Helical Spin Texture Research Articles

Visualization of Unconventional Rashba Bands and Vortex Zero Mode in the Topological Superconductor Candidate AuSn4.

The noble metal alloy AuSn4 has recently been identified as an intrinsic surface topological superconductor, promisingly hosting the Majorana zero mode (MZM) for topological quantum computing. However, the atomic visualization of its nontrivial surface states and MZM remains elusive. Here, we report the direct observation of unconventional surface states and vortex zero mode in AuSn4 by scanning tunneling microscopy/spectroscopy. Unlike the trivial metallic bulk states of Sn-terminated surfaces, the Au-terminated surfaces exhibit pronounced surface states near the Fermi level, arising from unconventional Rashba bands characterized by shared helical spin textures. In the superconducting state, the Sn-terminated surfaces exhibit conventional Caroli-de Gennes-Matricon bound states, while the Au-terminated surfaces display sharp zero-energy core states resembling MZMs in a nonquantum-limit condition. This distinction may result from the dominant contribution of unconventional Rashba bands on the Au-terminated surface. Our results provide a new platform for studying termination-dependent topological surface states and MZM in noble-metal-based superconductors.

Large-Gap and Topological Crystalline Insulating Phase in RbZnBi and CsZnBi.

Topological insulators (TIs) are a new class of materials with gapless boundary states inside the bulk insulating gap. This metallic boundary state hosts intriguing phenomena such as helical spin textures and Dirac crossing points. Here, we theoretically propose RbZnBi and CsZnBi as a new family of TIs exhibiting large bulk band gaps and unique gapless surface states. Our first-principles density functional calculations show that two materials can be stabilized in two different structures depending on the stacking order of hexagonal ZnBi layers. While both materials in the AA-stacked structure become TI, the AB-stacked RbZnBi and CsZnBi are topological crystalline insulators with hourglass-shaped Fermion surface states protected by nonsymmorphic glide symmetry. The calculated bulk gap is about 1.5-1.8 times larger than that of Bi2Se3, which makes RbZnBi and CsZnBi promising candidates for future applications.

Topological signatures of Mo2TiC2O2

Mo2TiC2 is the Ordered Double Transitional Metal Layered Carbides (ODTMLC) derived from its parent MAX phases Mo2TiAlC2 by a wet chemical etching. Its oxidation was done by a new ablated plasma thrust method in which the MXenes were at 750 °C under an oxygen background in the pulsed laser deposition chamber. The reflective high electron energy diffraction technique assures the oxidation at the ambient gas pressure p = 0.1 mbar, which was described in the previous paper. The obtained Mo2TiC2O2 was transferred for their topological test under angle-resolved photoemission spectroscopy, circular dichroism test, and Chemical Potential (CP) analysis. An indirect energy bandgap of 125 meV was obtained. The sine function of α along with period π and β with period 2π shows that there is a possibility of helical spin textures in both α (electron-like pocket around Γ̄) and β (elliptical electron-like pocket around M̄). The CP analysis shows the possibility of at least 100 meV bandgap creation on a single surface so that the surface charges will flow without any effect of bulk. The Mo2TiC2O2 can be used as topological insulating material.

Frequency-independent optical spin injection in Weyl semimetals

We demonstrate that in Weyl semimetals, the momentum-space helical spin texture can couple to the chirality of the Weyl node to generate a frequency-independent optical spin injection. This frequency-independence is rooted in the topology of the Weyl node. Since the helicity and the chirality are always locked for Weyl nodes, the injected spin from a pair of Weyl nodes always add up, implying no symmetry requirements for Weyl semimetals. Finally, we show that such frequency-independent spin injection is robust against multiband corrections and lattice-regularization effect and capable of realizing all-optical magnetization switching in the THz regime.

Quantum magnetotransports derived from the topological Dirac fermions in single-crystalline Pt3Te4 semimetal: Observations of chiral anomaly, quantum interference, and surface helical spin textures

This study investigated exotic quantum magnetotransports and magnetization properties of Pt3Te4 single crystals to probe the topological properties of the mitrofanovite Pt3Te4. The signature of helical spin texture from the topological surface state and the chiral anomaly associated with a linear-like energy dispersion of electronic states were detected. At low temperatures, the negative magnetoresistance in the low-field region could be explained with the transport formula containing the chiral-anomaly effect as well as the quantum interference of weak localization/antilocalization transports. Moreover, the high-field transverse magnetoresistance at temperatures below 60 K showed a non-saturating, linear-like behavior. This was examined using the theory of Abrikosov’s quantum magnetoresistance. The findings indicate a Dirac-cone-like dispersion in Pt3Te4 at low temperatures. This study's findings reveal the significant impact of the concept that the magnetotransport in Pt3Te4 can be dominated by the topological Dirac fermions in a surface state, which reveal the signatures of quantum magnetotransport, being a new candidate of Dirac semimetal.

Extracting unconventional spin texture in two dimensional topological crystalline insulator bismuthene via tuning bulk-edge interactions

Tuning the interaction between the bulk and edge states of topological materials is a powerful tool for manipulating edge transport behavior, opening up exciting opportunities for novel electronic and spintronic applications. This approach is particularly suited to topological crystalline insulators (TCI), a class of topologically nontrivial compounds that are endowed with multiple degrees of topological protection. In this study, we investigate how bulk-edge interactions can influence the edge transport in planar bismuthene, a TCI with metallic edge states protected by in-plane mirror symmetry, using first principles calculations and symmetrized Wannier tight-binding models. By exploring the impact of various perturbation effects, such as device size, substrate potentials, and applied transverse electric field, we examine the evolution of the electronic structure and edge transport in planar bismuthene. Our findings demonstrate that the TCI states of planar bismuthene can be engineered to exhibit either a gapped or conducting unconventional helical spin texture via a combination of substrate and electric field effects. Furthermore, under strong electric fields, the edge states can be stabilized through a delicate control of the bulk-edge interactions. These results open up new directions for discovering novel spin transport patterns in topological materials and provide critical insights for the fabrication of topological spintronic devices.

Unconventional hidden Rashba effects in two-dimensional InTe

Much attention has been paid to the hidden Rashba effect exhibiting an intriguing spin-layer locking phenomenon observed in two-dimensional materials with inversion symmetry. This effect provides a new possibility for manipulating Rashba spin polarization even in centrosymmetric materials. We propose a mechanism exhibiting an unconventional hidden Rashba effect showing a unique helical spin texture in which two Fermi circles in different bands have the same spin helicity exhibiting a complete spin separation in space. We demonstrate such an unconventional hidden Rashba effect by showing the unique electronic structures of two-dimensional InTe with inversion symmetry investigated by the first-principles calculations. It is found that spins in both the inner and outer bands with the one helicity are located in the top sublayer whereas spins with the other helicity are in the bottom sublayer indicating a complete spatial spin separation. Strong spin-orbit coupling and a band inversion among two pairs of spin-degenerate bands are the main origins for the unconventional hidden Rashba involving two pairs of spin-degenerate bands rather than one pair, which gets usually involved in the conventional (hidden) Rashba effects. This new type of the hidden Rashba effect observed in two-dimensional InTe would broaden our understanding of the underlying physics of spin polarization phenomena eventually leading to a potential application in future spintronics.

Rashba-like spin splitting around non-time-reversal-invariant momenta

The ubiquitous Rashba spin splitting occurring around time-reversal-invariant momenta (TRIM) reflects the fundamental interplay between spin-orbit coupling (SOC) and crystalline symmetry. Unexpectedly, recent measurements reveal novel Rashba spin splitting around the momenta lacking time-reversal symmetry (non-TRIM), whose mechanism remains elusive. Here, we theoretically elucidate the microscopic origin of Rashba spin splitting around non-TRIM and identify the design principles for its appearance. Conventionally, a Zeeman-like spin splitting dominates around non-TRIM due to the broken time-reversal symmetry and diminishes the Rashba-like features. Our results show that the Bloch wave function with specific orbital representation at certain non-TRIM could eliminate the first-order SOC effect. As a result, the corresponding little group hosts a type of quasisymmetry that commutes with the dominating SOC Hamiltonian, leading to a tiny SOC gap and helical spin texture. Furthermore, such a quasi-symmetry-induced tiny gap could manifest large Berry curvature, which is desirable for various topological applications. Our work expands the concept of Rashba physics beyond the conventional TRIM scenario, paving an avenue for designing novel spin-splitting materials through the cooperation of symmetry and orbital engineering.

Magnetic excitations in the helical Rashba superconductor

We investigate the magnetic excitation spectrum in the helical state of a noncentrosymmetric superconductor with inversion symmetry breaking and strong Rashba spin–orbit coupling. For this purpose we derive the general expressions of the dynamical spin response functions under the presence of strong Rashba splitting of conduction bands, superconducting gap and external field which lead to stabilization of Cooper pairs with finite overall momentum in a helical state. The latter is characterized by momentum space regions of paired and unpaired states with different quasiparticle dispersions. The magnetic response is determined by i) excitations within and between both paired and unpaired regions ii) anomalous coherence factors and iii) additional spin matrix elements due to helical Rashba spin texture of bands. We show that as a consequence typical correlated real space and spin space anisotropies appear in the dynamical susceptibility which would be observable as a characteristic fingerprint for a helical superconducting state in inelastic neutron scattering investigations.

Surface-induced ferromagnetism and anomalous Hall transport at Zr2S(001)

Two-dimensional layered electrides possessing anionic excess electrons in the interstitial spaces between cationic layers have attracted much attention due to their promising opportunities in both fundamental research and technological applications. Using first-principles calculations, we predict that the layered bulk electride ${\mathrm{Zr}}_{2}\mathrm{S}$ is nonmagnetic with massive Dirac nodal-line states arising from $\mathrm{Zr}\text{\ensuremath{-}}4d$ cationic and interlayer anionic electrons. However, the ${\mathrm{Zr}}_{2}\mathrm{S}(001)$ surface increases the density of states at the Fermi level due to the surface potential, thereby inducing a ferromagnetic order at the outermost Zr layer via the Stoner instability. Consequently, the time-reversal symmetry breaking at the surface not only generates spin-polarized topological surface states with intricate helical spin textures but also hosts an intrinsic anomalous Hall effect originating from the Berry curvature generated by spin-orbit coupling. Our findings offer a playground to investigate the emergence of ferromagnetism and anomalous Hall transport at the surface of nonmagnetic topological electrides.

Anisotropy of Electronic Spin Texture in the High-Temperature Cuprate Superconductor Bi2Sr2CaCu2O8+δ

Seeking new order parameters and the related broken symmetry and studying their relationship with phase transition have been important topics in condensed matter physics. Here, by using spin- and angle-resolved photoemission spectroscopy, we confirm the helical spin texture caused by spin-layer locking in the nodal region in the cuprate superconductor Bi2Sr2CaCu2O8+δ and discover the anisotropy of spin polarizations at nodes along Γ–X and Γ–Y directions. The breaking of C 4 rotational symmetry in electronic spin texture may give deeper insights into understanding the ground state of cuprate superconductors.

Temperature- and field angular-dependent helical spin period characterized by magnetic dynamics in a chiral helimagnet MnNb3S6

The chiral magnets with topological spin textures provide a rare platform to explore topology and magnetism for potential application implementation. Here, we study the magnetic dynamics of several spin configurations on the monoaxial chiral magnetic crystal MnNb3S6 via broadband ferromagnetic resonance (FMR) technique at cryogenic temperature. In the high-field forced ferromagnetic state (FFM) regime, the obtained frequency f vs. resonance field Hres dispersion curve follows the well-known Kittel formula for a single FFM, while in the low-field chiral magnetic soliton lattice (CSL) regime, the dependence of Hres on magnetic field angle can be well-described by our modified Kittel formula including the mixture of a helical spin segment and the FFM phase. Furthermore, compared with the sophisticated Lorentz micrograph technique, the observed magnetic dynamics corresponding to different spin configurations allow us to obtain temperature- and field-dependent proportion of helical spin texture and helical spin period ratio L(H)/L(0) via our modified Kittel formula. Our results demonstrated that field- and temperature-dependent nontrivial magnetic structures and corresponding distinct spin dynamics in chiral magnets can be an alternative and efficient approach to uncovering and controlling nontrivial topological magnetic dynamics.

Bipolar spin-conversion diode and quantum entanglement induced by the valley and pseudoparity mixing

Herein, we report on a zigzag graphene superconducting junction with a superconductor sandwiched in between two magnetized zigzag graphene nanoribbons, where the valley and pseudoparity mixing are shown to bring about peculiar properties. We find that the bipolar spin diode and spin-conversion diode in the ferromagnetic configuration as well as quantum entanglement in the antiferromagnetic one are exhibited. The noncollinear angle combined with the valley and pseudoparity mixing in arbitrary magnetic configurations exerts a significant influence on the transport properties. In addition, not only the bipolar spin diode and magnetic storage with high efficiencies but also the bipolar spin-conversion diode and quantum entanglement can coexist in one setup. Particularly, the bipolar spin-conversion diode can be used to directly detect and confirm the helical spin texture of the edge state in a quantum spin Hall insulator.

Spin-polarization of topological crystalline and normal insulator Pb[formula omitted]Sn[formula omitted]Se (111) epilayers probed by photoelectron spectroscopy

The helical spin texture on the surface of topological crystalline insulators (TCI) makes these materials attractive for application in spintronics. In this work, spin-polarization and electronic structure of surface states of (111)-oriented Pb1−xSnxSe TCI epitaxial films are examined by angle- as well as spin-resolved photoemission spectroscopy (SR-ARPES). High-quality epilayers with various Sn content are grown by the molecular beam epitaxy (MBE) method. Topological-normal insulator transition manifesting itself as band gap opening is observed. It is shown that the gap opening can be induced not only by changing the Sn content of the epilayer but also depositing a transition metal (TM) on its surface. In the latter case, the observed gaping of the surface states is caused by change in surface composition and not by magnetism. We also show that helical spin polarization is present not only for samples of topological composition but also for trivial ones (with an open band gap). The observed spin polarization reaches a value of 30% for the in-plane spin component and is almost absent for the out-of-plane one. We believe that our work will pave the way for the application of surface states not only of topological but also normal insulators based on lead–tin chalcogenides in spin-charge conversion devices.

Direct coupling-induced pseudoparity nonconservation scattering: bipolar spin diode and unipolar spin entanglement pairing

The zigzag graphene nanoribbon (ZR) is characterized by the distinct pseudoparity combined with valley-selection rule, which could feature exotic transport phenomena, especially in ZR-based superconducting spintronic devices. However, the ZR with superconductivity induced by proximity of a bulk superconductor (SC) on it still keeps original band properties. Herein, we present a superconducting heterostructure with an SC directly coupling to two ZRs, which is characteristic of pseudoparity-mixing, resulting in pseudoparity nonconservation elastic cotunneling (EC) and crossed Andreev reflection (CAR) processes. It is shown that the mixing leads to the switch effect of the EC and CAR processes manipulated by the SC length, particularly the full spin polarization. In the context of only one magnetized ZR lead, a novel bipolar spin diode behavior on a scale of small SC length and unipolar spin entanglement pairing at some large SC lengths, are both exhibited on a large scale of forward and/or reverse bias voltages. More importantly, the spin-diode can be combined with the quantum spin Hall (QSH) insulator to provide smoking gun evidence for the helical spin texture of the (QSH) insulator, which is still lacking.

Fermi surface chirality induced in a TaSe2 monosheet formed by a Ta/Bi2Se3 interface reaction.

Spin-momentum locking in topological insulators and materials with Rashba-type interactions is an extremely attractive feature for novel spintronic devices and is therefore under intense investigation. Significant efforts are underway to identify new material systems with spin-momentum locking, but also to create heterostructures with new spintronic functionalities. In the present study we address both subjects and investigate a van der Waals-type heterostructure consisting of the topological insulator Bi2Se3 and a single Se-Ta-Se triple-layer (TL) of H-type TaSe2 grown by a method which exploits an interface reaction between the adsorbed metal and selenium. We then show, using surface x-ray diffraction, that the symmetry of the TaSe2-like TL is reduced from D3h to C3v resulting from a vertical atomic shift of the tantalum atom. Spin- and momentum-resolved photoemission indicates that, owing to the symmetry lowering, the states at the Fermi surface acquire an in-plane spin component forming a surface contour with a helical Rashba-like spin texture, which is coupled to the Dirac cone of the substrate. Our approach provides a route to realize chiral two-dimensional electron systems via interface engineering in van der Waals epitaxy that do not exist in the corresponding bulk materials.

Two-dimensional Dirac semiconductor and its material realization

We propose a new concept of two-dimensional (2D) Dirac semiconductor which is characterized by the emergence of fourfold degenerate band crossings near the band edge and provide a generic approach to realize this novel semiconductor in the community of material science. Based on the first-principle calculations and symmetry analysis, we discover recently synthesised triple-layer (TL)-BiOS2 is such Dirac semiconductor that features Dirac cone at X/Y point, protected by nonsymmorphic symmetry. Due to sandwich-like structure, each Dirac fermion in TL-BiOS2 can be regarded as a combination of two Weyl fermions with opposite chiralities, degenerate in momentum-energy space but separated in real space. Such Dirac semiconductor carries layer-dependent helical spin textures that never been reported before. Moreover, novel topological phase transitions are flexibly achieved in TL-BiOS2: (i) an vertical electric field can drive it into Weyl semiconductor with switchable spin polarization direction, (ii) an extensive strain is able to generate ferroelectric polarization and actuate it into Weyl nodal ring around X point and into another type of four-fold degenerate point at Y point. Our work extends the Dirac fermion into semiconductor systems and provides a promising avenue to integrate spintronics and optoelectronics in topological materials.

Random-Gate-Voltage Induced Al’tshuler–Aronov–Spivak Effect in Topological Edge StatesSupported by the National Natural Science Foundation of China (Grant Nos. 12074172, 11674160, and 11974168), the StartupGrant at Nanjing University, the State Key Program for Basic Researches of China (Grant No. 2017YFA0303203), and the ExcellentProgramme at Nanjing University

Helical edge states are the hallmark of the quantum spin Hall insulator. Recently, several experiments have observed transport signatures contributed by trivial edge states, making it difficult to distinguish between the topologically trivial and nontrivial phases. Here, we show that helical edge states can be identified by the random-gate-voltage induced Φ 0/2-period oscillation of the averaged electron return probability in the interferometer constructed by the edge states. The random gate voltage can highlight the Φ 0/2-period Al’tshuler–Aronov–Spivak oscillation proportional to sin2(2πΦ/Φ 0) by quenching theΦ 0-period Aharonov–Bohm oscillation. It is found that the helical spin texture induced π Berry phase is key to such weak antilocalization behavior with zero return probability at Φ = 0. In contrast, the oscillation for the trivial edge states may exhibit either weak localization or antilocalization depending on the strength of the spin-orbit coupling, which has finite return probability at Φ = 0. Our results provide an effective way for the identification of the helical edge states. The predicted signature is stabilized by the time-reversal symmetry so that it is robust against disorder and does not require any fine adjustment of system.

Dirac nodal line and Rashba spin-split surface states in nonsymmorphic ZrGeTe

Dirac semimetals (DSMs) are three-dimensional analogue to graphene with symmetry enforced bulk Dirac nodes. Among various DSMs, ZrSiS has attracted great interests recently, due to its three dimensional Dirac nodal line protected by the nonsymmorphic symmetry. It belongs to a large family of isostructural compounds with rich quantum phenomenon. Here we present a comprehensive study of the first principle calculation, angle-resolved photoemission spectroscopy measurements, and scanning tunneling microscope experiments on ZrGeTe, a member of the ZrSiS family with stronger spin–orbit coupling (SOC). Our band structure calculation shows Dirac line nodes along and , the signature of linearly dispersive diamond-shaped band around , and the existence of floating gapless surface states at with Rashba spin-split helical spin texture. Furthermore, characteristic q-vectors including two Umklapp scattering vectors revealed by our quasiparticle scattering interference imaging can be identified with joint density of states simulation based on our calculated band structure. Our results demonstrate the effects of large SOC on the electronic structure of ZrGeTe, which may benefit the potential application by utilizing its exotic quantum states in the future.

Giant inverse Rashba-Edelstein effect: Application to monolayer OsBi2

We propose that the hybridization between two sets of Rashba bands can lead to an unconventional topology where the two Fermi circles from different bands own in-plane helical spin textures with the same chiralities, and possess group velocities with the same directions. Under the weak spin injection, the two Fermi circles both give the positive contributions to the spin-to-charge conversion and thus induce the giant inverse Rashba-Edelstein Effect with large conversion efficiency, which is very different from the conventional Rashba-Edelstein Effect. More importantly, through the first-principles calculations, we predict that monolayer OsBi2 could be a good candidate to realize the giant inverse Rashba-Edelstein Effect. Our studies not only demonstrate a new mechanism to achieve highly efficient spin-to-charge conversion in spintronics, but also provide a promising material to realize it.