Orbital Textures Research Articles

Controllable orbital angular momentum monopoles in chiral topological semimetals

AbstractThe emerging field of orbitronics aims to generate and control orbital angular momentum for information processing. Chiral crystals are promising orbitronic materials because they have been predicted to host monopole-like orbital textures, where the orbital angular momentum aligns isotropically with the electron’s crystal momentum. However, such monopoles have not yet been directly observed in chiral crystals. Here, we use circular dichroism in angle-resolved photoelectron spectroscopy to image orbital angular momentum monopoles in the chiral topological semimetals PtGa and PdGa. The spectra show a robust polar texture that rotates around the monopole as a function of photon energy. This is a direct consequence of the underlying magnetic orbital texture and can be understood from the interference of local atomic contributions. Moreover, we also demonstrate that the polarity of the monopoles can be controlled through the structural handedness of the host crystal by imaging orbital angular moment monopoles and antimonopoles in the two enantiomers of PdGa, respectively. Our results highlight the potential of chiral crystals for orbitronic device applications, and our methodology could enable the discovery of even more complicated nodal orbital angular momentum textures that could be exploited for orbitronics.

Incognizant 1T/1H Charge-Density-Wave Phases in Monolayer NbTe2.

While experimental realization of multiple charge-density waves (CDWs) has been ascribed to monolayer 1T-NbTe2, their atomic structures are still largely unclear, preventing a deep understanding of their novel electronic structures. Here, comparing first-principles-calculated orbital textures with reported STM measurements, we successfully identify multiple CDWs in monolayer NbTe2. Surprisingly, we reveal that both 1T/1H phases could exist in monolayer NbTe2, which was incognizant before. Particularly, we find that the experimentally observed 4 × 1 and 4 × 4 CDWs could be attributed to 1H stacking, while the observed phase could possess 1T stacking. The existence of 1T/1H phases results in competition between CDW, spin-density wave (SDW), and ferromagnetism in 1H stacking under an external field and results in CDW-induced quantum phase transitions from a Kramers-Weyl fermion to a topological insulator in 1T stacking. Our study suggests NbTe2 as an exotic platform to investigate the interplay between CDW, SDW, and topological phases, which are largely unexplored in current experiments.

Transition metal oxides: a new frontier in spintronics driven by novel quantum states and efficient charge-spin interconversion

Transition metal oxides (TMOs) have emerged as promising candidates for spintronic applications due to their unique electronic properties and novel quantum states. The intricate interplay between strong spin-orbit coupling and electronic correlations in TMOs gives rise to distinct spin and orbital textures, leading to enhanced spin-momentum locking and efficient charge-spin interconversion. Remarkably, recent researches have unveiled the significant and highly tunable nature of charge-spin interconversion efficiency in TMOs, which can be manipulated through strategies such as electric field gating, epitaxial strain, and heterostructure engineering. This review provides a comprehensive overview of the recent advances in understanding the electronic band structures of TMOs and their correlation with charge-spin interconversion mechanisms. We summarize the tunability of these properties through various experimental approaches and discuss the potential implications for spintronic device applications. The insights gained from this review can guide future research efforts towards the development of high-performance, energy-efficient spintronic devices based on TMOs.

Chirality-Driven Orbital Angular Momentum and Circular Dichroism in CoSi.

Chiral crystals and molecules were recently predicted to form an intriguing platform for unconventional orbital physics. Here, we report the observation of chirality-driven orbital textures in the bulk electronic structure of CoSi, a prototype member of the cubic B20 family of chiral crystals. Using circular dichroism in soft x-ray angle-resolved photoemission, we demonstrate the formation of a bulk orbital-angular-momentum texture and monopolelike orbital-momentum locking that depends on crystal handedness. We introduce the intrinsic chiral circular dichroism, icCD, as a differential photoemission observable and a natural probe of chiral electron states. Our findings render chiral crystals promising for spin-orbitronics applications.

Synthesis and Magnetic Properties of the Multiferroic [C(NH2)3]Cr(HCOO)3 Metal-Organic Framework: The Role of Spin-Orbit Coupling and Jahn-Teller Distortions.

We report for the first time the synthesis of [C(NH2)3]Cr(HCOO)3 stabilizing Cr2+ in formate perovskite, which adopts a polar structure and orders magnetically below 8 K. We discuss in detail the magnetic properties and their coupling to the crystal structure based on first-principles calculations, symmetry, and model Hamiltonian analysis. We establish a general model for the orbital magnetic moment of [C(NH2)3]M(HCOO)3 (M = Cr, Cu) based on perturbation theory, revealing the key role of the Jahn-Teller distortions. We also analyze their spin and orbital textures in k-space, which show unique characteristics.

Observation of Asymmetric Oxidation Catalysis with B20 Chiral Crystals**

AbstractThe study of heterogeneous reactions for enantiomeric processes based on inorganic crystals has been resurgent in recent years. However, the question remains how homochirality develops in nature and chemical reactions. Here, the successful growth of B20 group PdGa single crystals with different chiral lattices enabled us to achieve enantioselective recognition of 3,4‐dihydroxyphenylalanine (DOPA) based on a new mechanism, namely orbital angular momentum (OAM) polarization. The orbital textures of PdGa crystals indicate large OAM polarization near the Fermi level and carrying opposite signs. A positive or negative magnetization in the [111] direction is expected depending on the chiral lattice of PdGa crystals. Due to this, the adsorption energies of PdGa crystals and DOPA molecules differ depending on how well the O‐2p orbital of DOPA pairs with the Pd‐4d orbital of PdGa. The results provide one possible explanation for how chirality arises in nature by providing an enantioselective route with pure inorganic crystals.

Observation of Asymmetric Oxidation Catalysis with B20 Chiral Crystals.

The study of heterogeneous reactions for enantiomeric processes based on inorganic crystals has been resurgent in recent years. However, the question remains how homochirality develops in nature and chemical reactions. Here, the successful growth of B20 group PdGa single crystals with different chiral lattices enabled us to achieve enantioselective recognition of 3,4-dihydroxyphenylalanine (DOPA) based on a new mechanism, namely orbital angular momentum (OAM) polarization. The orbital textures of PdGa crystals indicate large OAM polarization near the Fermi level and carrying opposite signs. A positive or negative magnetization in the [111] direction is expected depending on the chiral lattice of PdGa crystals. Due to this, the adsorption energies of PdGa crystals and DOPA molecules differ depending on how well the O-2p orbital of DOPA pairs with the Pd-4d orbital of PdGa. The results provide one possible explanation for how chirality arises in nature by providing an enantioselective route with pure inorganic crystals.

Microscopic study of orbital textures

Many interesting spin and orbital transport phenomena originate from orbital textures, referring to k-dependent orbital states. Most of previous works are based on symmetry analysis to model the orbital texture and analyze its consequences. However the microscopic origins of orbital texture and its strength are largely unexplored. In this work, we derive the orbital texture Hamiltonians from microscopic tight-binding models for various situations. To form an orbital texture, k-dependent hybridization of orbital states are necessary. We reveal two microscopic mechanisms for the hybridization: (i) lattice structure effect and (ii) mediation by other orbital states. By considering the orbital hybridization, we not only reproduce the orbital Hamiltonian obtained by the symmetry analysis but also reveal previously unreported orbital textures like orbital Dresselhaus texture and anisotropic orbital texture. The orbital Hamiltonians obtained here would be useful for analyzing the orbital physics and designing the materials suitable for spin-orbitronic applications.

Direct visualization of Rashba-split bands and spin/orbital-charge interconversion at KTaO3 interfaces

Rashba interfaces have emerged as promising platforms for spin-charge interconversion through the direct and inverse Edelstein effects. Notably, oxide-based two-dimensional electron gases display a large and gate-tunable conversion efficiency, as determined by transport measurements. However, a direct visualization of the Rashba-split bands in oxide two-dimensional electron gases is lacking, which hampers an advanced understanding of their rich spin-orbit physics. Here, we investigate KTaO3 two-dimensional electron gases and evidence their Rashba-split bands using angle resolved photoemission spectroscopy. Fitting the bands with a tight-binding Hamiltonian, we extract the effective Rashba coefficient and bring insight into the complex multiorbital nature of the band structure. Our calculations reveal unconventional spin and orbital textures, showing compensation effects from quasi-degenerate band pairs which strongly depend on in-plane anisotropy. We compute the band-resolved spin and orbital Edelstein effects, and predict interconversion efficiencies exceeding those of other oxide two-dimensional electron gases. Finally, we suggest design rules for Rashba systems to optimize spin-charge interconversion performance.

Gate tunable anomalous Hall effect: Berry curvature probe at oxides interfaces

We present the theoretical prediction of a gate tunable anomalous Hall effect (AHE) in an oxide interface as a hallmark of spin-orbit coupling. The observed AHE at low-temperatures in the presence of an external magnetic field emerges from a complex structure of the Berry curvature of the electrons on the Fermi surface and strongly depends on the orbital character of the occupied bands. A detailed picture of the results comes from a multiband low-energy model with a generalized Rashba interaction that supports characteristic out-of-plane spin and orbital textures. We discuss strategies for optimizing the intrinsic AHE in (111) SrTiO$_3$ heterostructure interfaces.

Orbital Complexity in Intrinsic Magnetic Topological Insulators MnBi_{4}Te_{7} and MnBi_{6}Te_{10}.

Using angle-resolved photoelectron spectroscopy (ARPES), we investigate the surface electronic structure of the magnetic van der Waals compounds MnBi_{4}Te_{7} and MnBi_{6}Te_{10}, the n=1 and 2 members of a modular (Bi_{2}Te_{3})_{n}(MnBi_{2}Te_{4}) series, which have attracted recent interest as intrinsic magnetic topological insulators. Combining circular dichroic, spin-resolved and photon-energy-dependent ARPES measurements with calculations based on density functional theory, we unveil complex momentum-dependent orbital and spin textures in the surface electronic structure and disentangle topological from trivial surface bands. We find that the Dirac-cone dispersion of the topologial surface state is strongly perturbed by hybridization with valence-band states for Bi_{2}Te_{3}-terminated surfaces but remains preserved for MnBi_{2}Te_{4}-terminated surfaces. Our results firmly establish the topologically nontrivial nature of these magnetic van der Waals materials and indicate that the possibility of realizing a quantized anomalous Hall conductivity depends on surface termination.

Profiling spin and orbital texture of a topological insulator in full momentum space

We investigate the coupled spin and orbital textures of the topological surface state in ${\mathrm{Bi}}_{2}$(Te,${\mathrm{Se})}_{3}$(0001) across full momentum space using spin- and angle-resolved photoelectron spectroscopy and relativistic one-step photoemission theory. For an approximately isotropic Fermi surface in ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}\mathrm{Se}$, the measured intensity and spin momentum distributions, obtained with linearly polarized light, qualitatively reflect the orbital composition and the orbital-projected in-plane spin polarization, respectively. In ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, the in-plane lattice potential induces a hexagonal anisotropy of the Fermi surface, which manifests in an out-of-plane photoelectron spin polarization with a strong dependence on light polarization, excitation energy, and crystallographic direction.

Orbital Hall insulating phase in transition metal dichalcogenide monolayers

We show that H-phase transition metal dichalcogenides (TMDs) monolayers such as MoS$_2$ and WSe$_2$, are orbital Hall insulators. They present very large orbital Hall conductivity plateaus in their semiconducting gap, where the spin Hall conductivity vanishes. Our results open the possibility of using TMDs for orbital current injection and orbital torque transfers that surpass their spin-counterparts in spin-orbitronics devices. The orbital Hall effect (OHE) in TMD monolayers occurs even in the absence of spin-orbit coupling. It can be linked to exotic momentum-space Dresselhaus-like orbital textures, analogous to the spin-momentum locking in 2D Dirac fermions that arise from a combination of orbital attributes and lattice symmetry.

Two-dimensional orbital Hall insulators

The orbital-Hall effect (OHE), similarly to the spin-Hall effect (SHE), refers to the creation of a transverse flow of orbital angular momentum that is induced by a longitudinally applied electric field. For systems in which the spin-orbit coupling (SOC) is sizeable, the orbital and spin angular momentum degrees of freedom are coupled, and an interrelationship between charge, spin and orbital angular momentum excitations is naturally established. The OHE has been explored mostly in metallic systems, where it can be quite strong. However, several of its features remain unexplored in two-dimensional (2D) materials. Here, we investigate the role of orbital textures for the OHE displayed by multi-orbital 2D materials. We predict the appearance of a rather large orbital Hall effect in these systems both in their metallic and insulating phases. In some cases, the orbital Hall currents are larger than the spin Hall ones, and their use as information carriers widens the development possibilities of novel spin-orbitronic devices.

Real-Space Imaging of Orbital Selectivity on SrTiO3(001) Surface.

Real-space access of the orbital degree of freedom in complex oxides is still challenging due to intricate electronic hybridization. Here, we report a direct observation of reproducible orbital-selective tunneling on a novel SrTiO3(001) surface by scanning tunneling microscopy. The electronic structures reversibly switch between two different sets of symmetries depending on the sample bias, which is accompanied by a remarkable change in energy-dependent spectroscopy data. Tunneling spectrum combined with density functional theory calculations elucidates that symmetry-breaking at the surface determines the crystal-splitting field of eg/t2g orbitals with a strong in-plane anisotropy so that electrons alternatingly fill eg and t2g orbitals during the imaging process with different biases. This surface superstructure provides a new strategy toward understanding orbital textures and orbital selectivity in complex oxides.

Orbital Pseudospin-Momentum Locking in Two-Dimensional Chiral Borophene.

Recently, orbital-textures have been found in Rashba and topological insulator (TI) surface states as a result of the spin-orbit coupling (SOC). Here, we predict a px/py orbital texture, in linear dispersive Dirac bands, arising at the K/K' points of χ-h0 borophene chiral monolayer. Combining "first-principles" calculations with effective Hamiltonians, we show that the orbital pseudospin has its direction locked with the momentum in a similar way as TIs' spin-textures. Additionally, considering a layer pseudospin degree of freedom, this lattice allows stackings of layers with equivalent or opposite chiralities. In turn, we show a control of the orbital textures and layer localization through the designed stacking and external electric field. For instance, for the opposite chirality stacking, the electric field allows for an on/off switch of the orbital-textured Dirac cone.

Inherent orbital spin textures in Rashba effect and their implications in spin–orbitronics

The Rashba effect gives rise to the key feature of chiral spin texture. Recently it was demonstrated that the orbital angular momentum (OAM) texture forms the underlying basis for Rashba spin texture. Here we solve a model Hamiltonian of a generic p-orbital system in the presence of crystal field, internal spin–orbit coupling (SOC) and inversion symmetry breaking (ISB), and demonstrate, in addition to OAM and spin texture, the existence of orbital projection (OP) of the spin texture in a general Rashba system. The unique form of the OP pattern follows from the same condition for the existence of chirality of the spin texture. From the analytical results, we obtained the spin polarization as a function of parameters such as the SOC strength, crystal field splitting and degree of ISB, and compare them with those from numerical solutions and ab initio calculations. All three methods yield highly consistent results. Our results suggest means of external modulation, and elucidate the multi-orbital nature of the Rashba effect and the underlying OP of the spin texture. The understanding has potential applications in fields such as spin–orbitronics that requires delicate control between orbital occupancy and spin momentum.

Exciton-phonon cooperative mechanism of the triple- q charge-density-wave and antiferroelectric electron polarization in TiSe2

We investigate the microscopic mechanisms of the charge-density-wave (CDW) formation in a monolayer TiSe$_2$ using a realistic multiorbital $d$-$p$ model with electron-phonon coupling and intersite Coulomb (excitonic) interactions. First, we estimate the tight-binding bands of Ti $3d$ and Se $4p$ orbitals in the monolayer TiSe$_2$ on the basis of the first-principles band structure calculations. We thereby show orbital textures of the undistorted band structure near the Fermi level. Next, we derive the electron-phonon coupling using the tight-binding approximation and show that the softening occurs in the transverse phonon mode at the M point of the Brillouin zone. The stability of the triple-$q$ CDW state is thus examined to show that the transverse phonon modes at the M$_1$, M$_2$, and M$_3$ points are frozen simultaneously. Then, we introduce the intersite Coulomb interactions between the nearest-neighbor Ti and Se atoms that lead to the excitonic instability between the valence Se $4p$ and conduction Ti $3d$ bands. Treating the intersite Coulomb interactions in the mean-field approximation, we show that the electron-phonon and excitonic interactions cooperatively stabilize the triple-$q$ CDW state in TiSe$_2$. We also calculate a single-particle spectrum in the CDW state and reproduce the band folding spectra observed in photoemission spectroscopies. Finally, to clarify the nature of the CDW state, we examine the electronic charge density distribution and show that the CDW state in TiSe$_2$ is of a bond-type and induces a vortex-like antiferroelectric polarization in the kagome network of Ti atoms.

NMR in an electric field: A bulk probe of the hidden spin and orbital polarizations

Recent theoretical work has established the presence of hidden spin and orbital textures in non-magnetic materials with inversion symmetry. Here, we propose that these textures can be detected by nuclear magnetic resonance (NMR) measurements carried out in the presence of an electric field. In crystals with hidden polarizations, a uniform electric field produces a staggered magnetic field that points to opposite directions at atomic sites related by spatial inversion. As a result, the NMR resonance peak corresponding to inversion partner nuclei is split into two peaks. The magnitude of the splitting is proportional to the electric field and depends on the orientation of the electric field with respect to the crystallographic axes and the external magnetic field. As a case study, we present a theory of electric-field-induced splitting of NMR peaks for $^{77}$Se, $^{125}$Te and $^{209}$Bi in Bi$_2$Se$_3$ and Bi$_2$Te$_3$. In conducting samples with current densities of $\simeq 10^6\, {\rm A/cm}^2$, the splitting for Bi can reach $100\, {\rm kHz}$, which is comparable to or larger than the intrinsic width of the NMR lines. In order to observe the effect experimentally, the peak splitting must also exceed the linewidth produced by the Oersted field. In Bi$_2$Se$_3$, this requires narrow wires of radius $\lesssim 1\, \mu{\rm m}$. We also discuss other potentially more promising candidate materials, such as SrRuO$_3$ and BaIr$_2$Ge$_2$, whose crystal symmetry enables strategies to suppress the linewidth produced by the Oersted field.

Mottness Collapse in 1T−TaS2−xSex Transition-Metal Dichalcogenide: An Interplay between Localized and Itinerant Orbitals

The vicinity of a Mott insulating phase has constantly been a fertile ground for finding exotic quantum states, most notably the high Tc cuprates and colossal magnetoresistance manganites. The layered transition metal dichalcogenide 1T-TaS2 represents another intriguing example, in which the Mott insulator phase is intimately entangled with a series of complex charge-density-wave (CDW) orders. More interestingly, it has been recently found that 1T-TaS2 undergoes a Mott-insulator-to-superconductor transition induced by high pressure, charge doping, or isovalent substitution. The nature of the Mott insulator phase and transition mechanism to the conducting state is still under heated debate. Here, by combining scanning tunneling microscopy (STM) measurements and first-principles calculations, we investigate the atomic scale electronic structure of 1T-TaS2 Mott insulator and its evolution to the metallic state upon isovalent substitution of S with Se. We identify two distinct types of orbital textures - one localized and the other extended - and demonstrates that the interplay between them is the key factor that determines the electronic structure. Especially, we show that the continuous evolution of the charge gap visualized by STM is due to the immersion of the localized-orbital-induced Hubbard bands into the extended-orbital-spanned Fermi sea, featuring a unique evolution from a Mott gap to a charge-transfer gap. This new mechanism of orbital-driven Mottness collapse revealed here suggests an interesting route for creating novel electronic state and designing future electronic devices.