Matrix Element Effects Research Articles

Towards robust dichroism in angle-resolved photoemission

Dichroic techniques are highly relevant in the field of topological materials, layered systems, and spin-polarized electronic states. Dichroism in angle-resolved photoemission is per se a matrix element effect, which depends on the initial and final states as well as on the perturbation by the light field. Although matrix element effects in ARPES such as dichroism are important for addressing properties of the initial state wave functions, the results can strongly depend on experimental geometry or final state effects. Combining experimental data on bulk WSe2 taken at soft x-ray photon energies with state-of-the-art photoemission calculations, we demonstrate that a dichroic observable called time-reversal dichroism remains unaffected against variation of photon energy, light polarization, and the angle of incidence. We demonstrate a direct link of TRDAD obtained with both linearly and circularly polarized photons to the initial state properties indicating its broad applicability. The robustness of this matrix element effect indicates a considerable benefit over other dichroic techniques and encourages further experimental and theoretical investigations.

Exploring disorder correlations in superconducting systems: spectroscopic insights and matrix element effects.

Understanding the intricate interplay between disorder and superconductivity has become a key area of research in condensed matter physics, with profound implications for materials science. Recent studies have shown that spatial correlations of disorder potential can improve superconductivity, prompting a re-evaluation of some theoretical models. This paper explores the influence of disorder correlations on the fundamental properties of superconducting systems, going beyond the traditional assumption of spatially uncorrelated disorder. In particular, we investigate the influence of disorder correlations on key spectroscopic superconductor properties, including the density of states, as well as on the matrix elements of the superconducting coupling constant and their impact on the localization length. Our findings offer valuable insights into the role of disorder correlations in shaping the behavior of superconducting materials.

Observation of an anisotropic ultrafast spin relaxation process in large-area WTe2 films

Weyl semimetal Td-WTe2 hosts the natural broken inversion symmetry and strong spin–orbit coupling, which contains profound spin-related physics within a picosecond timescale. However, the comprehensive understanding of ultrafast spin behaviors in WTe2 is lacking due to its limited quality of large-scale films. Here, we report on an anisotropic ultrafast spin dynamics in highly oriented Td-WTe2 films using a femtosecond pump–probe technique at room temperature. A transient spin polarization-flip transition as fast as 0.8 ps is observed upon photoexcitation. The inversed spin is subsequently scattered by defects with a duration of about 5.9 ps. The whole relaxation process exhibits an intriguing dual anisotropy of sixfold and twofold symmetries, which stems from the energy band anisotropy of the WTe2 crystalline structure and the matrix element effect, respectively. Our work enriches the insights into the ultrafast opto-spintronics in topological Weyl semimetals.

Unveiling the orbital texture of 1T-TiTe2 using intrinsic linear dichroism in multidimensional photoemission spectroscopy

The momentum-dependent orbital character in crystalline solids, referred to as orbital texture, is of capital importance in the emergence of symmetry-broken collective phases, such as charge density waves as well as superconducting and topological states of matter. By performing extreme ultraviolet multidimensional angle-resolved photoemission spectroscopy for two different crystal orientations linked to each other by mirror symmetry, we isolate and identify the role of orbital texture in photoemission from the transition metal dichalcogenide 1T-TiTe2. By comparing our experimental results with theoretical calculations based on both a quantitative one-step model of photoemission and an intuitive tight-binding model, we unambiguously demonstrate the link between the momentum-dependent orbital orientation and the emergence of strong intrinsic linear dichroism in the photoelectron angular distributions. Our results represent an important step towards going beyond band structure (eigenvalues) mapping and learning about electronic wavefunction and orbital texture of solids by exploiting matrix element effects in photoemission spectroscopy.

Probing spin chirality of photoexcited topological insulators with circular dichroism: multi-dimensional time-resolved ARPES on Bi[formula omitted]Te[formula omitted]Se and Bi[formula omitted]Se[formula omitted

Using time-resolved multi-dimensional angle-resolved photoelectron spectroscopy (ARPES) we explore the angular momentum transfer of low energy polarized photons to two prototype topological insulators, Bi2Te2Se and Bi2Se3. Our comparative study is based on the analysis of circular dichroism in the photoemission yield of photoexcited Dirac states, and reveals that the spin vector of in-gap Dirac electrons in Bi2Te2Se presents a more pronounced out-of-plane component compared to that of Bi2Se3. We show that the multi-dimensional ARPES approach can be effectively used to observe the spin texture of photoexcited topological insulators, and to unambiguously disentangle experimental geometry and matrix element effects.

Photoemission signature of momentum-dependent hybridization in CeCoIn5

Hybridization between $f$ electrons and conduction bands ($c$-$f$ hybridization) is a driving force for many unusual phenomena. To provide insight into it, systematic studies of CeCoIn$_5$ heavy fermion superconductor have been performed by angle-resolved photoemission spectroscopy (ARPES) in a large angular range at temperature of $T=6$ K. The used photon energy of 122 eV corresponds to Ce $4d$-$4f$ resonance. Calculations carried out with relativistic multiple scattering Korringa-Kohn-Rostoker method and one-step model of photoemission yielded realistic simulation of the ARPES spectra indicating that Ce-In surface termination prevails. Surface states, which have been identified in the calculations, contribute significantly to the spectra. Effects of the hybridization strongly depend on wave vector. They include a dispersion of heavy electrons and bands gaining $f$-electron character when approaching Fermi energy. We have also observed a considerable variation of $f$-electron spectral weight at $E_F$, which is normally determined by both matrix element effects and wave vector dependent $c$-$f$ hybridization. Fermi surface scans covering a few Brillouin zones revealed large matrix element effects. A symmetrization of experimental Fermi surface, which reduces matrix element contribution, yielded a specific variation of $4f$-electron enhanced spectral intensity at $E_F$ around $\bar{\Gamma}$ and $\bar{M}$ points. Tight-binding approximation calculations for Ce-In plane provided the same universal distribution of $4f$-electron density for a range of values of the parameters used in the model.

Measuring spin-polarized electronic states of quantum materials: 2H−NbSe2

Probing the energy and spin electron properties of materials by means of photoemission spectroscopy gives insights into the low-energy phenomena of matter driven by spin orbit coupling or exchange interaction. The information that can be derived from complete photoelectron spectroscopy experiments, beyond $E$(k), is contained in the photoemission transition matrix elements that determine peak intensities. We present here a complete photoemission study of the spin-polarized bands of $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$, a material that presents a surface spin-texture. Circular dichroism in angular-resolved photoemission spectroscopy (CD-ARPES) data are compared with spin-polarized angular-resolved spectra (SARPES) as measured with linearly polarized radiation in a well-characterized experimental chirality, at selected photon energy values. CD-ARPES is due to a matrix element effect that depends strongly on photon energy and experimental geometry: we show that it cannot be used to infer intrinsic spin properties in $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$. On the other hand, SARPES data provide reliable direct information on the spin properties of the electron states. The results on $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$ are discussed, and general methodological conclusions are drawn on the best experimental approach to the determination of the spin texture of quantum materials.

Photoinduced long-lived state in FeSe0.4Te0.6

FeSexTe1−x compounds display a rich phase diagram, ranging from the nematicity of FeSe to the (π,π) magnetism of FeTe. We focus on FeSe0.4Te0.6, and exploit tr-ARPES to study its ultrafast electron dynamics following photoexcitation by near-infrared pump pulses. By exploiting probe-polarization-dependent matrix element effects, we reveal a photoinduced long-lived state, lasting for a few tens of picoseconds, showing features compatible with a nematic state. The possibility to induce a long-lived state in this compound by using ultra-short pulses might shed a new light on the driving force behind the nematic symmetry breaking in iron-based superconductors. With the aid of a phenomenological model, we illustrate how our results possibly question the common belief that a low-energy coupling with fluctuations is a necessary condition to stabilize the nematic order. On the contrary, the tendency towards orbital differentiation due to strong electronic correlations induced by the Hund’s coupling could be at the origin of the nematic order in iron-based superconductors.

Bulk electronic structure of lanthanum hexaboride ( LaB6 ) by hard x-ray angle-resolved photoelectron spectroscopy

In the last decade rare-earth hexaborides have been investigated for their fundamental importance in condensed matter physics, and for their applications in advanced technological fields. Among these compounds, LaB$_6$ has a special place, being a traditional d-band metal without additional f- bands. In this paper we investigate the bulk electronic structure of LaB$_6$ using hard x-ray photoemission spectroscopy, measuring both core-level and angle-resolved valence-band spectra. By comparing La 3d core level spectra to cluster model calculations, we identify well-screened peak residing at a lower binding energy compared to the main poorly-screened peak; the relative intensity between these peaks depends on how strong the hybridization is between La and B atoms. We show that the recoil effect, negligible in the soft x-ray regime, becomes prominent at higher kinetic energies for lighter elements, such as boron, but is still negligible for heavy elements, such as lanthanum. In addition, we report the bulk-like band structure of LaB$_6$ determined by hard x-ray angle-resolved photoemission spectroscopy (HARPES). We interpret HARPES experimental results by the free-electron final-state calculations and by the more precise one-step photoemission theory including matrix element and phonon excitation effects. In addition, we consider the nature and the magnitude of phonon excitations in HARPES experimental data measured at different temperatures and excitation energies. We demonstrate that one step theory of photoemission and HARPES experiments provide, at present, the only approach capable of probing true bulk-like electronic band structure of rare-earth hexaborides and strongly correlated materials.

The relevance of ARPES to high-Tc superconductivity in cuprates

Angle-resolved photoemission spectroscopy, visualizing the superconducting gap in k-space, plays a pivotal role in research on cuprates and other high-Tc superconducting materials. However, there has always been an imminent doubt whether this technique truly represents the intrinsic bulk spectral function, whose response can be distorted by energy- and k-dependence of the photoexcitation matrix element, and by a small photoelectron escape depth of few surface atomic layers. Here, we address this fundamental question with soft-X-ray photoemission measurements of the superconducting gap in the paradigm high-Tc cuprate Bi2Sr2CaCu2O8. We vary the matrix element by spanning a dense k-space grid, formed by the lattice superstructure, and the probing depth by changing the emission angle. The measured gap appears independent of the matrix element effects, probing depth or photoexcitation energy. This fact proves the relevance of photoemission studies for the bulk superconductivity in Bi2Sr2CaCu2O8, and calls for similar verification experiments on other high-Tc compounds, in particular more three-dimensional ones. Bi2Sr2CaCu2O8 shows an anomalously fast decay of the coherent spectral weight with photon energy, tracing back to strong electron–phonon interaction or relaxation of the lattice coherence.

Ab initio phonon self-energies and fluctuation diagnostics of phonon anomalies: Lattice instabilities from Dirac pseudospin physics in transition metal dichalcogenides

We present an ab initio approach for the calculation of phonon self-energies and their fluctuation diagnostics, which allows us to identify the electronic processes behind phonon anomalies. Application to the transition-metal-dichalcogenide monolayer 1H-TaS$_2$ reveals that coupling between the longitudinal-acoustic phonons and the electrons from an isolated low-energy metallic band is entirely responsible for phonon anomalies such as the mode softening and associated charge-density waves observed in this material. Our analysis allows us to distinguish between different mode-softening mechanisms including matrix-element effects, Fermi-surface nesting, and Van Hove scenarios. We find that matrix-element effects originating from a peculiar type of Dirac pseudospin textures control the charge-density-wave physics in 1H-TaS$_2$ and similar transition metal dichalcogenides.

Selective hybridization between the main band and the superstructure band in the Bi2Sr2CaCu2O8+δ superconductor

High-resolution laser-based angle-resolved photoemission measurements have been carried out on Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) and Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ (Bi2201) superconductors. Unexpected hybridization between the main band and the superstructure band in Bi2212 is clearly revealed. In the momentum space where one main Fermi surface intersects with one superstructure Fermi surface, four bands are observed instead of two. The hybridization exists in both superconducting state and normal state, and in Bi2212 samples with different doping levels. Such a hybridization is not observed in Bi2201. This phenomenon can be understood by considering the bilayer splitting in Bi2212, the selective hybridization of two bands with peculiar combinations, and the altered matrix element effects of the hybridized bands. These observations provide strong evidence on the origin of the superstructure band which is intrinsic to the CuO$_2$ planes. Therefore, understanding physical properties and superconductivity mechanism in Bi2212 should consider the complete Fermi surface topology which involves the main bands, the superstructure bands and their interactions.

Nonlinear optical effects in inversion-symmetry-breaking superconductors

We study nonlinear optical responses in superconducting systems with inversion ($\mathcal{I}$) symmetry-breaking order parameters. We first show that any superconducting system with $\mathcal{I}$ and time-reversal ($\mathcal{T}$) symmetries requires an $\mathcal{I}$-breaking order parameter to support optical transitions between particle-hole pair bands. We then use a 1D toy model of an $\mathcal{I}$-breaking superconductor to numerically calculate linear and nonlinear conductivities, including shift current and second harmonic generations (SHG) responses. We find that the magnitude of the signal is significantly larger in shift current/SHG response compare to the linear response due to the matrix element effect. We also present various scaling behaviors of the SHG signal, which may be relevant to the recent experimental observation of SHG in cuprates [1]. Finally, we confirm the generality of our observations regarding nonlinear responses of $\mathcal{I}$-breaking superconductors, by analyzing other models including a 1D three-band model and 2D square lattice model.

Computational framework chinook for angle-resolved photoemission spectroscopy

We have developed the numerical software package chinook for the simulation of photoemission matrix elements. This quantity encodes a depth of information regarding the orbital structure of the underlying wavefunctions from which photoemission occurs. Extraction of this information is often nontrivial, owing to the influence of the experimental geometry and photoelectron interference, precluding straightforward solutions. The chinook code has been designed to simulate and predict the ARPES intensity measured for arbitrary experimental configuration, including photon-energy, polarization, and spin-projection, as well as consideration of both surface-projected slab and bulk models. This framework then facilitates an efficient interpretation of the ARPES, allowing for a deeper understanding of the electronic structure in addition to the design of new experiments which leverage the matrix element effects towards the objective of selective photoemission from states of particular interest.

Circular-polarized-light-induced spin polarization characterized for the Dirac-cone surface state at W(110) with C2v symmetry

The C2v surface symmetry of W(110) strongly influences a spin-orbit-induced Dirac-cone-like surface state and its characterization by spin- and angle-resolved photoelectron spectroscopy. In particular, using circular polarized light, a distinctive k-dependent spin texture is observed along the overline{{boldsymbol{Gamma }}{boldsymbol{H}}} direction of the surface Brillouin zone. For all spin components Px, Py, and Pz, non-zero values are detected, while the initial-state spin polarization has only a Py component due to mirror symmetry. The observed complex spin texture of the surface state is controlled by transition matrix element effects, which include orbital symmetries of the involved electron states as well as the geometry of the experimental set-up.

Pairing from dynamically screened Coulomb repulsion in bismuth

Recently, Prakash et. al. have discovered bulk superconductivity in single crystals of bismuth, which is a semi metal with extremely low carrier density. At such low density, we argue that conventional electron-phonon coupling is too weak to be responsible for the binding of electrons into Cooper pairs. We study a dynamically screened Coulomb interaction with effective attraction generated on the scale of the collective plasma modes. We model the electronic states in bismuth to include three Dirac pockets with high velocity and one hole pocket with a significantly smaller velocity. We find a weak coupling instability, which is greatly enhanced by the presence of the hole pocket. Therefore, we argue that bismuth is the first material to exhibit superconductivity driven by retardation effects of Coulomb repulsion alone. By using realistic parameters for bismuth we find that the acoustic plasma mode does not play the central role in pairing. We also discuss a matrix element effect, resulting from the Dirac nature of the conduction band, which may affect $T_c$ in the $s$-wave channel without breaking time-reversal symmetry.

Fermi surface and effective masses in photoemission response of the (Ba1\u2212xKx)Fe2As2 superconductor

The angle-resolved photoemission spectra of the superconductor (Ba1−xKx)Fe2As2 have been investigated accounting coherently for spin-orbit coupling, disorder and electron correlation effects in the valence bands combined with final state, matrix element and surface effects. Our results explain the previously obscured origins of all salient features of the ARPES response of this paradigm pnictide compound and reveal the origin of the Lifshitz transition. Comparison of calculated ARPES spectra with the underlying DMFT band structure shows an important impact of final state effects, which result for three-dimensional states in a deviation of the ARPES spectra from the true spectral function. In particular, the apparent effective mass enhancement seen in the ARPES response is not an entirely intrinsic property of the quasiparticle valence bands but may have a significant extrinsic contribution from the photoemission process and thus differ from its true value. Because this effect is more pronounced for low photoexcitation energies, soft-X-ray ARPES delivers more accurate values of the mass enhancement due to a sharp definition of the 3D electron momentum. To demonstrate this effect in addition to the theoretical study, we show here new state of the art soft-X-ray and polarisation dependent ARPES measurments.

Rotation symmetry breaking in La2−xSrxCuO4 revealed by angle-resolved photoemission spectroscopy

Using angle-resolved photoemission spectroscopy it is revealed that in the vicinity of optimal doping the electronic structure of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ cuprate undergoes an electronic reconstruction associated with a wave vector ${\mathbit{q}}_{\mathbit{a}}=(\ensuremath{\pi},0)$. The reconstructed Fermi surface and folded band are distinct to the shadow bands observed in BSCCO cuprates and in underdoped ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ with $x\ensuremath{\le}0.12$, which shift the primary band along the zone diagonal direction. Furthermore, the folded bands appear only with ${\mathbit{q}}_{\mathbit{a}}=(\ensuremath{\pi},0)$ vector, but not with ${\mathbit{q}}_{\mathbit{b}}=(0,\ensuremath{\pi})$. We demonstrate that the absence of ${\mathbit{q}}_{\mathbit{b}}$ reconstruction is not due to the matrix-element effects in the photoemission process, which indicates the fourfold symmetry is broken in the system.

Laser angle-resolved photoemission as a probe of initial statekzdispersion, final-state band gaps, and spin texture of Dirac states in theBi2Te3topological insulator

Angle-resolved photoemission spectroscopy (ARPES) is widely used to investigate topological states and their spin textures in topological materials. Here, the authors examine the role of the ARPES matrix element in laser-ARPES spectra, and delineate how imprints of the Dirac states and their spin textures are encoded in these spectra in terms of the character and symmetry of the underlying initial and final states. For this purpose, they collect laser-ARPES spectra from the exemplar topological insulator material Bi${}_{2}$Te${}_{3}$ over a wide range of momenta in the ${k}_{x}$-k${}_{y}$ plane at energies ranging from 5.57--6.70 eV for two different linear polarizations of the incident light. The experimental results are analyzed via first-principles fully relativistic calculations of ARPES intensities within the framework of the one-step model of photoemission. These include effects of the ARPES matrix element from a semi-infinite solid surface. The authors obtain new insight into the nature of the laser-ARPES spectra from topological materials, and show how these spectra contain fingerprints of the initial state ${k}_{z}$ dispersions and spin textures of the Dirac-cone states, and how laser-ARPES could open a previously unrecognized window on the presence of delicate gaps in the final-state spectra.

Directly Characterizing the Relative Strength and Momentum Dependence of Electron-Phonon Coupling Using Resonant Inelastic X-Ray Scattering

The coupling between lattice and charge degrees of freedom in condensed matter materials is ubiquitous and can often result in interesting properties and ordered phases, including conventional superconductivity, charge density wave order, and metal-insulator transitions. Angle-resolved photoemission spectroscopy and both neutron and non-resonant x-ray scattering serve as effective probes for determining the behavior of appropriate, individual degrees of freedom -- the electronic structure and lattice excitation, or phonon dispersion, respectively. However, each provides less direct information about the mutual coupling between the degrees of freedom, usual through self-energy effects, which tend to renormalize and broaden spectral features precisely where the coupling is strong, impacting ones ability to quantitively characterize the coupling. Here we demonstrate that resonant inelastic x-ray scattering, or RIXS, can be an effective tool to directly determine the relative strength and momentum dependence of the electron-phonon coupling in condensed matter systems. Using a diagrammatic approach for an 8-band model of copper oxides, we study the contributions from the lowest order diagrams to the full RIXS intensity for a realistic scattering geometry, accounting for matrix element effects in the scattering cross-section as well as the momentum dependence of the electron-phonon coupling vertex. A detailed examination of these maps offers a unique perspective into the characteristics of electron-phonon coupling, which complements both neutron and non-resonant x-ray scattering, as well as Raman and infrared conductivity.