Shen [Phys. Rev. Lett. 112, 146601 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.146601] on magnetically doped topological insulators predicts that quantum corrections Δκ to the temperature dependence of conductivity can change sign across the Curie transition. This phenomenon has been attributed to a suppression of the Berry phase of the topological surface states at the Fermi level, caused by a magnetic energy gap. Here, we demonstrate experimentally that Δκ can reverse its sign even when the Berry phase at the Fermi level remains unchanged. The contradictory behavior to theory predictions is resolved by extending the model by Lu and Shen to a nonmonotonic temperature scaling of the inelastic scattering length showing a turning point at the Curie transition.

Epitaxial Growth of PbSe Few-Layers on SrTiO3: The Effect of Compressive Strain and Potential Two-Dimensional Topological Crystalline Insulator

The freestanding PbSe monolayer has been predicted as a candidate of the two-dimensional topological crystalline insulator, which possesses the Dirac-cone-like edge states resided at the edge. Up to now, however, direct experimental evidence of topological PbSe monolayer has not yet been reported. Here, we report the epitaxial growth and scanning tunneling microscopy study of few-layers PbSe islands grown on SrTiO₃ substrate. From the investigation of different thickness, we discover the release of compressive strain and the reduction of bandgap as the thickness becomes thick. Following detailed spectroscopic measurements, a signature of Dirac-like edge states is observed at the edge of seventh-layer PbSe. In conjunction with first-principle calculations, we find that compressive-strain-induced buckling adjusts the topological band inversion and eventually leads to a phase transition from nontrivial two-dimensional topological crystalline insulator to trivial insulator, which match well with our experimental observations. Therefore, both theoretical calculations and experimental observations reveal that the strain can effectively affect the property of epitaxial PbSe, meanwhile demonstrate seventh-layer PbSe as a potential candidate of 2D TCI.

Quasiparticle Interference Studies of Quantum Materials

Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy studies of these surface states have provided a wealth of spectroscopic characterization, with the successful cooperation of ab initio calculations. The method of quasiparticle interference imaging proves to be particularly useful for probing the dispersion relation of the surface bands. Herein, how a variety of additional fundamental electronic properties can be probed via this method is reviewed. It is demonstrated how quasiparticle interference measurements entail mesoscopic size quantization and the electronic phase coherence in semiconducting nanowires; helical spin protection and energy-momentum fluctuations in a topological insulator; and the structure of the Bloch wave function and the relative insusceptibility of topological electronic states to surface potential in a topological Weyl semimetal.

Suppression of transport spin-polarization of surface states with emergence of ferromagnetism in Mn-doped Bi2Se3

The surface states of topological insulators (TI) are protected by time reversal symmetry and they display intrinsic spin helicity where the momentum of the charge carriers decides their spin states. As a consequence, a current injected through the surface states becomes spin polarized and this transport spin-polarization leads to a proportionate suppression of Andreev reflection in superconductor/TI junctions. Here we show that upon doping Bi₂Se₃ with Mn, the transport spin-polarization is seen to be monotonically suppressed. The parent compound Bi₂Se₃ is found to exhibit a transport spin-polarization of about 63% whereas crystals with 10% Mn doping show transport spin-polarization of about 48%. This suppression is accompanied by an increasing ferromagnetic order of the crystals with Mn doping. Scanning tunneling spectroscopy shows that the topological protection of the surface states reduces due to Mn doping. The net measured transport spin-polarization is due to a competition of this effect with the increased magnetization on Mn doping. The present results provide important insights for the choice of magnetic topological insulators for spintronic applications.

Scanning tunneling microscopy investigations of unoccupied surface states in two-dimensional semiconducting β-√3 × √3-Bi/Si(111) surface

Two-dimensional surface structures often host a surface state in the bulk gap, which plays a crucial role in the surface electron transport. The diversity of in-gap surface states extends the category of two-dimensional systems and gives us more choices in material applications. In this article, we investigated the surface states of β-√3 × √3-Bi/Si(111) surface by scanning tunneling microscopy. Two nearly free electron states in the bulk gap of silicon were found in the unoccupied states. Combined with first-principles calculations, these two states were verified to be the Bi-contributed surface states and electron-accumulation-induced quantum well states. Due to the spin-orbit coupling of Bi atoms, Bi-contributed surface states exhibit free-electron Rashba splitting. The in-gap surface states with spin splitting can possibly be used for spin polarized electronics applications.

Solution to the Hole-Doping Problem and Tunable Quantum Hall Effect in Bi2Se3 Thin Films

Bi₂Se₃, one of the most widely studied topological insulators (TIs), is naturally electron-doped due to n-type native defects. However, many years of efforts to achieve p-type Bi₂Se₃ thin films have failed so far. Here, we provide a solution to this long-standing problem, showing that the main culprit has been the high density of interfacial defects. By suppressing these defects through an interfacial engineering scheme, we have successfully implemented p-type Bi₂Se₃ thin films down to the thinnest topological regime. On this platform, we present the first tunable quantum Hall effect (QHE) study in Bi₂Se₃ thin films and reveal not only significantly asymmetric QHE signatures across the Dirac point but also the presence of competing anomalous states near the zeroth Landau level. The availability of doping tunable Bi₂Se₃ thin films will now make it possible to implement various topological quantum devices, previously inaccessible.

Atomically Abrupt Topological p-n Junction

Topological insulators (TI's) are a new class of quantum matter with extraordinary surface electronic states, which bear great potential for spintronics and error-tolerant quantum computing. In order to put a TI into any practical use, these materials need to be fabricated into devices whose basic units are often p-n junctions. Interesting electronic properties of a 'topological' p-n junction were proposed theoretically such as the junction electronic state and the spin rectification. However, the fabrication of a lateral topological p-n junction has been challenging because of materials, process, and fundamental reasons. Here, we demonstrate an innovative approach to realize a p-n junction of topological surface states (TSS's) of a three-dimensional (3D) topological insulator (TI) with an atomically abrupt interface. When a ultrathin Sb film is grown on a 3D TI of Bi₂Se₃ with a typical n-type TSS, the surface develops a strongly p-type TSS through the substantial hybridization between the 2D Sb film and the Bi₂Se₃ surface. Thus, the Bi₂Se₃ surface covered partially with Sb films bifurcates into areas of n- and p-type TSS's as separated by atomic step edges with a lateral electronic junction of as short as 2 nm. This approach opens a different avenue toward various electronic and spintronic devices based on well-defined topological p-n junctions with the scalability down to atomic dimensions.

Semirelativity in semiconductors: a review

An analogy between behavior of electrons in narrow-gap semiconductors (NGS) and relativistic electrons in vacuum is reviewed. Energy band structures [Formula: see text] are considered for various NGS materials and their correspondence to the energy-momentum relation in special relativity is emphasized. It is indicated that special relativity for vacuum is analogous to a two-band [Formula: see text] description for NGS. The maximum electron velocity in NGS is [Formula: see text], which corresponds to the light velocity in vacuum. An effective mass of charge carriers in semiconductors is introduced, relating their velocity to quasimomentum and it is shown that this mass depends on electron energy (or velocity) in a way similar to the mass of free relativistic electrons. In [Formula: see text] alloys one can reach vanishing energy gap at which electrons and light holes become three-dimensional massless Dirac fermions. A wavelength [Formula: see text] is defined for NGS, in analogy to the Compton wavelength in relativistic quantum mechanics. It is estimated that [Formula: see text] is on the order of tens of Angstroms in typical semiconducting materials which is experimentally confirmed in tunneling experiments on energy dispersion in the forbidden gap. Statistical properties of the electron gas in NGS are calculated and their similarity is demonstrated to those of the Juttner gas of relativistic particles. Interband electron tunneling in NGS is described and shown to be in close analogy to the predicted but unobserved tunneling between negative and positive energies resulting from the Dirac equation for free electrons. It is demonstrated that the relativistic analogy holds for orbital and spin properties of electrons in the presence of an external magnetic field. In particular, it is shown that the spin magnetic moment of both NGS electrons and relativistic electrons approaches zero with increasing energy. This conclusion is confirmed experimentally for NGS. Electrons in crossed electric and magnetic fields are described theoretically and experimentally. It is only the two-band description for NGS, equivalent to the Dirac or Klein-Gordon equations for free particles, that gives a correct account of experimental results in this situation. A transverse Doppler shift in the cyclotron resonance observed in crossed fields in InSb indicates that there exists a time dilatation between an oscillating electron and an observer. The phenomenon of Zitterbewegung (ZB, trembling motion) for electrons in NGS is considered theoretically, following the original proposition of Schrödinger for free relativistic electrons in vacuum. The two descriptions are in close analogy, but the frequency of ZB for electrons in NGS is orders of magnitude lower and its amplitude orders of magnitude higher making possible experimental observations in semiconductors considerably more favorable. Finally, graphene and carbon nanotubes, as well as topological insulators are considered in the framework of relativistic analogy. These systems, with their linear energy-quasimomentum dispersions, illustrate the extreme semirelativistic regime. Experimental results for the energy dispersions and the Landau quantizations in the presence of a magnetic field are quoted and their analogy to the behavior of free relativistic electrons is discussed. Approximations and restrictions of the relativistic analogy are emphasized. On the other hand, it is indicated that in various situations it is considerably easier to observe semirelativistic effects in semiconductors than the relativistic effects in vacuum.

Two-Dimensional Massless Dirac Fermions in Antiferromagnetic AFe_{2}As_{2} (A=Ba,Sr)

We report infrared studies of AFe_{2}As_{2} (A=Ba, Sr), two representative parent compounds of iron-arsenide superconductors, at magnetic fields (B) up to 17.5 T. Optical transitions between Landau levels (LLs) were observed in the antiferromagnetic states of these two parent compounds. Our observation of a sqrt[B] dependence of the LL transition energies, the zero-energy intercepts at B=0  T under the linear extrapolations of the transition energies and the energy ratio (∼2.4) between the observed LL transitions, combined with the linear band dispersions in two-dimensional (2D) momentum space obtained by theoretical calculations, demonstrates the existence of massless Dirac fermions in the antiferromagnet BaFe_{2}As_{2}. More importantly, the observed dominance of the zeroth-LL-related absorption features and the calculated bands with extremely weak dispersions along the momentum direction k_{z} indicate that massless Dirac fermions in BaFe_{2}As_{2} are 2D. Furthermore, we find that the total substitution of the barium atoms in BaFe_{2}As_{2} by strontium atoms not only maintains 2D massless Dirac fermions in this system, but also enhances their Fermi velocity, which supports that the Dirac points in iron-arsenide parent compounds are topologically protected.

A low-temperature scanning tunneling microscope capable of microscopy and spectroscopy in a Bitter magnet at up to 34 T

We present the design and performance of a cryogenic scanning tunneling microscope (STM) which operates inside a water-cooled Bitter magnet, which can attain a magnetic field of up to 38 T. Due to the high vibration environment generated by the magnet cooling water, a uniquely designed STM and a vibration damping system are required. The STM scan head is designed to be as compact and rigid as possible, to minimize the effect of vibrational noise as well as fit the size constraints of the Bitter magnet. The STM uses a differential screw mechanism for coarse tip-sample approach, and operates in helium exchange gas at cryogenic temperatures. The reliability and performance of the STM are demonstrated through topographic imaging and scanning tunneling spectroscopy on highly oriented pyrolytic graphite at T = 4.2 K and in magnetic fields up to 34 T.

Determination of the energy band gap of Bi2Se3

Despite intensive investigations of Bi₂Se₃ in past few years, the size and nature of the bulk energy band gap of this well-known 3D topological insulator still remain unclear. Here we report on a combined magneto-transport, photoluminescence and infrared transmission study of Bi₂Se₃, which unambiguously shows that the energy band gap of this material is direct and reaches E_g = (220 ± 5) meV at low temperatures.

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.

Single Electron Gating of Topological Insulators

The effective gating of topological insulators is demonstrated, through the coupling of molecules to their surface. By using electric fields, they allow for dynamic control of the interface charge state by adding or removing single electrons. This process creates a robust transconductance bistability resembling a single-electron transistor. These findings make hybrid molecule/topological interfaces functional elements while at the same time pushing miniaturization to its ultimate limit.

Unconventional quantum Hall effect in Floquet topological insulators

We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the light's polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity [Formula: see text] at zero Fermi energy, to a Hall insulator state with [Formula: see text]. These findings open new possibilities for experimentally realizing nontrivial quantum states and unusual quantum Hall plateaus at [Formula: see text].

Indirect Interlayer Bonding in Graphene-Topological Insulator van der Waals Heterostructure: Giant Spin-Orbit Splitting of the Graphene Dirac States

van der Waals (vdW) heterostructures of two-dimensional materials exhibit properties and functionalities that can be tuned by stacking order and interlayer coupling. Although direct covalent bonding is not expected at the heterojunction, the formation of an interface nevertheless breaks the symmetries of the layers, and the orthogonal requirement of the wave functions can lead to indirect interfacial coupling, creating new properties and functionalities beyond their constituent layers. Here, we fabricate graphene/topological insulator vdW heterostructure by transferring chemical vapor deposited graphene onto Bi2Se3 grown by molecular beam epitaxy. Using scanning tunneling microscopy/spectroscopy, we observe a giant spin-orbit splitting of the graphene Dirac states up to 80 meV. Density functional theory calculations further reveal that this splitting of the graphene bands is a consequence of the breaking of inversion symmetry and the orthogonalization requirement on the overlapping wave functions at the interface, rather than simple direct bonding. Our findings reveal two intrinsic characteristics-the symmetry breaking and orthogonalization of the wave functions at the interface-that underlines the properties of vdW heterostructures.

Electronic and optical properties of graphene nanoribbons in external fields

A review work is done for the electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields. Effects due to the lateral confinement, curvature, stacking, non-uniform subsystems and hybrid structures are taken into account. The special electronic properties, induced by complex competitions between external fields and geometric structures, include many one-dimensional parabolic subbands, standing waves, peculiar edge-localized states, width- and field-dependent energy gaps, magnetic-quantized quasi-Landau levels, curvature-induced oscillating Landau subbands, crossings and anti-crossings of quasi-Landau levels, coexistence and combination of energy spectra in layered structures, and various peak structures in the density of states. There exist diverse absorption spectra and different selection rules, covering edge-dependent selection rules, magneto-optical selection rule, splitting of the Landau absorption peaks, intragroup and intergroup Landau transitions, as well as coexistence of monolayer-like and bilayer-like Landau absorption spectra. Detailed comparisons are made between the theoretical calculations and experimental measurements. The predicted results, the parabolic subbands, edge-localized states, gap opening and modulation, and spatial distribution of Landau subbands, have been identified by various experimental measurements.

Toward the Intrinsic Limit of the Topological Insulator Bi_{2}Se_{3}

Combining high resolution scanning tunneling microscopy and first principles calculations, we identified the major native defects, in particular the Se vacancies and Se interstitial defects, that are responsible for the bulk conduction and nanoscale potential fluctuations in single crystals of archetypal topological insulator Bi_{2}Se_{3}. Here it is established that the defect concentrations in Bi_{2}Se_{3} are far above the thermodynamic limit, and that the growth kinetics dominate the observed defect concentrations. Furthermore, through careful control of the synthesis, our tunneling spectroscopy suggests that our best samples are approaching the intrinsic limit with the Fermi level inside the band gap without introducing extrinsic dopants.

Bandgap modulation in photoexcited topological insulator Bi2Te3 via atomic displacements

The atomic and electronic dynamics in the topological insulator (TI) Bi2Te3 under strong photoexcitation were characterized with time-resolved electron diffraction and time-resolved mid-infrared spectroscopy. Three-dimensional TIs characterized as bulk insulators with an electronic conduction surface band have shown a variety of exotic responses in terms of electronic transport when observed under conditions of applied pressure, magnetic field, or circularly polarized light. However, the atomic motions and their correlation between electronic systems in TIs under strong photoexcitation have not been explored. The artificial and transient modification of the electronic structures in TIs via photoinduced atomic motions represents a novel mechanism for providing a comparable level of bandgap control. The results of time-domain crystallography indicate that photoexcitation induces two-step atomic motions: first bismuth and then tellurium center-symmetric displacements. These atomic motions in Bi2Te3 trigger 10% bulk bandgap narrowing, which is consistent with the time-resolved mid-infrared spectroscopy results.

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.

Surface Landau levels and spin states in bismuth (111) ultrathin films

The development of next-generation electronics is much dependent on the discovery of materials with exceptional surface-state spin and valley properties. Because of that, bismuth has attracted a renewed interest in recent years. However, despite extensive studies, the intrinsic electronic transport properties of Bi surfaces are largely undetermined due to the strong interference from the bulk. Here we report the unambiguous determination of the surface-state Landau levels in Bi (111) ultrathin films using scanning tunnelling microscopy under magnetic fields perpendicular to the surface. The Landau levels of the electron-like and the hole-like carriers are accurately characterized and well described by the band structure of the Bi (111) surface from density functional theory calculations. Some specific surface spin states with a large g-factor are identified. Our findings shed light on the exploiting surface-state properties of Bi for their applications in spintronics and valleytronics.

Nanoclusters of CaSe in calcium-doped Bi2Se3 grown by molecular-beam epitaxy

In calcium (Ca) doped Bi2Se3 films grown by molecular beam epitaxy, nanoclusters of CaSe are revealed by high-angle annular dark field imaging and energy dispersive x-ray spectroscopy analysis using a scanning transmission electron microscope. As the interface between the ordinary insulator CaSe and topological insulator, Bi2Se3, can host topological nontrivial interface state, this represents an interesting material system for further studies. We show by first principles total energy calculations that aggregation of Ca atoms in Bi2Se3 is driven by energy minimization and a preferential intercalation of Ca in the van der Waals gap between quintuple layers of Bi2Se3 induces reordering of atomic stacking and causes an increasing amount of stacking faults in film. The above findings also provide an explanation of less-than-expected electrical carrier (hole) concentrations in Ca-doped samples.

Kondo-like zero-bias conductance anomaly in a three-dimensional topological insulator nanowire

Zero-bias anomalies in topological nanowires have recently captured significant attention, as they are possible signatures of Majorana modes. Yet there are many other possible origins of zero-bias peaks in nanowires--for example, weak localization, Andreev bound states, or the Kondo effect. Here, we discuss observations of differential-conductance peaks at zero-bias voltage in non-superconducting electronic transport through a 3D topological insulator (Bi(1.33)Sb(0.67))Se3 nanowire. The zero-bias conductance peaks show logarithmic temperature dependence and often linear splitting with magnetic fields, both of which are signatures of the Kondo effect in quantum dots. We characterize the zero-bias peaks and discuss their origin.

Weak antilocalization and electron-electron interaction in coupled multiple-channel transport in a Bi2Se3 thin film

The electron transport properties of a topological insulator Bi2Se3 thin film are studied in Hall-bar geometry. The film with a thickness of 10 nm is grown by van der Waals epitaxy on fluorophlogopite mica and Hall-bar devices are fabricated from the as-grown film directly on the mica substrate. Weak antilocalization and electron-electron interaction effects are observed and analyzed at low temperatures. The phase-coherence length extracted from the measured weak antilocalization characteristics shows a strong power-law increase with decreasing temperature and the transport in the film is shown to occur via coupled multiple (topological surface and bulk states) channels. The conductivity of the film shows a logarithmical decrease with decreasing temperature and thus the electron-electron interaction plays a dominant role in quantum corrections to the conductivity of the film at low temperatures.

Current response of a topological insulator to a static Zeeman field

We study the magnetoelectric coupling at the surface of a topological insulator. We are particularly interested in the surface current induced by a static Zeeman/exchange field. This surface current can be related to the orbital magnetization of the system. For an insulator with zero Chern number, the orbital magnetization is independent of the details at the boundary. With the appearance of surface states in the topological insulator, it is not immediately obvious if the response is affected by the conditions at the surface. We investigate this question using exact diagonalization to a lattice model. By applying a time-reversal symmetry-breaking term near the boundary, even if the surface states are gapped out, we still find no change in the surface current. This arises from cancelations between Pauli and Van Vleck contributions between surface and bulk scattering states. We also show that the surface current response is independent of the chemical potential when it is within the bulk gap. Our results are consistent with the claim that orbital magnetization is a bulk property.

Tuning the Fermi level with topological phase transition by internal strain in a topological insulator Bi2Se3 thin film

In a three-dimensional topological insulator Bi2Se3, a stress control for band gap manipulation was predicted but no systematic investigation has been performed yet due to the requirement of large external stress. We report herein on the strain-dependent results for Bi2Se3 films of various thicknesses that are grown via a self-organized ordering process. Using small angle X-ray scattering and Raman spectroscopy, the changes of d-spacings in the crystal structure and phonon vibration shifts resulted from stress are clearly observed when the film thickness is below ten quintuple layers. From the UV photoemission/inverse photoemission spectroscopy (UPS/IPES) results and ab initio calculations, significant changes of the Fermi level and band gap were observed. The deformed band structure also exhibits a Van Hove singularity at specific energies in the UV absorption experiment and ab initio calculations. Our results, including the synthesis of a strained ultrathin topological insulator, suggest a new direction for electronic and spintronic applications for the future.

Spin-Based Mach-Zehnder Interferometry in Topological Insulator p-n Junctions

Transport in three-dimensional topological insulators relies on the existence of a spin-momentum locked surface state that encloses the insulating bulk. In this work we show how, in a topological insulator p-n junction, a magnetic field turns this surface state into an electronic Mach-Zehnder interferometer. Transmission of the junction can be tuned from zero to unity, resulting in virtually perfect visibility of the interference pattern, and the reflected and transmitted currents carry opposite spin polarization so that the junction also acts as a spin filter. Our setup therefore realizes a novel and highly tunable spintronic device where the effects of spin-momentum locking in topological insulator surface states can be probed directly in a transport experiment.