Revealing Hidden Orbital Pseudospin Texture with Time-Reversal Dichroism in Photoelectron Angular Distributions

Excited State Band Mapping and Ultrafast Nonequilibrium Dynamics in Topological Dirac Semimetal 1T-ZrTe2

We performed time- and polarization-resolved extreme ultraviolet momentum microscopy on the topological Dirac semimetal candidate 1T-ZrTe2. Excited state band mapping uncovers the previously inaccessible linear dispersion of the Dirac cone above the Fermi level. We study the orbital texture of bands using linear dichroism in photoelectron angular distributions. These observations provide hints about the topological character of 1T-ZrTe2. Time-, energy-, and momentum-resolved nonequilibrium carrier dynamics reveal that intra- and interband scattering processes play a major role in the relaxation mechanism, leading to multivalley electron-hole accumulation near the Fermi level. We also show that electrons' inverse lifetime has a linear dependence as a function of their excess energy. Our time- and polarization-resolved XUV photoemission results shed light on the excited state electronic structure of 1T-ZrTe2 and provide valuable insights into the relatively unexplored field of quantum-state-resolved ultrafast dynamics in 3D topological Dirac semimetals.

Magnetic parity violation and parity-time-reversal-symmetric magnets

Parity-time-reversal symmetry (PTsymmetry), a symmetry for the combined operations of space inversion (P) and time reversal (T), is a fundamental concept of physics and characterizes the functionality of materials as well asPandTsymmetries. In particular, thePT-symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leavesPTsymmetry intact, the simultaneous violation ofPandTsymmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagneticP-symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion.

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.

Layer Hall effect induced by hidden Berry curvature in antiferromagnetic insulators

The layer Hall effect describes electrons spontaneously deflected to opposite sides at different layers, which has been experimentally reported in the MnBi2Te4 thin films under perpendicular electric fields. Here, we reveal a universal origin of the layer Hall effect in terms of the so-called hidden Berry curvature, as well as material design principles. Hence, it gives rise to zero Berry curvature in momentum space but non-zero layer-locked hidden Berry curvature in real space. We show that, compared to that of a trivial insulator, the layer Hall effect is significantly enhanced in antiferromagnetic topological insulators. Our universal picture provides a paradigm for revealing the hidden physics as a result of the interplay between the global and local symmetries, and can be generalized in various scenarios.

Signatures of a surface spin-orbital chiral metal

The relation between crystal symmetries, electron correlations and electronic structure steers the formation of a large array of unconventional phases of matter, including magneto-electric loop currents and chiral magnetism1-6. The detection of such hidden orders is an important goal in condensed-matter physics. However, until now, non-standard forms of magnetism with chiral electronic ordering have been difficult to detect experimentally7. Here we develop a theory for symmetry-broken chiral ground states and propose a methodology based on circularly polarized, spin-selective, angular-resolved photoelectron spectroscopy to study them. We use the archetypal quantum material Sr2RuO4 and reveal spectroscopic signatures that, despite being subtle, can be reconciled with the formation of spin-orbital chiral currents at the surface of the material8-10. As we shed light on these chiral regimes, our findings pave the way for a deeper understanding of ordering phenomena and unconventional magnetism.

Mapping Light-Dressed Floquet Bands by Highly Nonlinear Optical Excitations and Valley Polarization

Ultrafast nonlinear optical phenomena in solids have been attracting a great deal of interest as novel methodologies for the femtosecond spectroscopy of electron dynamics and control of the properties of materials. Here, we theoretically investigate strong-field nonlinear optical transitions in a prototypical two-dimensional material, hBN, and show that the k-resolved conduction band charge occupation patterns induced by an elliptically polarized laser can be understood in a multiphoton resonant picture, but, remarkably, only if using the Floquet light-dressed states instead of the undressed matter states. Our work demonstrates that Floquet dressing affects ultrafast charge dynamics and photoexcitation even from a single pump pulse and establishes a direct measurable signature for band dressing in nonlinear optical processes in solids, opening new paths for ultrafast spectroscopy and valley manipulation.

Uncovering spin-orbit coupling-independent hidden spin polarization of energy bands in antiferromagnets

Many textbook physical effects in crystals are enabled by some specific symmetries. In contrast to such 'apparent effects', 'hidden effect X' refers to the general condition where the nominal global system symmetry would disallow the effect X, whereas the symmetry of local sectors within the crystal would enable effect X. Known examples include the hidden Rashba and/or hidden Dresselhaus spin polarization that require spin-orbit coupling, but unlike their apparent counterparts are demonstrated to exist in non-magnetic systems even in inversion-symmetric crystals. Here, we discuss hidden spin polarization effect in collinear antiferromagnets without the requirement for spin-orbit coupling (SOC). Symmetry analysis suggests that antiferromagnets hosting such effect can be classified into six types depending on the global vs local symmetry. We identify which of the possible collinear antiferromagnetic compounds will harbor such hidden polarization and validate these symmetry enabling predictions with first-principles density functional calculations for several representative compounds. This will boost the theoretical and experimental efforts in finding new spin-polarized materials.

Ultrafast Hidden Spin Polarization Dynamics of Bright and Dark Excitons in 2H-WSe_{2}

We performed spin-, time- and angle-resolved extreme ultraviolet photoemission spectroscopy of excitons prepared by photoexcitation of inversion-symmetric 2H-WSe_{2} with circularly polarized light. The very short probing depth of XUV photoemission permits selective measurement of photoelectrons originating from the top-most WSe_{2} layer, allowing for direct measurement of hidden spin polarization of bright and momentum-forbidden dark excitons. Our results reveal efficient chiroptical control of bright excitons' hidden spin polarization. Following optical photoexcitation, intervalley scattering between nonequivalent K-K^{'} valleys leads to a decay of bright excitons' hidden spin polarization. Conversely, the ultrafast formation of momentum-forbidden dark excitons acts as a local spin polarization reservoir, which could be used for spin injection in van der Waals heterostructures involving multilayer transition metal dichalcogenides.

Circular dichroism in hard X-ray photoelectron diffraction observed by time-of-flight momentum microscopy

X-ray photoelectron diffraction (XPD) is a powerful technique that yields detailed structural information of solids and thin films that complements electronic structure measurements. Among the strongholds of XPD we can identify dopant sites, track structural phase transitions, and perform holographic reconstruction. High-resolution imaging of k_ll-distributions (momentum microscopy) presents a new approach to core-level photoemission. It yields full-field k_x-k_y XPD patterns with unprecedented acquisition speed and richness in details. Here, we show that beyond the pure diffraction information, XPD patterns exhibit pronounced circular dichroism in the angular distribution (CDAD) with asymmetries up to 80%, alongside with rapid variations on a small k_ll-scale (0.1 Å^-1). Measurements with circularly-polarized hard X-rays (hν = 6 keV) for a number of core levels, including Si, Ge, Mo and W, prove that core-level CDAD is a general phenomenon that is independent of atomic number. The fine structure in CDAD is more pronounced compared to the corresponding intensity patterns. Additionally, they obey the same symmetry rules as found for atomic and molecular species, and valence bands. The CD is antisymmetric with respect to the mirror planes of the crystal, whose signatures are sharp zero lines. Calculations using both the Bloch-wave approach and one-step photoemission reveal the origin of the fine structure that represents the signature of Kikuchi diffraction. To disentangle the roles of photoexcitation and diffraction, XPD has been implemented into the Munich SPRKKR package to unify the one-step model of photoemission and multiple scattering theory.

Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides

Monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase have been recently classified as higher-order topological insulators (HOTIs), protected by C_{3} rotation symmetry. In addition, theoretical calculations show an orbital Hall plateau in the insulating gap of TMDs, characterized by an orbital Chern number. We explore the correlation between these two phenomena in TMD monolayers in two structural phases: the noncentrosymmetric 2H and the centrosymmetric 1T. Using density functional theory, we confirm the characteristics of 2H TMDs and reveal that 1T TMDs are identified by a Z_{4} topological invariant. As a result, when cut along appropriate directions, they host conducting edge states, which cross their bulk energy-band gaps and can transport orbital angular momentum. Our linear response calculations thus indicate that the HOTI phase is accompanied by an orbital Hall effect. Using general symmetry arguments, we establish a connection between the two phenomena with potential implications for orbitronics and spin orbitronics.

Probing magnetic orbitals and Berry curvature with circular dichroism in resonant inelastic X-ray scattering

Resonant inelastic X-ray scattering (RIXS) can probe localized excitations at selected atoms in materials, including particle-hole transitions between the valence and conduction bands. These transitions are governed by fundamental properties of the corresponding Bloch wave functions, including orbital and magnetic degrees of freedom, and quantum geometric properties such as the Berry curvature. In particular, orbital angular momentum (OAM), which is closely linked to the Berry curvature, can exhibit a nontrivial momentum dependence. We demonstrate how information on such OAM textures can be extracted from the circular dichroism in RIXS. Based on accurate modeling with a first-principles treatment of the key ingredient-the light-matter interaction-we simulate dichroic RIXS spectra for the prototypical transition-metal dichalcogenide MoSe2 and the two-dimensional topological insulator 1T'-MoS2. Guided by an intuitive picture of the optical selection rules, we discuss how the momentum-dependent OAM manifests itself in the dichroic RIXS signal if one controls the momentum transfer. Our calculations are performed for typical experimental geometries and parameter regimes, and demonstrate the possibility of observing the predicted circular dichroism in forthcoming experiments. Thus, our work establishes a new avenue for observing Berry curvature and topological states in quantum materials.

Direct Optical Probe of Magnon Topology in Two-Dimensional Quantum Magnets

Controlling edge states of topological magnon insulators is a promising route to stable spintronics devices. However, to experimentally ascertain the topology of magnon bands is a challenging task. Here we derive a fundamental relation between the light-matter coupling and the quantum geometry of magnon states. This allows us to establish the two-magnon Raman circular dichroism as an optical probe of magnon topology in honeycomb magnets, in particular of the Chern number and the topological gap. Our results pave the way for interfacing light and topological magnons in functional quantum devices.

Role of Hidden Spin Polarization in Nonreciprocal Transport of Antiferromagnets

The discovery of hidden spin polarization (HSP) in centrosymmetric nonmagnetic crystals, i.e., spatially distributed spin polarization originated from local symmetry breaking, has promised an expanded material pool for future spintronics. However, the measurements of such exotic effects have been limited to subtle space- and momentum-resolved techniques, unfortunately, hindering their applications. Here, we theoretically predict macroscopic non-reciprocal transports induced by HSP when coupling another spatially distributed quantity, such as staggered local moments in a space-time PT-symmetric antiferromagnet. By using a four-band model Hamiltonian, we demonstrate that HSP plays a crucial role in determining the asymmetric bands with respect to opposite momenta. Such band asymmetry leads to non-reciprocal nonlinear conductivity, exemplified by tetragonal CuMnAs via first-principles calculations. We further provide the material design principles for large nonlinear conductivity, including two-dimensional nature, multiple band crossings near the Fermi level, and symmetry protected HSP. Our Letter not only reveals direct spintronic applications of HSP (such as Néel order detection), but also sheds light on finding observables of other hidden effects, such as hidden optical polarization and hidden Berry curvature.

Assessing Nontrivial Topology in Weyl Semimetals by Dichroic Photoemission

The electronic structure of Weyl semimetals features Berry flux monopoles in the bulk and Fermi arcs at the surface. While angle-resolved photoelectron spectroscopy (ARPES) is successfully used to map the bulk and surface bands, it remains a challenge to explicitly resolve and pinpoint these topological features. Here we combine state-of-the-art photoemission theory and experiments over a wide range of excitation energies for the Weyl semimetals TaAs and TaP. Our results show that simple surface-band-counting schemes, proposed previously to identify nonzero Chern numbers, are ambiguous due to pronounced momentum-dependent spectral weight variations and the pronounced surface-bulk hybridization. Instead, our findings indicate that dichroic ARPES provides an improved approach to identify Fermi arcs but requires an accurate description of the photoelectron final state.

Hidden spin-orbital texture at the [Formula: see text]-located valence band maximum of a transition metal dichalcogenide semiconductor

Finding stimuli capable of driving an imbalance of spin-polarised electrons within a solid is the central challenge in the development of spintronic devices. However, without the aid of magnetism, routes towards this goal are highly constrained with only a few suitable pairings of compounds and driving mechanisms found to date. Here, through spin- and angle-resolved photoemission along with density functional theory, we establish how the p-derived bulk valence bands of semiconducting 1T-HfSe2 possess a local, ground-state spin texture spatially confined within each Se-sublayer due to strong sublayer-localised electric dipoles orientated along the c-axis. This hidden spin-polarisation manifests in a 'coupled spin-orbital texture' with in-equivalent contributions from the constituent p-orbitals. While the overall spin-orbital texture for each Se sublayer is in strict adherence to time-reversal symmetry (TRS), spin-orbital mixing terms with net polarisations at time-reversal invariant momenta are locally maintained. These apparent TRS-breaking contributions dominate, and can be selectively tuned between with a choice of linear light polarisation, facilitating the observation of pronounced spin-polarisations at the Brillouin zone centre for all kz. We discuss the implications for the generation of spin-polarised populations from 1T-structured transition metal dichalcogenides using a fixed energy, linearly polarised light source.

Through the Lens of a Momentum Microscope: Viewing Light-Induced Quantum Phenomena in 2D Materials

Van der Waals (vdW) materials at their 2D limit are diverse, flexible, and unique laboratories to study fundamental quantum phenomena and their future applications. Their novel properties rely on their pronounced Coulomb interactions, variety of crystal symmetries and spin-physics, and the ease of incorporation of different vdW materials to form sophisticated heterostructures. In particular, the excited state properties of many 2D semiconductors and semi-metals are relevant for their technological applications, particularly those that can be induced by light. In this paper, the recent advances made in studying out-of-equilibrium, light-induced, phenomena in these materials are reviewed using powerful, surface-sensitive, time-resolved photoemission-based techniques, with a particular emphasis on the emerging multi-dimensional photoemission spectroscopy technique of time-resolved momentum microscopy. The advances this technique has enabled in studying the nature and dynamics of occupied excited states in these materials are discussed. Then, the future research directions opened by these scientific and instrumental advancements are projected for studying the physics of 2D materials and the opportunities to engineer their band-structure and band-topology by laser fields.

Chirality of Valley Excitons in Monolayer Transition-Metal Dichalcogenides

By enabling control of valley degrees of freedom in transition-metal dichalcogenides, valley-selective circular dichroism has become a key concept in valleytronics. Herein, we show that valley excitons, bound electron-hole pairs formed at the K or K̅ valleys upon absorption of circularly polarized light, are chiral quasiparticles characterized by a finite orbital angular momentum (OAM). We further formulate an ab initio many-body theory of valley-selective circular dichroism and valley excitons based on the Bethe-Salpeter equation. Besides governing the interaction with circularly polarized light, the OAM confers upon excitons a finite magnetization that manifests itself through an excitonic Zeeman splitting upon interaction with external magnetic fields. The good agreement between our ab initio calculations and recent experimental measurements of the exciton Zeeman shifts corroborates this picture, indicating that valley excitons can carry angular momentum even in their singlet state.

Structure of the moiré exciton captured by imaging its electron and hole

Interlayer excitons (ILXs) - electron-hole pairs bound across two atomically thin layered semiconductors - have emerged as attractive platforms to study exciton condensation^1-4, single-photon emission and other quantum information applications^5-7. Yet, despite extensive optical spectroscopic investigations^8-12, critical information about their size, valley configuration and the influence of the moiré potential remains unknown. Here, in a WSe₂/MoS₂ heterostructure, we captured images of the time-resolved and momentum-resolved distribution of both of the particles that bind to form the ILX: the electron and the hole. We thereby obtain a direct measurement of both the ILX diameter of around 5.2 nm, comparable with the moiré-unit-cell length of 6.1 nm, and the localization of its centre of mass. Surprisingly, this large ILX is found pinned to a region of only 1.8 nm diameter within the moiré cell, smaller than the size of the exciton itself. This high degree of localization of the ILX is backed by Bethe-Salpeter equation calculations and demonstrates that the ILX can be localized within small moiré unit cells. Unlike large moiré cells, these are uniform over large regions, allowing the formation of extended arrays of localized excitations for quantum technology.

Momentum-Resolved Observation of Exciton Formation Dynamics in Monolayer WS2

The dynamics of momentum-dark exciton formation in transition metal dichalcogenides is difficult to measure experimentally, as many momentum-indirect exciton states are not accessible to optical interband spectroscopy. Here, we combine a tunable pump, high-harmonic probe laser source with a 3D momentum imaging technique to map photoemitted electrons from monolayer WS₂. This provides momentum-, energy- and time-resolved access to excited states on an ultrafast time scale. The high temporal resolution of the setup allows us to trace the early-stage exciton dynamics on its intrinsic time scale and observe the formation of a momentum-forbidden dark KΣ exciton a few tens of femtoseconds after optical excitation. By tuning the excitation energy, we manipulate the temporal evolution of the coherent excitonic polarization and observe its influence on the dark exciton formation. The experimental results are in excellent agreement with a fully microscopic theory, resolving the temporal and spectral dynamics of bright and dark excitons in WS₂.

Hard x-ray photoelectron spectroscopy: a snapshot of the state-of-the-art in 2020

Hard x-ray photoelectron spectroscopy (HAXPES) is establishing itself as an essential technique for the characterisation of materials. The number of specialised photoelectron spectroscopy techniques making use of hard x-rays is steadily increasing and ever more complex experimental designs enable truly transformative insights into the chemical, electronic, magnetic, and structural nature of materials. This paper begins with a short historic perspective of HAXPES and spans from developments in the early days of photoelectron spectroscopy to provide an understanding of the origin and initial development of the technique to state-of-the-art instrumentation and experimental capabilities. The main motivation for and focus of this paper is to provide a picture of the technique in 2020, including a detailed overview of available experimental systems worldwide and insights into a range of specific measurement modi and approaches. We also aim to provide a glimpse into the future of the technique including possible developments and opportunities.

Suppression of the vacuum space-charge effect in fs-photoemission by a retarding electrostatic front lens

The performance of time-resolved photoemission experiments at fs-pulsed photon sources is ultimately limited by the e-e Coulomb interaction, downgrading energy and momentum resolution. Here, we present an approach to effectively suppress space-charge artifacts in momentum microscopes and photoemission microscopes. A retarding electrostatic field generated by a special objective lens repels slow electrons, retaining the k-image of the fast photoelectrons. The suppression of space-charge effects scales with the ratio of the photoelectron velocities of fast and slow electrons. Fields in the range from -20 to -1100 V/mm for E_kin = 100 eV to 4 keV direct secondaries and pump-induced slow electrons back to the sample surface. Ray tracing simulations reveal that this happens within the first 40 to 3 μm above the sample surface for E_kin = 100 eV to 4 keV. An optimized front-lens design allows switching between the conventional accelerating and the new retarding mode. Time-resolved experiments at E_kin = 107 eV using fs extreme ultraviolet probe pulses from the free-electron laser FLASH reveal that the width of the Fermi edge increases by just 30 meV at an incident pump fluence of 22 mJ/cm² (retarding field -21 V/mm). For an accelerating field of +2 kV/mm and a pump fluence of only 5 mJ/cm², it increases by 0.5 eV (pump wavelength 1030 nm). At the given conditions, the suppression mode permits increasing the slow-electron yield by three to four orders of magnitude. The feasibility of the method at high energies is demonstrated without a pump beam at E_kin = 3830 eV using hard x rays from the storage ring PETRA III. The approach opens up a previously inaccessible regime of pump fluences for photoemission experiments.

Disentangling Orbital and Valley Hall Effects in Bilayers of Transition Metal Dichalcogenides

It has been recently shown that monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase exhibit relatively large orbital Hall conductivity plateaus within their energy band gaps, where their spin Hall conductivities vanish [Canonico et al., Phys. Rev. B 101, 161409 (2020)PRBMDO2469-995010.1103/PhysRevB.101.161409; Bhowal and Satpathy, Phys. Rev. B 102, 035409 (2020)PRBMDO2469-995010.1103/PhysRevB.102.035409]. However, since the valley Hall effect (VHE) in these systems also generates a transverse flow of orbital angular momentum, it becomes experimentally challenging to distinguish between the two effects in these materials. The VHE requires inversion symmetry breaking to occur, which takes place in the TMD monolayers but not in the bilayers. We show that a bilayer of 2H-MoS_{2} is an orbital Hall insulator that exhibits a sizeable orbital Hall effect in the absence of both spin and valley Hall effects. This phase can be characterized by an orbital Chern number that assumes the value C_{L}=2 for the 2H-MoS_{2} bilayer and C_{L}=1 for the monolayer, confirming the topological nature of these orbital-Hall insulator systems. Our results are based on density functional theory and low-energy effective model calculations and strongly suggest that bilayers of TMDs are highly suitable platforms for direct observation of the orbital Hall insulating phase in two-dimensional materials. Implications of our findings for attempts to observe the VHE in TMD bilayers are also discussed.

A quantitative comparison of time-of-flight momentum microscopes and hemispherical analyzers for time- and angle-resolved photoemission spectroscopy experiments

Time-of-flight-based momentum microscopy has a growing presence in photoemission studies, as it enables parallel energy- and momentum-resolved acquisition of the full photoelectron distribution. Here, we report table-top extreme ultraviolet time- and angle-resolved photoemission spectroscopy (trARPES) featuring both a hemispherical analyzer and a momentum microscope within the same setup. We present a systematic comparison of the two detection schemes and quantify experimentally relevant parameters, including pump- and probe-induced space-charge effects, detection efficiency, photoelectron count rates, and depth of focus. We highlight the advantages and limitations of both instruments based on exemplary trARPES measurements of bulk WSe₂. Our analysis demonstrates the complementary nature of the two spectrometers for time-resolved ARPES experiments. Their combination in a single experimental apparatus allows us to address a broad range of scientific questions with trARPES.