Circular Dichroism ARPES Simulations Overview

• Circular dichroism ARPES simulations are advanced computational frameworks combining DFT, Wannier models, and one-step methods to resolve orbital angular momentum effects.
• They accurately predict dichroic signals from left- and right-circularly polarized light by incorporating inter-atomic interference, final-state scattering, and surface symmetry breaking.
• Practical insights include tuning parameters like photon energy and inelastic mean free path to reproduce experimental sign reversals and oscillatory behavior in dichroic spectra.

Circular dichroism in angle-resolved photoemission spectroscopy (CD-ARPES) simulations constitute a rigorous theoretical and computational effort to predict, interpret, and disentangle the physical contributions to dichroic photoemission signals under left- and right-circularly polarized probe light. The technique probes not only the local electronic orbital angular momentum (OAM) and associated Berry curvature in symmetry-broken and topological materials but is also sensitive to multiple extrinsic effects stemming from the photoemission process itself. Modern CD-ARPES simulations combine ab initio electronic structure theory, tight-binding and Wannier models, explicit construction of initial and final electronic states, and full calculations of photoemission matrix elements with proper treatment of scattering, symmetry-breaking, and experimental geometry. This article presents a comprehensive overview of core principles, methodological approaches, computational workflows, and representative results in state-of-the-art CD-ARPES simulations, with direct reference to recent advances (Sidilkover et al., 13 Mar 2025, Boban et al., 2024, Yen et al., 2024, Parusa et al., 18 Jan 2026).

1. Fundamental Formalism: CD-ARPES Observable and Matrix Elements

CD-ARPES simulates the difference in photocurrent as a function of in-plane momentum $\mathbf{k}_\parallel$ and energy $E$ when a sample is probed by left- $(I^{(-)})$ and right-circularly $(I^{(+)})$ polarized light. The foundational formula for the CD-ARPES intensity is given by Fermi’s Golden Rule,

$$I^{(\pm)}(\mathbf{k}_\parallel, E) = \sum_\alpha \left| M^{(\pm)}_\alpha(\mathbf{k}_\parallel, E) \right|^2 \delta(\varepsilon_\alpha(\mathbf{k})+\hbar\omega - E - \Phi)$$

where $M^{(\pm)}_\alpha$ is the dipole matrix element between the initial Bloch state $|\psi_{\mathbf{k}\alpha}\rangle$ and a photoelectron final state $|\chi_{\mathbf{p}}\rangle$, with polarization vector $\mathbf{\epsilon}^{(\pm)}$, work function $\Phi$, and photon energy $\hbar\omega$.

The normalized dichroism (CD asymmetry) is typically defined as: $$A_\mathrm{CD}(\mathbf{k}_\parallel, E) = \frac{I^{(+)} - I^{(-)}}{I^{(+)} + I^{(-)}}$$ This form enables direct simulation of the experimental ARPES dichroic contrast.

2. Orbital-Resolved Expansion and "Hidden" Atomic OAM

To resolve matrix elements at the orbital and site level, initial Bloch states are expanded in a localized Wannier basis: $$\psi_{\mathbf{k}\alpha}(\mathbf{r}) = \frac{1}{\sqrt{N}} \sum_j C_{j\alpha}(\mathbf{k}) e^{i\mathbf{k}\cdot\mathbf{r}_j} \phi_j(\mathbf{r}-\mathbf{r}_j)$$ Here, $j$ labels atomic site and orbital, and $C_{j\alpha}(\mathbf{k})$ are projection coefficients. The matrix element in the atomic-center approximation incorporates geometric phase factors and attenuation due to the finite inelastic mean free path (IMFP) $\lambda$: $$M^{(\pm)}_\alpha(\mathbf{k}_\parallel, E) = \sqrt{N} \sum_j C_{j\alpha}(\mathbf{k}_\parallel) e^{-i\mathbf{p}\cdot\mathbf{r}_j} e^{z_j/\lambda} M^{\rm orb}_{j,\,(\pm)}(\mathbf{k}_\parallel, E)$$ The intra-atomic term $M^{\rm orb}_{j,\,(\pm)}$ involves explicit overlap integrals of initial and final atomic-like orbitals with the polarization.

Despite global inversion symmetry (as in many topological insulator bulks), finite $\lambda$ introduces incomplete cancellation of local OAM at paired atomic sites, yielding a "hidden" site-resolved OAM contribution that directly affects $I^{(+)} - I^{(-)}$ even in otherwise OAM-forbidden bulk bands (Sidilkover et al., 13 Mar 2025).

3. Inter-Atomic Interference, Scattering, and Final-State Effects

Beyond intra-atomic processes, inter-atomic interference terms

$$T_{jj'}(\mathbf{k}_\parallel, E) = e^{-i\mathbf{p}\cdot(\mathbf{r}_j-\mathbf{r}_{j'})} e^{(z_j+z_{j'})/\lambda} \Big[ M^{\rm orb}_{j,(+)*} M^{\rm orb}_{j',(+)} - M^{\rm orb}_{j,(-)*} M^{\rm orb}_{j',(-)} \Big]$$

generate strong photon-energy-dependent oscillations and sign reversals in the CD-ARPES signal. These arise from phase accumulation between emitting sites, amplified by the final photoelectron momentum and geometric arrangement of atoms (Boban et al., 2024, Yen et al., 2024). In practical simulations, these inter-atomic (or inter-layer) terms dominate photon-energy dependence, particularly in bulk bands.

Full multiple-scattering (one-step) descriptions of the photoelectron final state, such as solving the time-reversed Low-Energy Electron Diffraction (TR-LEED) problem within Korringa-Kohn-Rostoker (KKR) or SPR-KKR frameworks, are required to accurately capture final-state resonances and multiple-scattering phase shifts essential for reproducing experimental dichroism patterns, including sign flips and spectral peak shifts as functions of photon energy (Sidilkover et al., 13 Mar 2025, Boban et al., 2024, Parusa et al., 18 Jan 2026).

4. Surface Symmetry Breaking and Layer-Dependent Effects

Explicit modeling of the sample as a finite slab (e.g., 7-quintuple-layer Bi₂Se₃ slab) incorporates broken inversion symmetry at the surface, which is necessary for surface-state OAM and dichroism. However, bulk simulations show that surface-induced OAM is sharply localized to the topmost atomic layers; the bulk dichroism remains primarily governed by IMFP-induced hidden OAM and inter-atomic phase interference (Sidilkover et al., 13 Mar 2025). Layer-resolved OAM calculations verify exact cancellation in the bulk, which is broken only near the surface.

5. Computational Protocols and Parameterization

Matrix Element and Final-State Construction

The simulation procedure typically requires:

• Density Functional Theory (DFT) ground-state calculation with spin-orbit coupling (typically using PBE functional and QUANTUM ESPRESSO or WIEN2k);
• Generation of atomic-like Wannier functions (using WANNIER90), retaining non-maximally localized orbitals for atomic character;
• Construction of tight-binding Hamiltonians or slab models for geometry-specific OAM mapping;
• Calculation of atomic dipole matrix elements using isolated-atom radial equations; inclusion of distortion in the final state (partial-wave expansions up to $\ell=2$ or higher);
• Explicit inclusion of attenuation ($\lambda\approx8$–12 Å in the relevant photon energy range 25–50 eV for Bi₂Se₃).

One-Step and Multiple-Scattering Approaches

The one-step photoemission formalism incorporates:

• LDA potentials in muffin-tin or full-potential approximation;
• Large real-space clusters (e.g., $R_{\max}=15$–20 Å, hundreds of atoms) for multiple-scattering calculations (e.g., EDAC, SPR-KKR);
• $k$-mesh sizes of at least $24\times24$—up to $60\times60$ for high-resolution features;
• Angular-momentum cutoff up to $\ell_{\max}=3$–5;
• Control of IMFP via an imaginary potential $V_i$ in the final-state Hamiltonian.

Simulations must carefully include all scattering mechanisms and attenuation to avoid artificial suppression or enhancement of dichroic signals. Comparison against experiment consistently shows that intra-atomic (site OAM) dichroism is nearly photon-energy-independent, whereas inter-atomic and scattering-induced dichroism oscillates and reverses sign as a function of photon energy, in direct agreement with both experiment and advanced simulation (Sidilkover et al., 13 Mar 2025, Boban et al., 2024).

6. Interpretation of CD-ARPES and Connection to Material Topology

While CD-ARPES is often interpreted as a direct probe of OAM and Berry curvature, comprehensive simulation studies establish that the measured dichroic signal encodes both intrinsic (momentum-resolved OAM, hidden OAM due to IMFP) and extrinsic (inter-atomic interference, final-state resonance, surface symmetry-breaking, experimental geometry) contributions (Sidilkover et al., 13 Mar 2025, Boban et al., 2024, Yen et al., 2024). In light of these findings:

• Bulk dichroism in inversion-symmetric materials generally arises from extrinsic absence of perfect OAM cancellation due to finite mean-free-path and geometric phase accrual.
• Photon-energy dependence, including sign reversals of the dichroic signal, is strongly modulated by inter-atomic interference, final-state scattering, and multiple-scattering resonances.
• Surface-state dichroism and angular dependencies (e.g., Dirac cone sign flips) can be fully explained only with one-step final-state treatments accounting for all resonances and scattering (Sidilkover et al., 13 Mar 2025).

Moreover, attempts to extract local Berry curvature or Chern number from CD-ARPES require disentangling these extrinsic mechanisms, ideally through multi-photon-energy and symmetry-based analysis as implemented in state-of-the-art studies (Yen et al., 2024).

7. Representative Results and Best Practices

The two-pronged advanced simulation approach—(i) Wannier-resolved expansion to separate hidden OAM and interference, (ii) fully relativistic SPR-KKR one-step modeling for final-state resonances—successfully reconstructs both the unexpectedly large dichroic response in inversion-symmetric bulk bands and the rapid, oscillatory, photon-energy-dependent dichroism in both bulk and surface states (Sidilkover et al., 13 Mar 2025).

Recommended simulation practices include:

• Always include full multiple scattering when atomic numbers or off-normal incidence are significant, as atomic-only models fail to capture intra-band sign flips and dark-corridor features (Boban et al., 2024).
• Adjust IMFP and inner-potential parameters to match experimental resonance conditions and dichroic sign reversals.
• Benchmark implementations against both all-electron and pseudopotential approaches, verifying convergence of dichroism with respect to $k$-mesh, energy cutoff, and angular-momentum expansion (Parusa et al., 18 Jan 2026).
• Decompose tensor contributions (intra-atomic, inter-atomic) to diagnose the microscopic origin of dichroic signals.

Extensive studies confirm that reliable, quantitative simulation of CD-ARPES in complex materials must resolve the full hierarchy of atomic, geometric, and scattering-driven effects, thereby providing both a predictive and interpretive framework for ongoing and future experimental studies (Sidilkover et al., 13 Mar 2025, Boban et al., 2024, Yen et al., 2024, Parusa et al., 18 Jan 2026).