---
title: Circular Dichroism ARPES Simulations Overview
url: https://www.emergentmind.com/topics/circular-dichroism-arpes-simulations
type: topic
---

# Circular Dichroism ARPES Simulations Overview

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 [2503.10388, 2410.19652, 2402.14496, 2601.12490].

## 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 [2503.10388].

## 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 [2410.19652, 2402.14496]. 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 [2503.10388, 2410.19652, 2601.12490].

## 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 [2503.10388]. 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 [2503.10388, 2410.19652].

## 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 [2503.10388, 2410.19652, 2402.14496]. 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 [2503.10388].

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 [2402.14496].

## 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 [2503.10388].

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 [2410.19652].
- 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 [2601.12490].
- 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 [2503.10388, 2410.19652, 2402.14496, 2601.12490].

Source: https://www.emergentmind.com/topics/circular-dichroism-arpes-simulations