STM imaging of electronic waves on the surface of Bi2Te3: topologically protected surface states and hexagonal warping effects

Spin logic enabled by current vector adder

In order to advance the silicon integrated circuit technology, researchers have been searching for memory and logic devices with new physical state variables other than charge. Spin logic device that adds one degree of freedom-electron spin to charge has been considered as a promising candidate due to its low power consumption, built-in memory, and high scalability. Here, we demonstrate that a new variable - current direction on the sample can be introduced into the spin logic operation. The current direction of the sample is considered as a vector. For the various input currents along different directions, the direction of vector sum (vector adder) determines the output and therefore can enable complex logic functions. We have realized the basic Boolean logic gates including AND, OR, NAND, NOR, and even complicated IMPLY in a single device and further constructed a full adder with only 2 devices.

LDOS of electron pair and the role of the Pauli exclusion principle

The local density of states (LDOS) for a pair of non-relativistic electrons, influenced by repulsive Coulomb forces, is expressed in term of one-dimensional integrals over Whittaker functions. The computation of the electron pair's LDOS relies on a two-particle Green's function (GF), a generalization of the one-particle GF applicable to a charged particle in an attractive Coulomb potential. By incorporating electron spins and considering the Pauli exclusion principle, the resulting LDOS consists of two components: one originating from an exchange-even two-particle GF and the other from an exchange-odd two-particle GF. The calculated LDOS reveals its dependence on both inter-electron distance and energy. The pseudo-LDOS, derived from the two-body contribution to the LDOS, is examined. This term ensures complete LDOS suppression atr = 0, exhibiting a limited spatial extent, and the reasons for its emergence are elucidated. It is shown that for energies exceeding the effective Hartree energy and inter-electron distances beyond the effective Bohr radius, the impact of many-body contributions to the LDOS can be disregarded. The induced LDOS for an electron pair subjected to an attractive contact potential in two dimensions is evaluated. At small distancesafrom the potential center, a predicted relative difference in LDOS between even and odd state pair reaches approximately 8%. The calculated LDOS is compared with available experimental findings from a two-dimensional electron gas (2DEG). Both exhibit similar oscillation periods; however, the LDOS of the electron pair decays as1/a3, significantly faster than the1/adecay observed for free electrons in a 2DEG.

Atomically Resolved Defect-Engineering Scattering Potential in 2D Semiconductors

Engineering atomic-scale defects has become an important strategy for the future application of transition metal dichalcogenide (TMD) materials in next-generation electronic technologies. Thus, providing an atomic understanding of the electron-defect interactions and supporting defect engineering development to improve carrier transport is crucial to future TMDs technologies. In this work, we utilize low-temperature scanning tunneling microscopy/spectroscopy (LT-STM/S) to elicit how distinct types of defects bring forth scattering potential engineering based on intervalley quantum quasiparticle interference (QPI) in TMDs. Furthermore, quantifying the energy-dependent phase variation of the QPI standing wave reveals the detailed electron-defect interaction between the substitution-induced scattering potential and the carrier transport mechanism. By exploring the intrinsic electronic behavior of atomic-level defects to further understand how defects affect carrier transport in low-dimensional semiconductors, we offer potential technological applications that may contribute to the future expansion of TMDs.

Helical Topological Superconducting Pairing at Finite Excitation Energies

We propose helical topological superconductivity away from the Fermi surface in three-dimensional time-reversal-symmetric odd-parity multiband superconductors. In these systems, pairing between electrons originating from different bands is responsible for the corresponding topological phase transition. Consequently, a pair of helical topological Dirac surface states emerges at finite excitation energies. These helical Dirac surface states are tunable in energy by chemical potential and strength of band splitting. They are protected by time-reversal symmetry combined with crystalline twofold rotation symmetry. We suggest concrete materials in which this phenomenon could be observed.

Nanowires: Exponential speedup in quantum computing

This review paper examines the crucial role of nanowires in the field of quantum computing, highlighting their importance as versatile platforms for qubits and vital building blocks for creating fault-tolerant and scalable quantum information processing systems. Researchers are studying many categories of nanowires, including semiconductor, superconducting, and topological nanowires, to explore their distinct quantum features that play a role in creating various qubit designs. The paper explores the interdisciplinary character of quantum computing, combining the fields of quantum physics and materials science. This text highlights the significance of quantum gate operations in manipulating qubits for computation, thus creating the toolbox of quantum algorithms. The paper emphasizes the key research areas in quantum technology, such as entanglement engineering, quantum error correction, and a wide range of applications spanning from encryption to climate change modeling. The research highlights the importance of tackling difficulties related to decoding mitigation, error correction, and hardware scalability to fully utilize the transformative potential of quantum computing in scientific, technical, and computational fields.

Tuning of thermoelectric performance by modulating vibrational properties in Ni-doped Sb2Te3

Sb2Te3, a binary chalcogenide-based 3D topological insulator, attracts significant attention for its exceptional thermoelectric performance. We report the vibrational properties of magnetically doped Sb2Te3thermoelectric material. Ni doping induces defect/disorder in the system and plays a positive role in engineering the thermoelectric properties through tuning the vibrational phonon modes. Synchrotron powder x-ray diffraction study confirms good crystalline quality and single-phase nature of the synthesized samples. The change in structural parameters, includingBisoand strain, further corroborate with structural disorder. Detailed modification of phonon modes with doping and temperature variation is analysed from temperature-dependent Raman spectroscopic measurement. Compressive lattice strain is observed from the blue shift of Raman peaks owing to Ni incorporation in Sb site. An attempt is made to extract the lattice thermal conductivity from total thermal conductivity estimated through optothermal Raman studies. Hall concentration data support the change in temperature-dependent resistivity and thermopower. Remarkable increase in thermopower is observed after Ni doping. Simulation of the Pisarenko model, indicating the convergence of the valence band, explains the observed enhancement of thermopower in Sb2-xNixTe3. The energy gap between the light and heavy valence band at Γ point is found to be 30 meV (for Sb2Te3), which is reduced to 3 meV (in Sb1.98Ni0.02Te3). A significant increase in thermoelectric power factor is obtained from 715 μWm-1K-2for pristine Sb2Te3to 2415 μWm-1K-2for Ni-doped Sb2Te3sample. Finally, the thermoelectric figure of merit,ZTis found to increase by four times in Sb1.98Ni0.02Te3than that of its pristine counterpart.

Imaging the Breakdown and Restoration of Topological Protection in Magnetic Topological Insulator MnBi2Te4

Quantum anomalous Hall (QAH) insulators transport charge without resistance along topologically protected chiral 1D edge states. Yet, in magnetic topological insulators to date, topological protection is far from robust, with zero-magnetic field QAH effect only realized at temperatures an order of magnitude below the Néel temperature TN, though small magnetic fields can stabilize QAH effect. Understanding why topological protection breaks down is therefore essential to realizing QAH effect at higher temperatures. Here a scanning tunneling microscope is used to directly map the size of exchange gap (Eg,ex) and its spatial fluctuation in the QAH insulator 5-layer MnBi2Te4. Long-range fluctuations of Eg,ex are observed, with values ranging between 0 (gapless) and 70 meV, appearing to be uncorrelated to individual surface point defects. The breakdown of topological protection is directly imaged, showing that the gapless edge state, the hallmark signature of a QAH insulator, hybridizes with extended gapless regions in the bulk. Finally, it is unambiguously demonstrated that the gapless regions originate from magnetic disorder, by demonstrating that a small magnetic field restores Eg,ex in these regions, explaining the recovery of topological protection in magnetic fields. The results indicate that overcoming magnetic disorder is the key to exploiting the unique properties of QAH insulators.

Symmetry-selective quasiparticle scattering and electric field tunability of the ZrSiS surface electronic structure

Three-dimensional Dirac semimetals with square-net non-symmorphic symmetry, such as ternary ZrXY (X = Si, Ge; Y = S, Se, Te) compounds, have attracted significant attention owing to the presence of topological nodal lines, loops, or networks in their bulk. Orbital symmetry plays a profound role in such materials as the different branches of the nodal dispersion can be distinguished by their distinct orbital symmetry eigenvalues. The presence of different eigenvalues suggests that scattering between states of different orbital symmetry may be strongly suppressed. Indeed, in ZrSiS, there has been no clear experimental evidence of quasiparticle scattering reported between states of different symmetry eigenvalues at small wave vectorq⃗.Here we show, using quasiparticle interference, that atomic step-edges in the ZrSiS surface facilitate quasiparticle scattering between states of different symmetry eigenvalues. This symmetry eigenvalue mixing quasiparticle scattering is the first to be reported for ZrSiS and contrasts quasiparticle scattering with no mixing of symmetry eigenvalues, where the latter occurs with scatterers preserving the glide mirror symmetry of the crystal lattice, e.g. native point defects in ZrSiS. Finally, we show that the electronic structure of the ZrSiS surface, including its unique floating band surface state, can be tuned by a vertical electric field locally applied by the tip of a scanning tunneling microscope (STM), enabling control of a spin-orbit induced avoided crossing near the Fermi level by as much as 300%.

Room Temperature Spin-to-Charge Conversion in Amorphous Topological Insulating Gd-Alloyed BixSe1-x/CoFeB Bilayers

Disordered topological insulator (TI) films have gained intense interest by benefiting from both the TI's exotic transport properties and the advantage of mass production by sputtering. Here, we report on the clear evidence of spin-charge conversion (SCC) in amorphous Gd-alloyed BixSe1-x (BSG)/CoFeB bilayers fabricated by sputtering, which could be related to the amorphous TI surface states. Two methods have been employed to study SCC in BSG (tBSG = 6-16 nm)/CoFeB(5 nm) bilayers with different BSG thicknesses. First, spin pumping is used to generate a spin current in CoFeB and detect SCC by the inverse Edelstein effect (IEE). The maximum SCC efficiency (SCE) is measured to be as large as 0.035 nm (IEE length λIEE) in a 6 nm thick BSG sample, which shows a strong decay when tBSG increases due to the increase of BSG surface roughness. The second method is THz time-domain spectroscopy, which reveals a small tBSG dependence of SCE, validating the occurrence of a pure interface state-related SCC. Furthermore, our angle-resolved photoemission spectroscopy data show dispersive two-dimensional surface states that cross the bulk gap until the Fermi level, strengthening the possibility of SCC due to the amorphous TI states. Our studies provide a new experimental direction toward the search for topological systems in amorphous solids.

Electronic Band Structure and Surface States in Dirac Semimetal LaAgSb2

LaAgSb2 is a Dirac semimetal showing charge density wave (CDW) order. Previous angle-resolved photoemission spectroscopy (ARPES) results suggest the existence of the Dirac-cone-like structure in the vicinity of the Fermi level along the Γ-M direction. This paper is devoted to a complex analysis of the electronic band structure of LaAgSb2 by means of ARPES and theoretical studies within the ab initio method as well as tight binding model formulation. To investigate the possible surface states, we performed the direct DFT slab calculation and the surface Green function calculation for the (001) surface. The appearance of the surface states, which depends strongly on the surface, points to the conclusion that LaSb termination is realized in the cleaved crystals. Moreover, the surface states predicted by our calculations at the Γ and X points are found by ARPES. Nodal lines, which exist along the X-R and M-A paths due to crystal symmetry, are also observed experimentally. The calculations reveal other nodal lines, which originate from the vanishing of spin-orbit splitting and are located at the X-M-A-R plane at the Brillouin zone boundary. In addition, we analyze the band structure along the Γ-M path to verify whether Dirac surface states can be expected. Their appearance in this region is not confirmed.

Bilinear Magnetoresistance in HgTe Topological Insulator: Opposite Signs at Opposite Surfaces Demonstrated by Gate Control

Spin-orbit effects appearing in topological insulators (TI) and at Rashba interfaces are currently revolutionizing how we can manipulate spins and have led to several newly discovered effects, from spin-charge interconversion and spin-orbit torques to novel magnetoresistance phenomena. In particular, a puzzling magnetoresistance has been evidenced as bilinear in electric and magnetic fields. Here, we report the observation of bilinear magnetoresistance (BMR) in strained HgTe, a prototypical TI. We show that both the amplitude and sign of this BMR can be tuned by controlling with an electric gate the relative proportions of the opposite contributions of opposite surfaces. At magnetic fields of 1 T, the magnetoresistance is of the order of 1% and has a larger figure of merit than previously measured TIs. We propose a theoretical model giving a quantitative account of our experimental data. This phenomenon, unique to TI, offers novel opportunities to tune their electrical response for spintronics.

Nanometric Moiré Stripes on the Surface of Bi2Se3 Topological Insulator

Mismatch between adjacent atomic layers in low-dimensional materials, generating moiré patterns, has recently emerged as a suitable method to tune electronic properties by inducing strong electron correlations and generating novel phenomena. Beyond graphene, van der Waals structures such as three-dimensional (3D) topological insulators (TIs) appear as ideal candidates for the study of these phenomena due to the weak coupling between layers. Here we discover and investigate the origin of 1D moiré stripes on the surface of Bi₂Se₃ TI thin films and nanobelts. Scanning tunneling microscopy and high-resolution transmission electron microscopy reveal a unidirectional strained top layer, in the range 14-25%, with respect to the relaxed bulk structure, which cannot be ascribed to the mismatch with the substrate lattice but rather to strain induced by a specific growth mechanism. The 1D stripes are characterized by a spatial modulation of the local density of states, which is strongly enhanced compared to the bulk system. Density functional theory calculations confirm the experimental findings, showing that the TI surface Dirac cone is preserved in the 1D moiré stripes, as expected from the topology, though with a heavily renormalized Fermi velocity that also changes between the top and valley of the stripes. The strongly enhanced density of surface states in the TI 1D moiré superstructure can be instrumental in promoting strong correlations in the topological surface states, which can be responsible for surface magnetism and topological superconductivity.

Large magnetoelectric resistance in the topological Dirac semimetal α-Sn

The spin-momentum locking of surface states in topological materials can produce a resistance that scales linearly with magnetic and electric fields. Such a bilinear magnetoelectric resistance (BMER) effect offers a new approach for information reading and field sensing applications, but the effects demonstrated so far are too weak or for low temperatures. This article reports the first observation of BMER effects in topological Dirac semimetals; the BMER responses were measured at room temperature and were substantially stronger than those reported previously. The experiments used topological Dirac semimetal α-Sn thin films grown on silicon substrates. The films showed BMER responses that are 10⁶ times larger than previously measured at room temperature and are also larger than those previously obtained at low temperatures. These results represent a major advance toward realistic BMER applications. Significantly, the data also yield the first characterization of three-dimensional Fermi-level spin texture of topological surface states in α-Sn.

Quantum transport and potential of topological states for thermoelectricity in Bi2Te3thin films

This paper reviews recent developments in quantum transport and it presents current efforts to explore the contribution of topological insulator boundary states to thermoelectricity in Bi₂Te₃thin films. Although Bi₂Te₃has been used as a thermoelectric material for many years, it is only recently that thin films of this material have been synthesized as 3D topological insulators with interesting physics and potential applications related to topologically protected surface states. A major bottleneck in Bi₂Te₃thin films has been eliminating its bulk conductivity while increasing its crystal quality. The ability to grow epitaxial films with high crystal quality and to fabricate sophisticated Bi₂Te₃-based devices is attractive for implementing a variety of topological quantum devices and exploring the potential of topological states to improve thermoelectric properties. Special emphasis is laid on preparing low-defect-density Bi₂Te₃epitaxial films, gate-tuning of normal-state transport and Josephson supercurrent in topological insulator/superconductor hybrid devices. Prospective quantum transport experiments on Bi₂Te₃thin-film devices are discussed as well. Finally, an overview of current progress on the contribution of topological insulator boundary states to thermoelectricity is presented. Future explorations to reveal the potential of topological states for improving thermoelectric properties of Bi₂Te₃films and realizing high-performance thermoelectric devices are discussed.

Franckeite as an Exfoliable Naturally Occurring Topological Insulator

Franckeite is a natural superlattice composed of two alternating layers of different composition which has shown potential for optoelectronic applications. In part, the interest in franckeite lies in its layered nature which makes it easy to exfoliate into very thin heterostructures. Not surprisingly, its chemical composition and lattice structure are so complex that franckeite has escaped screening protocols and high-throughput searches of materials with nontrivial topological properties. On the basis of density functional theory calculations, we predict a quantum phase transition originating from stoichiometric changes in one of franckeite composing layers (the quasihexagonal one). While for a large concentration of Sb, franckeite is a sequence of type-II semiconductor heterojunctions, for a large concentration of Sn, these turn into type-III, much alike InAs/GaSb artificial heterojunctions, and franckeite becomes a strong topological insulator. Transmission electron microscopy observations confirm that such a phase transition may actually occur in nature.

Synthesis and characterization of a Sb2Te3/Bi2Te3 p-n junction heterostructure via electrodeposition in nanoporous membranes

Topological insulators (TIs) are bulk insulators with metallic surface states that can be described by a single Dirac cone. However, low-dimensional solids such as nanowires (NWs) are a challenge, due to the difficulty of separating surface contributions from bulk carriers. Fabrication of NWs with high surface-to-volume ratio can be realized by different methods such as chemical vapor transport, molecular beam epitaxy, and electrodeposition. The last method is used in the present work allowing the growth of structures such as p-n junctions, intercalation of magnetic or superconducting dots. We report the synthesis of high-quality TI NW: Bi₂Te₃, Sb₂Te₃ and p-n junction via electrodeposition. Structural, morphological, and nanostructure properties of NWs have been investigated by various characterization techniques. Interface structures and lateral heterojunctions (LHJ) in p-n junction NWs has also been made.

Competing Energy Scales in Topological Superconducting Heterostructures

Artificially engineered topological superconductivity has emerged as a viable route to create Majorana modes. In this context, proximity-induced superconductivity in materials with a sizable spin-orbit coupling has been intensively investigated in recent years. Although there is convincing evidence that superconductivity may indeed be induced, it has been difficult to elucidate its topological nature. Here, we engineer an artificial topological superconductor by progressively introducing superconductivity (Nb), strong spin-orbital coupling (Pt), and topological states (Bi₂Te₃). Through spectroscopic imaging of superconducting vortices within the bare s-wave superconducting Nb and within proximitized Pt and Bi₂Te₃ layers, we detect the emergence of a zero-bias peak that is directly linked to the presence of topological surface states. Our results are rationalized in terms of competing energy trends which are found to impose an upper limit to the size of the minigap separating Majorana and trivial modes, its size being ultimately linked to fundamental materials properties.

Disorder-Promoted Splitting in Quasiparticle Interference at Nesting Vectors

Inelastic interactions of quantum systems with the environment usually wash coherent effects out. In the case of Friedel oscillations, the presence of disorder leads to a fast decay of the oscillation amplitude. Here we show both experimentally and theoretically that in three-dimensional topological insulator Bi₂Te₃ there is a nesting-induced splitting of coherent scattering vectors which follows a peculiar evolution in energy. The effect becomes experimentally observable when the lifetime of quasiparticles shortens due to disorder. The amplitude of the splitting allows an evaluation of the lifetime of the electrons. A similar phenomenon should be observed in any system with a well-defined scattering vector regardless of its topological properties.

Topological insulator metamaterial with giant circular photogalvanic effect

One of the most notable manifestations of electronic properties of topological insulators is the dependence of the photocurrent direction on the helicity of circularly polarized optical excitation. The helicity-dependent photocurrents, underpinned by spin-momentum locking of surface Dirac electrons, are weak and easily overshadowed by bulk contributions. Here, we show that the chiral response can be enhanced by nanostructuring. The tight confinement of electromagnetic fields in the resonant nanostructure enhances the photoexcitation of spin-polarized surface states of topological insulator Bi1.5Sb0.5Te1.8Se1.2, leading to an 11-fold increase of the circular photogalvanic effect and a previously unobserved photocurrent dichroism (ρcirc = 0.87) at room temperature. The control of spin transport in topological materials by structural design is a previously unrecognized ability of metamaterials that bridges the gap between nanophotonics and spin electronics, providing opportunities for developing polarization-sensitive photodetectors.

Ultrafast evolution of bulk, surface and surface resonance states in photoexcited [Formula: see text]

We use circular dichroism (CD) in time- and angle-resolved photoemission spectroscopy (trARPES) to measure the femtosecond charge dynamics in the topological insulator (TI) [Formula: see text]. We detect clear CD signatures from topological surface states (TSS) and surface resonance (SR) states. In time-resolved measurements, independently from the pump polarization or intensity, the CD shows a dynamics which provides access to the unexplored electronic evolution in unoccupied states of [Formula: see text]. In particular, we are able to disentangle the unpolarized electron dynamics in the bulk states from the spin-textured TSS and SR states on the femtosecond timescale. Our study demonstrates that photoexcitation mainly involves the bulk states and is followed by sub-picosecond transport to the surface. This provides essential details on intra- and interband scattering in the relaxation process of TSS and SR states. Our results reveal the significant role of SRs in the subtle ultrafast interaction between bulk and surface states of TIs.

Electronic properties of Bi2Se3 dopped by 3d transition metal (Mn, Fe, Co, or Ni) ions

Topological insulators are characterized by the existence of band inversion and the possibility of the realization of surface states. Doping with a magnetic atom, which is a source of the time-reversal symmetry breaking, can lead to realization of novel magneto-electronic properties of the system. In this paper, we study effects of substitution by the transition metal ions (Mn, Fe, Co and Ni) into Bi₂Se₃ on its electric properties. Using the ab inito supercell technique, we investigate the density of states and the projected band structure. Under such substitution the shift of the Fermi level is observed. We find the existence of nearly dispersionless bands around the Fermi level associated with substituted atoms, especially, in the case of the Co and Ni. Additionally, we discuss the modification of the electron localization function as well as charge and spin redistribution in the system. Our study shows a strong influence of the transition metal-Se bond on local modifications of the physical properties. The results are also discussed in the context of the interplay between energy levels of the magnetic impurities and topological surface states.

Identifying Native Point Defects in the Topological Insulator Bi2Te3

We successfully identified native point defects that occur in Bi₂Te₃ crystals by combining high-resolution bias-dependent scanning tunneling microscopy and density functional theory based calculations. As-grown Bi₂Te₃ crystals contain vacancies, antisites, and interstitial defects that may result in bulk conductivity and therefore may change the insulating bulk character. Here, we demonstrate the interplay between the growth conditions and the density of different types of native near-surface defects. In particular, scanning tunneling spectroscopy reveals the dependence on not only the local atomic environment but also on the growth kinetics and the resulting sample doping from n-type toward intrinsic crystals with the Fermi level positioned inside the energy gap. Our results establish a bias-dependent STM signature of the Bi₂Te₃ native defects and shed light on the link between the native defects and the electronic properties of Bi₂Te₃, which is relevant for the synthesis of topological insulator materials and the related functional properties.

STM and STS studies of topological n-type (Bi, In)2(Te, Se, S)3thermoelectrics

In topological n-type thermoelectrics based on Bi2Te3with atomic substitutions Bi → In, Te → Se, S, the morphology and the surface states of Dirac fermions on the interlayer (0001) surface of van der Waals were studied by scanning tunneling microscopy and spectroscopy (STM/STS) techniques. By the STM method, the dark and light spots on the surface were found, which intensities depend on the composition and thermoelectric properties of solid solutions such as the Seebeck coefficient and thermoelectric power factor. The observed surface morphology features in the solid solutions are explained by distortions of surface electronic states originated from atomic substitutions, the influence of doping impurity, and formation mainly of substitutional impurity defects in thermoelectrics. The dips associated with substitutional impurities and antisite defects were found from the analysis of the height profiles obtained on the (0001) surface. Fast Fourier transform of the morphology STM images of the (0001) surface were used to obtain the interference patterns of the quasiparticles excitation caused by surface electrons scattering by defects. The Dirac point energy and its fluctuations, peak energies of surface defects, the positions of the valence and conduction band edges, and the energy gap were determined from an analysis of tunneling spectra. A correlation between the parameters of surface states of Dirac fermions and thermoelectric properties was found. Thus, a contribution of the fermions surface states increases with rise of the surface concentration in solid solutions with high power factor, and the largest concentration value was observed in the Bi1.98In0.02Te2.85Se0.15composition. The dependences of Fermi energy on the wave vector for different solid solutions are described by a set of Dirac cone sections located within the limits of the fluctuations of the Dirac point energy that explained by weak changes of the Fermi velocity for studied atomic substitutions in sublattices of bismuth telluride.

Observation of backscattering induced by magnetism in a topological edge state

The boundary modes of topological insulators are protected by the symmetries of the nontrivial bulk electronic states. Unless these symmetries are broken, they can give rise to novel phenomena, such as the quantum spin Hall effect in one-dimensional (1D) topological edge states, where quasiparticle backscattering is suppressed by time-reversal symmetry (TRS). Here, we investigate the properties of the 1D topological edge state of bismuth in the absence of TRS, where backscattering is predicted to occur. Using spectroscopic imaging and spin-polarized measurements with a scanning tunneling microscope, we compared quasiparticle interference (QPI) occurring in the edge state of a pristine bismuth bilayer with that occurring in the edge state of a bilayer, which is terminated by ferromagnetic iron clusters that break TRS. Our experiments on the decorated bilayer edge reveal an additional QPI branch, which can be associated with spin-flip scattering across the Brioullin zone center between time-reversal band partners. The observed QPI characteristics exactly match with theoretical expectations for a topological edge state, having one Kramer's pair of bands. Together, our results provide further evidence for the nontrivial nature of bismuth and in particular, demonstrate backscattering inside a helical topological edge state induced by broken TRS through local magnetism.

Few-layer hexagonal bismuth telluride (Bi2Te3) nanoplates with high-performance UV-Vis photodetection

It is widely known that the excellent intrinsic electronic and optoelectronic advantages of bismuthene and tellurene make them attractive for applications in transistors and logic and optoelectronic devices. However, their poor optoelectronic performances, such as photocurrent density and photoresponsivity, under ambient conditions severely hinder their practical application. To satisfy the demand of high-performance optoelectronic devices and topological insulators, bismuth telluride nanoplates (Bi2Te3 NPs) with different sizes, successfully synthesized by a solvothermal approach have been, for the first time, employed to fabricate a working electrode for photoelectrochemical (PEC)-type photodetection. It is demonstrated that the as-prepared Bi2Te3 NP-based photodetectors exhibit remarkably improved photocurrent density, enhanced photoresponsivity, and faster response time and recovery time in the UV-Vis region, compared to bismuthene and tellurene-based photodetectors. Additionally, the PEC stability measurements show that Bi2Te3 NPs have a comparable long-term stability for on/off switching behaviour for the bismuthene and tellurene-based photodetectors. Therefore, it is anticipated that the present work can provide fundamental acknowledgement of the optoelectronic performance of a PEC-type Bi2Te3 NP-based photodetector, shedding light on new designs of high-performance topological insulator-based optoelectronic devices.

Selective trapping of hexagonally warped topological surface states in a triangular quantum corral

The surface of a three-dimensional topological insulator (TI) hosts two-dimensional massless Dirac fermions (DFs), the gapless and spin-helical nature of which leads to their high transmission through surface defects or potential barriers. Here, we report the behaviors of topological surface states (TSS) in a triangular quantum corral (TQC) which, unlike a circular corral, is supposed to be totally transparent for DFs. By real-space mapping of the electronic structure of TQCs, both the trapping and detrapping behaviors of the TSS are observed. The selection rules are found to be governed by the geometry and spin texture of the constant energy contour of TSS upon the strong hexagonal warping in Bi₂Te₃. Our work indicates the extended nature of TSS and elucidates the selection rules of the trapping of TSS in the presence of a complicated surface state structure, giving insights into the effective engineering of DFs in TIs.

Nonlayered tellurene as an elemental 2D topological insulator: experimental evidence from scanning tunneling spectroscopy

We report the formation of a nonlayered tellurene monolayer in its alpha-phase through an anisotropic ultrasonication method. The nonlayered tellurene has so far been predicted to exhibit a topologically insulating state of matter in two-dimensional (2D) form with an insulating interior and metallic edge states propagating along the perimeter of the 2D objects. In this work, we report direct evidence of elemental topological insulator behavior in the material through a localized mode of measurement, that is, scanning tunneling spectroscopic studies. We moreover deliberate on the length scale the time-reversal symmetry-protected edge states extend towards the interior. The metallic edge, which has been found to span over a 3 nm region, opens and widens monotonically into gapped states. The appearance of the elemental 2D topological insulator phase has been explained in terms of built-in strains in the systems as viewed through a shift in the Raman modes.

Three-Dimensional Topological Insulator Bi2Te3/Organic Thin Film Heterojunction Photodetector with Fast and Wideband Response from 450 to 3500 Nanometers

In the pursuit of broadband photodetection materials from visible to mid-IR region, the fresh three-dimensional topological insulators (3D TIs) are theoretically predicted to be a promising candidate due to its Dirac-like stable surface state and high absorption rate. In this work, a self-powered inorganic/organic heterojunction photodetector based on n-type 3D TIs Bi₂Te₃ combined with p-type pentacene thin film was designed and fabricated. Surprisingly, it was found that the Bi₂Te₃/pentacene heterojunction photodetector exhibited a fast and wideband response from 450 to 3500 nm. The optimized responsivity of photodetector reached 14.89 A/W, along with the fast response time of 1.89 ms and the ultrahigh external quantum efficiency of 2840%. Moreover, at the mid-IR 3500 nm, our devices demonstrated a responsivity of 1.55 AW^-1, which was several orders of magnitude higher than that of previous 3D TIs photodetector. These excellent properties indicate that the inorganic/organic heterojunction, that is, the combination of 3D TIs with organic materials, is an exciting structure for high performance photodetectors in the wideband detection region. On account of the fact that the device is constructed on mica substrate, this work also represents a potential scenario for flexible optoelectronic devices.

An ultrafast symmetry switch in a Weyl semimetal

Topological quantum materials exhibit fascinating properties^1-3, with important applications for dissipationless electronics and fault-tolerant quantum computers^4,5. Manipulating the topological invariants in these materials would allow the development of topological switching applications analogous to switching of transistors⁶. Lattice strain provides the most natural means of tuning these topological invariants because it directly modifies the electron-ion interactions and potentially alters the underlying crystalline symmetry on which the topological properties depend^7-9. However, conventional means of applying strain through heteroepitaxial lattice mismatch¹⁰ and dislocations¹¹ are not extendable to controllable time-varying protocols, which are required in transistors. Integration into a functional device requires the ability to go beyond the robust, topologically protected properties of materials and to manipulate the topology at high speeds. Here we use crystallographic measurements by relativistic electron diffraction to demonstrate that terahertz light pulses can be used to induce terahertz-frequency interlayer shear strain with large strain amplitude in the Weyl semimetal WTe₂, leading to a topologically distinct metastable phase. Separate nonlinear optical measurements indicate that this transition is associated with a symmetry change to a centrosymmetric, topologically trivial phase. We further show that such shear strain provides an ultrafast, energy-efficient way of inducing robust, well separated Weyl points or of annihilating all Weyl points of opposite chirality. This work demonstrates possibilities for ultrafast manipulation of the topological properties of solids and for the development of a topological switch operating at terahertz frequencies.

Surface-mediated spin dynamics probed by optical-pump–probe scanning tunneling microscopy

In current materials science and technologies, surface effects on carrier and spin dynamics in functional materials and devices are of great importance.

Selection Rules for Quasiparticle Interference with Internal Nonsymmorphic Symmetries

We study how nonsymmorphic symmetries that commute with lattice translations are reflected in the quasiparticle interference (QPI) maps measured by scanning tunneling microscopy (STM). QPI maps, which result from scattering of Bloch states off impurities, record the interference of incoming and scattered waves as a function of energy and tip's position. Although both the impurity and the tip generically break spatial symmetries, we find that the QPI maps provide universal information on these symmetries. The symmetries impose constraints on the relation between various momentum components of the Bloch functions. These relations result in selection rules on certain momentum transfers in QPI maps. We find that universal information is encoded in the absence of QPI signal, or in the relative intensity of its replications. We show examples for one-dimensional chains and an effective model of the layered compound ZrSiS. We discuss the implications of our theory in the analysis of observed QPI of the Weyl semimetal TaAs. Our theory is particularly relevant for materials in rod and layer space groups, or when a correlated order parameter, such as antiferromagnetism, enlarges the unit cell.

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.

Noise-Induced Backscattering in a Quantum Spin Hall Edge

Time-reversal symmetry suppresses electron backscattering in a quantum-spin-Hall edge, yielding quantized conductance at zero temperature. Understanding the dominant corrections in finite-temperature experiments remains an unsettled issue. We study a novel mechanism for conductance suppression: backscattering caused by incoherent electromagnetic noise. Specifically, we show that an electric potential fluctuating randomly in time can backscatter electrons inelastically without constraints faced by electron-electron interactions. We quantify noise-induced corrections to the dc conductance in various regimes and propose an experiment to test this scenario.

Transport theory for electrical detection of the spin-momentum locking of topological surface states

We provide a general transport theory for spin-polarized scanning tunneling microscopy (STM) through a doped topological insulator (TI) surface. It is found that different from the conventional magnetic substrate, the tunneling conductance through the tip-TI surface acquires an extra component determined by the in-plane spin texture, exclusively associated with the spin momentum locking. Importantly, this extra conductance unconventionally depends on the spatial azimuthal angle of the magnetized STM tip. By introducing a magnetic impurity to break the symmetry of rotation and local time reversal of the TI surface, we find that the measurement of the spatial resolved conductance can reconstruct the helical structure of spin texture, from which the spin-momentum locking angle can be extracted if the in-plane magnetization is induced purely by the spin-orbit coupling of surface Dirac electrons. Our theory offers an alternative way, differing from existing in-plane-current polarization probed in a multi-terminal setup or angle resolved photoemission spectroscopy, to electrically identify the helical spin texture on TI surfaces.

Bi2Se3 topological insulator at the 2D-limit: role of halide-doping on Dirac point

2D topological insulators exhibit insulating bulk and conducting edge states with a Dirac point, which at times is within the energy gap and could be on either side of the Fermi energy. In this study, we demonstrate a method to tune the energy of the Dirac edge state by introducing halides as dopants in Bi₂Se₃. We chose halides to substitute the anion, so that due to higher atomic number (of iodine, for example) with respect to selenium, the spin-orbit coupling parameter could be enhanced, leading to the significant separation of the Dirac point from the Fermi energy. With different halogens having different atomic numbers on either side of selenium, the Dirac point could hence be tuned towards both directions. The dopants, due to their heterovalent nature with respect to selenide, introduce carriers in the lattice and consequently, also shift the Fermi energy. We show that the Dirac point with respect to Fermi energy could be correlated to the dopant's atomic number and thus the atomic-number-induced spin-orbit coupling parameter. Strains developed in the lattice due to a mismatch in the effective ionic radii of the dopants and the host anion affected distribution of band energies, leaving the (distribution of) Dirac point unaffected due to its topologically protected nature.

Dirac Signature in Germanene on Semiconducting Substrate

2D Dirac materials supported by nonmetallic substrates are of particular interest due to their significance for the realization of the quantum spin Hall effect and their application in field-effect transistors. Here, monolayer germanene is successfully fabricated on semiconducting germanium film with the support of a Ag(111) substrate. Its linear-like energy-momentum dispersion and large Fermi velocity are derived from the pronounced quasiparticle interference patterns in a √3 × √3 superstructure. In addition to Dirac fermion characteristics, the theoretical simulations reveal that the energy gap opens at the Brillouin zone center of the √3 × √3 restructured germanene, which is evoked by the symmetry-breaking perturbation potential. These results demonstrate that the germanium nanosheets with √3 × √3 germanene can be an ideal platform for fundamental research and for the realization of high-speed and low-energy-consumption field-effect transistors.

Suppression of Quasiparticle Scattering Signals in Bilayer Graphene Due to Layer Polarization and Destructive Interference

We study chemically gated bilayer graphene using scanning tunneling microscopy and spectroscopy complemented by tight-binding calculations. Gating is achieved by intercalating Cs between bilayer graphene and Ir(111), thereby shifting the conduction band minima below the chemical potential. Scattering between electronic states (both intraband and interband) is detected via quasiparticle interference. However, not all expected processes are visible in our experiment. We uncover two general effects causing this suppression: first, intercalation leads to an asymmetrical distribution of the states within the two layers, which significantly reduces the scanning tunneling spectroscopy signal of standing waves mainly present in the lower layer; second, forward scattering processes, connecting points on the constant energy contours with parallel velocities, do not produce pronounced standing waves due to destructive interference. We present a theory to describe the interference signal for a general n-band material.

Photoinduced Inverse Spin Hall Effect of Surface States in the Topological Insulator Bi2Se3

The three-dimensional (3D) topological insulator (TI) Bi₂Se₃ exhibits topologically protected, linearly dispersing Dirac surface states (SSs). To access the intriguing properties of these SSs, it is important to distinguish them from the coexisting two-dimensional electron gas (2DEG) on the surface. Here, we use circularly polarized light to induce the inverse spin Hall effect in a Bi₂Se₃ thin film at different temperatures (i.e., from 77 to 300 K). It is demonstrated that the photoinduced inverse spin Hall effect (PISHE) of the top SSs and the 2DEG can be separated based on their opposite signs. The temperature and power dependence of the PISHE also confirms our method. Furthermore, it is found that the PISHE in the 2DEG is dominated by the extrinsic mechanism, as revealed by the temperature dependence of the PISHE.

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.

Structure-Dependent Optical Properties of Self-Organized Bi2Se3 Nanostructures: From Nanocrystals to Nanoflakes

Bismuth selenide (Bi₂Se₃), with a wide bulk band gap and single massless Dirac cone at the surface, is a promising three-dimensional topological insulator. Bi₂Se₃ possesses gapless surface states and an insulator-like bulk band gap as a new type of quantum matter. Different Bi₂Se₃ nanostructures were prepared using electron beam evaporation with high production efficiency. Structural investigations by energy-dispersive X-ray analysis, scanning electron microscopy, and X-ray diffraction revealed the sample stoichiometries and the structural transition mechanism from nanocrystals to nanoflakes. The optical properties systematically probed and analyzed by spectroscopic ellipsometry showed strong dependence on the nanostructures and were also predicted to have structure-modifiable technological prospects. The optical parameters, plasma frequencies, scattering rates of the free electrons, and optical band gaps were related to the topological properties of the Bi₂Se₃ nanostructures via light-matter interactions, offering new opportunities and approaches for studies on topological insulators and spintronics. The high-quality Bi₂Se₃ nanostructures provide advantages in exploring novel physics and exploiting prospective applications.

Scanning probe microscopy induced surface modifications of the topological insulator Bi2Te3 in different environments

We investigated the topological insulator (TI) Bi₂Te₃ in four different environments (ambient, ultra-high vacuum (UHV), nitrogen gas and organic solvent environment) using scanning probe microscopy (SPM) techniques. Upon prolonged exposure to ambient conditions and organic solvent environments the cleaved surface of the pristine Bi₂Te₃ is observed to be strongly modified during SPM measurements, while imaging of freshly cleaved Bi₂Te₃ in UHV and nitrogen gas shows considerably less changes of the Bi₂Te₃ surface. We conclude that the reduced surface stability upon exposure to ambient conditions is triggered by adsorption of molecular species from ambient, including H₂O, CO₂, etc which is verified by Auger electron spectroscopy. Our findings of the drastic impact of exposure to ambient on the Bi₂Te₃ surface are crucial for further in-depth studies of the intrinsic properties of the TI Bi₂Te₃ and for potential applications that include room temperature TI based devices operated under ambient conditions.

Ultrafast spin-polarized electron dynamics in the unoccupied topological surface state of Bi2Se3

The three-dimensional topological insulator Bi₂Se₃ presents two cone-like dispersive topological surface states centered at the [Formula: see text] point. One of them is unoccupied in equilibrium conditions and located 1.8 eV above the other one lying close to the Fermi level. In this work we employ time- and angle-resolved photoemission spectroscopy with circularly polarized pump photons to selectively track the spin dynamics of the empty topological states. We observe that spin-polarized electrons flow along the topological cone and recombine towards the unpolarized bulk states on a timescale of few tens of femtoseconds. This provides direct evidence of the capability to trigger a spin current with circularly polarized light.

High-performance nanoscale topological energy transduction

The realization of high-performance, small-footprint, on-chip inductors remains a challenge in radio-frequency and power microelectronics, where they perform vital energy transduction in filters and power converters. Modern planar inductors consist of metallic spirals that consume significant chip area, resulting in low inductance densities. We present a novel method for magnetic energy transduction that utilizes ferromagnetic islands (FIs) on the surface of a 3D time-reversal-invariant topological insulator (TI) to produce paradigmatically different inductors. Depending on the chemical potential, the FIs induce either an anomalous or quantum anomalous Hall effect in the topological surface states. These Hall effects direct current around the FIs, concentrating magnetic flux and producing a highly inductive device. Using a novel self-consistent simulation that couples AC non-equilibrium Green functions to fully electrodynamic solutions of Maxwell's equations, we demonstrate excellent inductance densities up to terahertz frequencies, thus harnessing the unique properties of topological materials for practical device applications.

Odd-frequency superconductivity induced in topological insulators with and without hexagonal warping

We study the effect of the Fermi surface anisotropy on the odd-frequency spin-triplet pairing component of the induced pair potential. We consider a superconductor/ ferromagnetic insulator (S/FI) hybrid structure formed on the 3D topological insulator (TI) surface. In this case three ingredients ensure the possibility of the odd-frequency pairing: (1) the topological surface states, (2) the induced pair potential, and (3) the magnetic moment of a nearby ferromagnetic insulator. We take into account the strong anisotropy of the Dirac point in topological insulators when the chemical potential lies well above the Dirac cone and its constant energy contour has a snowflake shape. Within this model, we propose that the S/FI boundary should be properly aligned with respect to the snowflake constant energy contour to have an odd-frequency symmetry of the corresponding pairing component and to insure the Majorana bound state at the S/FI boundary. For arbitrary orientation of the boundary, the Majorana bound state is absent. This provides a selection rule to the realization of Majorana modes in S/FI hybrid structures, formed on the topological insulator surface.

Chemical Disorder in Topological Insulators: A Route to Magnetism Tolerant Topological Surface States

We show that the chemical inhomogeneity in ternary three-dimensional topological insulators preserves the topological spin texture of their surface states against a net surface magnetization. The spin texture is that of a Dirac cone with helical spin structure in the reciprocal space, which gives rise to spin-polarized and dissipation-less charge currents. Thanks to the nontrivial topology of the bulk electronic structure, this spin texture is robust against most types of surface defects. However, magnetic perturbations break the time-reversal symmetry, enabling magnetic scattering and loss of spin coherence of the charge carriers. This intrinsic incompatibility precludes the design of magnetoelectronic devices based on the coupling between magnetic materials and topological surface states. We demonstrate that the magnetization coming from individual Co atoms deposited on the surface can disrupt the spin coherence of the carriers in the archetypal topological insulator Bi₂Te₃, while in Bi₂Se₂Te the spin texture remains unperturbed. This is concluded from the observation of elastic backscattering events in quasiparticle interference patterns obtained by scanning tunneling spectroscopy. The mechanism responsible for the protection is investigated by energy resolved spectroscopy and ab initio calculations, and it is ascribed to the distorted adsorption geometry of localized magnetic moments due to Se-Te disorder, which suppresses the Co hybridization with the surface states.

Electrical resistance of individual defects at a topological insulator surface

Three-dimensional topological insulators host surface states with linear dispersion, which manifest as a Dirac cone. Nanoscale transport measurements provide direct access to the transport properties of the Dirac cone in real space and allow the detailed investigation of charge carrier scattering. Here we use scanning tunnelling potentiometry to analyse the resistance of different kinds of defects at the surface of a (Bi_0.53Sb_0.47)₂Te₃ topological insulator thin film. We find the largest localized voltage drop to be located at domain boundaries in the topological insulator film, with a resistivity about four times higher than that of a step edge. Furthermore, we resolve resistivity dipoles located around nanoscale voids in the sample surface. The influence of such defects on the resistance of the topological surface state is analysed by means of a resistor network model. The effect resulting from the voids is found to be small compared with the other defects.

Exploiting topological insulator surface states in electronic devices requires an understanding of the factors that affect transport. Here, the authors use scanning tunnelling potentiometry to determine the contributions of different kinds of surface defects to the electrical resistance.

Thickness-dependent Dirac dispersions of few-layer topological insulators supported by metal substrate

The surface states protected by time-reversal symmetry in 3-dimensional topological insulators have recently been confirmed by angle-resolved photoemission spectroscopy, scanning tunneling microscopy, quantum transport and so on. However, the electronic properties of ultra-thin topological insulator films have not been extensively studied, especially when the films are grown on metal substrates. In this paper, we have elucidated the local behaviors of the electronic states of ultra-thin topological insulator Bi₂Se₃ grown with molecular beam epitaxy on Au(111) using scanning tunneling microscopy/spectroscopy. We have observed linear dispersion of electron interference patterns at higher energies than the Fermi energy that were not accessible by conventional angle-resolved photoemission spectroscopy. Moreover, the dispersion of the interference patterns varies with the film thickness, which is explained by band bending near the interface between the topological insulator and the metal substrate. Our experiments demonstrate that interfacial effects in thin topological insulator films on metal substrate can be sensed using scanning tunneling spectroscopy.

Energy-Dependent Chirality Effects in Quasifree-Standing Graphene

We present direct experimental evidence of broken chirality in graphene by analyzing electron scattering processes at energies ranging from the linear (Dirac-like) to the strongly trigonally warped region. Furthermore, we are able to measure the energy of the van Hove singularity at the M point of the conduction band. Our data show a very good agreement with theoretical calculations for free-standing graphene. We identify a new intravalley scattering channel activated in case of a strongly trigonally warped constant energy contour, which is not suppressed by chirality. Finally, we compare our experimental findings with T-matrix simulations with and without the presence of a pseudomagnetic field and suggest that higher order electron hopping effects are a key factor in breaking the chirality near to the van Hove singularity.

Disorder enabled band structure engineering of a topological insulator surface

Three-dimensional topological insulators are bulk insulators with Z₂ topological electronic order that gives rise to conducting light-like surface states. These surface electrons are exceptionally resistant to localization by non-magnetic disorder, and have been adopted as the basis for a wide range of proposals to achieve new quasiparticle species and device functionality. Recent studies have yielded a surprise by showing that in spite of resisting localization, topological insulator surface electrons can be reshaped by defects into distinctive resonance states. Here we use numerical simulations and scanning tunnelling microscopy data to show that these resonance states have significance well beyond the localized regime usually associated with impurity bands. At native densities in the model Bi₂X₃ (X=Bi, Te) compounds, defect resonance states are predicted to generate a new quantum basis for an emergent electron gas that supports diffusive electrical transport.

The surface electrons in a topological insulator are resistant to localization by nonmagnetic disorder, but are affected by lattice disorder. Here, the authors show that resonance states near lattice defects on the surface have significance beyond the localized regime usually associated with impurity bands.