Helical Spin Texture Research Articles

Tuning of Topological Dirac States via Modification of van der Waals Gap in Strained Ultrathin Bi2Se3 Films

Robust massless Dirac states with helical spin textures were realized at the boundaries of topological insulators such as van der Waals (vdW) layered Bi2Se3 family compounds. Topological properties of massless Dirac states can be controlled by varying the film thickness, external stimuli, or environmental factors. Here, we report single-crystal-quality growth of ultrathin Bi2Se3 films on flexible polyimide sheets and manipulation of the Dirac states by varying the vdW gap. X-ray diffraction unambiguously demonstrates that under uniaxial bending stress the vdW gap substantially changes with interatomic-layer distances unaltered. Terahertz and photoelectron spectroscopy indicate tuning of the number of quantum conducting channels and of work function, by the stress, respectively. Surprisingly, under compressive strain, transport measurements reveal dimensional crossover and suppressed weak antilocalization. First-principles calculations support the observation. Our findings suggest that variation of vdW gap...

Topological phases in the TaSe3 compound

Based on first-principles calculations, we show that stoichiometric TaSe3, synthesized in space group P21/m, belongs to a three-dimensional (3D) strong topological insulator (TI) phase with Z2 invariants (1;100). The calculated surface spectrum shows clearly a single Dirac cone on surfaces, with helical spin texture at a constant energy contour. To check the stability of the topological phase, strain effects have been systematically investigated, showing that many topological phases survive in a wide range of the strains along both the a- and c-axes, such as strong TI (STI), weak TI (WTI) and Dirac semimetal phases. TaSe3 provides us an ideal platform for experimental study of topological phase transitions. More interestingly, since superconductivity in TaSe3 has been reported for a long time, the co-existence of topological phases and superconducting phase suggests that TaSe3 is a realistic system to study the interplay between topological and superconducting phases in the future.

Orbital-dependent spin textures in Bi2Se3 quantum well states

Author(s): Lin, CY; Gotlieb, K; Jozwiak, C; Hussain, Z; Lanzara, A | Abstract: Understanding the fine interplay between spin and orbital degrees of freedom in the surface states of topological insulators is the key to the development of next-generation spintronics devices. So far, the majority of studies have focused on the helical spin texture of the topologically protected surface state (TSS) and little attention has been devoted to the spin texture of the other surface states: the bulk-originated quantum well states (QWSs). This paper presents such study in a prototypical topological insulator, Bi2Se3. By using spin- and angle-resolved photoemission spectroscopy, we reveal a full momentum-dependent spin texture of the QWSs and their response to light polarization. We find that these states share a similar spin-orbital texture with the TSS. This paper shows an intimate correlation between the surface and bulk states, which was overseen before, and provides relevant information to understand how the surface states evolve with the bulk states.

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.

Fundamental limits to helical edge conductivity due to spin-phonon scattering

We study the effect of electron-phonon interactions on the electrical conductance of a helical edge state of a two-dimensional topological insulator. We show that the edge deformation caused by bulk acoustic phonons modifies the spin texture of the edge state, and that the resulting spin-phonon coupling leads to inelastic backscattering which makes the transport diffusive. Using a semiclassical Boltzmann equation we compute the electrical conductivity and show that it exhibits a metallic Bloch-Gr\"uneisen law. At temperatures on the order of the Debye temperature of the host material, spin-phonon scattering thus lowers the conductivity of the edge state drastically. Transport remains ballistic only for short enough edges, and in this case the correction to the quantized conductance vanishes as $\delta G \propto T^5$ at low temperatures. Relying only on parallel transport of the helical spin texture along the deformed edge, the coupling strength is determined by the host material's density and sound velocity. Our results impose fundamental limits for the finite-temperature conductivity of a helical edge channel.

Topological states induced by local structural modification of the polar BiTeI(0001) surface

The layered polar semiconductor BiTeI exhibits large Rashba-type spin–orbit splittings in its bulk and surface electronic structure. Here we report an artificial structural modification near the surface of BiTeI(0001) induced by annealing in vacuum. Using scanning tunneling microscopy we show that the annealing-induced change in the near-surface stoichiometry results in a structural change from a non-centrosymmetric triple-layered to a quintuple-layered structure. The structural change gives rise to the emergence of topological surface states with helical spin texture as demonstrated by angle-resolved photoemission experiments and relativistic first-principles calculations. The results provide a way to modify the electronic structure of layered materials by a controlled manipulation of the atomic stacking sequences.

Superconductivity switch from spin-singlet to -triplet pairing in a topological superconducting junction

The interedge coupling is the cardinal characteristic of the narrow quantum spin Hall (QSH) insulator, and thus could bring about exotic transport phenomena. Herein, we present a theoretical investigation of the spin-resolved Andreev reflection (AR) in a QSH insulator strip touching on two neighbouring ferromagnetic insulators and one s-wave superconductor. It is demonstrated that, due to the interplay of the interedge coupling and ferromagnetic configuration, there could be not only usual local ARs leading to the spin-singlet pairing with the incident electron and Andreev-reflected hole from different spin subbands, but also novel local ARs giving rise to the spin-triplet pairing from the same spin subband. However, only the latter exists in the absence of the interedge coupling, and therefore the two pairings in turn testify the helical spin texture of the edge states. By proper tuning of the band structures of the ferromagnetic layers, under the resonance bias voltage, the usual and novel local ARs of can be all exhibited, resulting in fully spin-polarized pure spin-singlet superconductivity and pure spin-triplet superconductivity, respectively, which suggests a superconductivity switch from spin-singlet to -triplet pairing by electrical control. The results can be experimentally confirmed by the tunneling conductance and the noise power.

Generation and control of noncollinear magnetism by supercurrent

When superconductivity couples with noncollinear spin textures, rich physics arises; for instance, singlet Cooper pairs can be converted to triplet pairs, and topological superconductors can be realized. For their applications, the controllability of noncollinear magnetism is a crucial issue. Here, we propose that a supercurrent can induce and control noncollinear magnetic orders in a correlated metal on top of a singlet superconductor. We show that the magnetic instability in the correlated metal is enhanced by the proximity effect of supercurrents, which leads to phase transitions from a paramagnetic state to noncollinear magnetic phases with helical or vortexlike spin textures. Furthermore, these magnetic orders can be switched by the direction of the supercurrent. We also discuss the effect of the Rashba spin-orbit coupling and the experimental realization.

Topological Electride Y2C.

Two-dimensional (2D) electrides are layered ionic crystals in which anionic electrons are confined in the interlayer space. Here, we report a discovery of nontrivial [Formula: see text] topology in the electronic structures of 2D electride Y2C. Based on first-principles calculations, we found a topological [Formula: see text] invariant of (1; 111) for the bulk band and topologically protected surface states in the surfaces of Y2C, signifying its nontrivial electronic topology. We suggest a spin-resolved angle-resolved photoemission spectroscopy (ARPES) measurement to detect the unique helical spin texture of the spin-polarized topological surface state, which will provide characteristic evidence for the nontrivial electronic topology of Y2C. Furthermore, the coexistence of 2D surface electride states and topological surface state enables us to explain the outstanding discrepancy between the recent ARPES experiments and theoretical calculations. Our findings establish a preliminary link between the electride in chemistry and the band topology in condensed-matter physics, which are expected to inspire further interdisciplinary research between these fields.

Visualizing the evolution of surface localization in the topological state of Bi2Se3 by circular dichroism in laser-based angle-resolved photoemission spectroscopy

We use angle-resolved photoemission spectroscopy with a circularly polarized 7-eV laser, and find that the angle-resolved pattern of circular dichroism (CD) for the topological surface state of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is dramatically changed with surface aging. Shortly after sample cleaving, the CD pattern exhibits a $\mathrm{sin}(\ensuremath{\phi}$)-like modulation ($\ensuremath{\phi}$ is the Fermi surface angle) reminiscent of the helical spin texture. Intriguingly, this pattern gradually changes with time, and eventually turns into a $\mathrm{sin}(2\ensuremath{\phi})$-like modulation on the aged surface. These two patterns are also revealed in quantum well states with different quantum numbers, indicating that the CD pattern is a valid measure to identify the surface confinement of electrons. Our experiments thus demonstrate the time evolution of electron localization in the topological surface state.

Atomic structure governed diversity of exchange-driven spin helices in Fe nanoislands: Experiment and theory

We combine spin-polarized scanning tunneling microscopy (SP-STM) and first-principles calculations to demonstrate the control of the wavelength of helical spin textures in Fe nanoislands by varying their atomic structure. We make use of the complexity of submonolayer growth of Fe on Cu(111) to prepare nanoislands characterized by different thickness and in-plane atomic structure. SP-STM results reveal that the magnetic states of different nanoislands are spin helices. The wavelength of the spin helices varies strongly. Calculations performed for Fe films with different thickness and in-plane atomic structure explain the strong variation of the wavelength by a subtle balance in the competition between ferromagnetic and antiferromagnetic exchange interactions. We identify the crucial role of the effectively enhanced weak antiferromagnetic exchange interactions between distant atoms.

High quality atomically thin PtSe2 films grown by molecular beam epitaxy

Atomically thin PtSe2 films have attracted extensive research interests for potential applications in high-speed electronics, spintronics and photodetectors. Obtaining high quality thin films with large size and controlled thickness is critical. Here we report the first successful epitaxial growth of high quality PtSe2 films by molecular beam epitaxy. Atomically thin films from 1 ML to 22 ML have been grown and characterized by low-energy electron diffraction, Raman spectroscopy and x-ray photoemission spectroscopy. Moreover, a systematic thickness dependent study of the electronic structure is revealed by angle-resolved photoemission spectroscopy (ARPES), and helical spin texture is revealed by spin-ARPES. Our work provides new opportunities for growing large size single crystalline films to investigate the physical properties and potential applications of PtSe2.

Supercurrent switch in \u03c0 topological junctions based upon a narrow quantum spin Hall insulator

The narrow quantum spin Hall (QSH) insulator is characterized by interedge coupling, which could feature exotic transport phenomena, and thus serves as the key element for topological superconducting electronic devices. Herein, we theoretically explore possible Josephson π states in a QSH insulator strip touching on two s-wave superconductors in the presence of the interedge coupling. It is shown that the interedge coupling could give rise to a 0 − π transition modulated by the gate voltage, originating from an additional π phase difference caused by the interedge backscattering. The 0 − π transition in turn can manifest the helical spin texture of the edge states. A considerable residual value of the supercurrent at the 0 − π transition point is always exhibited, suggesting a very efficient performance of the device as a supercurrent switch. Moreover, the region of coexisting 0 and π states is found fairly large, which can be used to improve accuracy in the design of a π superconducting quantum interference device.

Proximity Band Structure and Spin Textures on Both Sides of Topological-Insulator/Ferromagnetic-Metal Interface and Their Charge Transport Probes.

The control of recently observed spintronic effects in topological-insulator/ferromagnetic-metal (TI/FM) heterostructures is thwarted by the lack of understanding of band structure and spin textures around their interfaces. Here we combine density functional theory with Green's function techniques to obtain the spectral function at any plane passing through atoms of Bi2Se3 and Co or Cu layers comprising the interface. Instead of naively assumed Dirac cone gapped by the proximity exchange field spectral function, we find that the Rashba ferromagnetic model describes the spectral function on the surface of Bi2Se3 in contact with Co near the Fermi level EF0, where circular and snowflake-like constant energy contours coexist around which spin locks to momentum. The remnant of the Dirac cone is hybridized with evanescent wave functions from metallic layers and pushed, due to charge transfer from Co or Cu layers, a few tenths of an electron-volt below EF0 for both Bi2Se3/Co and Bi2Se3/Cu interfaces while hosting distorted helical spin texture wounding around a single circle. These features explain recent observation of sensitivity of spin-to-charge conversion signal at TI/Cu interface to tuning of EF0. Crucially for spin-orbit torque in TI/FM heterostructures, few monolayers of Co adjacent to Bi2Se3 host spectral functions very different from the bulk metal, as well as in-plane spin textures (despite Co magnetization being out-of-plane) due to proximity spin-orbit coupling in Co induced by Bi2Se3. We predict that out-of-plane tunneling anisotropic magnetoresistance in Cu/Bi2Se3/Co vertical heterostructure can serve as a sensitive probe of the type of spin texture residing at EF0.

Bulk Rashba Semiconductors and Related Quantum Phenomena

Bithmuth tellurohalides BiTeX (X = Cl, Br and I) are model examples of bulk Rashba semiconductors, exhibiting a giant Rashba-type spin splitting among their both valence and conduction bands. Extensive spectroscopic and transport experiments combined with the state-of-the-art first-principles calculations have revealed many unique quantum phenomena emerging from the bulk Rashba effect in these systems. The novel features such as the exotic inter- and intra-band optical transitions, enhanced magneto-optical response, divergent orbital dia-/para-magnetic susceptibility and helical spin textures with a nontrivial Berry's phase in the momentum space are among the salient discoveries, all arising from this effect. Also, it is theoretically proposed and indications have been experimentally reported that bulk Rashba semiconductors such as BiTeI have the capability of becoming a topological insulator under the application of a hydrostatic pressure. Here, we overview these studies and show that BiTeX are an ideal platform to explore the next aspects of quantum matter, which could ultimately be utilized to create spintronic devices with novel functionalities.

Lattice-matched heterojunctions between topological and normal insulators: A first-principles study

Gapless boundary modes at the interface between topologically distinct regions are one of the most salient manifestations of topology in physics. Metallic boundary states of time-reversal-invariant topological insulators (TIs), a realization of topological order in condensed matter, have been of much interest not only due to such a fundamental nature, but also due to their practical significance. These boundary states are immune to backscattering and localization owing to their topological origin, thereby opening up the possibility to tailor them for potential uses in spintronics and quantum computing. The heterojunction between a TI and a normal insulator (NI) is a representative playground for exploring such a topologically protected metallic boundary state and expected to constitute a building block for future electronic and spintronic solid-state devices based on TIs. Here, we report a first-principles study of two experimentally realized lattice-matched heterojunctions between TIs and NIs, ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$(0001)/InP(111) and ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$(0001)/${\mathrm{BaF}}_{2}$(111). We evaluate the band offsets at these interfaces from many-body perturbation theory within the $GW$ approximation as well as density-functional theory. Furthermore, we investigate the topological interface states, demonstrating that at these lattice-matched heterointerfaces, they are strictly localized and their helical spin textures are as well preserved as those at the vacuum-facing surfaces. These results taken together may help in designing devices relying on spin-helical metallic boundary states of TIs.

Direct observation of spin-layer locking by local Rashba effect in monolayer semiconducting PtSe2 film

The generally accepted view that spin polarization in non-magnetic solids is induced by the asymmetry of the global crystal space group has limited the search for spintronics materials mainly to non-centrosymmetric materials. In recent times it has been suggested that spin polarization originates fundamentally from local atomic site asymmetries and therefore centrosymmetric materials may exhibit previously overlooked spin polarizations. Here, by using spin- and angle-resolved photoemission spectroscopy, we report the observation of helical spin texture in monolayer, centrosymmetric and semiconducting PtSe2 film without the characteristic spin splitting in conventional Rashba effect (R-1). First-principles calculations and effective analytical model analysis suggest local dipole induced Rashba effect (R-2) with spin-layer locking: opposite spins are degenerate in energy, while spatially separated in the top and bottom Se layers. These results not only enrich our understanding of the spin polarization physics but also may find applications in electrically tunable spintronics.

Coexistence of topological Dirac fermions on the surface and three-dimensional Dirac cone state in the bulk of ZrTe5 single crystal

Although, the long-standing debate on the resistivity anomaly in ZrTe5 somewhat comes to an end, the exact topological nature of the electronic band structure remains elusive till today. Theoretical calculations predicted that bulk ZrTe5 to be either a weak or a strong three-dimensional (3D) topological insulator. However, the angle resolved photoemission spectroscopy and transport measurements clearly demonstrate 3D Dirac cone state with a small mass gap between the valence band and conduction band in the bulk. From the magnetization and magneto-transport measurements on ZrTe5 single crystal, we have detected both the signature of helical spin texture from topological surface state and chiral anomaly associated with the 3D Dirac cone state in the bulk. This implies that ZrTe5 hosts a novel electronic phase of material, having massless Dirac fermionic excitation in its bulk gap state, unlike earlier reported 3D topological insulators. Apart from the band topology, it is also apparent from the resistivity and Hall measurements that the anomalous peak in the resistivity can be shifted to a much lower temperature (T < 2 K) by controlling impurity and defects.

π Spin Berry Phase in a Quantum-Spin-Hall-Insulator-Based Interferometer: Evidence for the Helical Spin Texture of the Edge States.

The quantum spin Hall insulator is characterized by helical edge states, with the spin polarization of the electron being locked to its direction of motion. Although the edge-state conduction has been observed, unambiguous evidence of the helical spin texture is still lacking. Here, we investigate the coherent edge-state transport in an interference loop pinched by two point contacts. Because of the helical character, the forward interedge scattering enforces a π spin rotation. Two successive processes can only produce a nontrivial 2π or trivial 0 spin rotation, which can be controlled by the Rashba spin-orbit coupling. The nontrivial spin rotation results in a geometric π Berry phase, which can be detected by a π phase shift of the conductance oscillation relative to the trivial case. Our results provide smoking gun evidence for the helical spin texture of the edge states. Moreover, it also provides the opportunity to all electrically explore the trajectory-dependent spin Berry phase in condensed matter.

Unconventional spin texture in a noncentrosymmetric quantum spin Hall insulator

We propose that the simultaneous presence of both Rashba and band inversion can lead to a Rashba-like spin splitting formed by two bands with the same in-plane helical spin texture. Because of this unconventional spin texture, the backscattering is forbidden in edge and bulk conductivity channels. We propose a noncentrosymmetric honeycomb-lattice quantum spin Hall (QSH) insulator family formed by the IV, V, and VII elements with this property. The system formed by Bi, Pb, and I atoms is mechanically stable and has both a large Rashba spin splitting of 60 meV and a large nontrivial band gap of 0.14 eV. Since the edge and the bulk states are protected by the time-reversal (TR) symmetry, contrary to what happens in most doped QSH insulators, the bulk states do not contribute to the backscattering in the electronic transport, allowing the construction of a spintronic device with less energy loss.