Accurate and efficient simulation of photoemission spectroscopy via Kohn-Sham scattering states

We introduce an efficient first-principles framework for simulating angle-resolved photoemission spectroscopy (ARPES) based on the direct computation of photoelectron states as solutions of the Kohn-Sham equation with scattering boundary conditions. While the one-step theory of photoemission has a long and successful history, existing implementations are often tied to specialized electronic-structure formalisms. Our approach is formally equivalent to the Lippmann-Schwinger formulation, and it is directly compatible with standard plane-wave and real-space density functional theory codes, enabling seamless integration with advanced exchange-correlation functionals and modern electronic-structure workflows. By providing explicit photoelectron wave functions, the method allows for a transparent analysis of matrix-element effects, multiple scattering, and experimental geometry. We demonstrate the accuracy and predictive power of the framework through circular-dichroism ARPES simulations for monolayer graphene and bulk $2H$-WSe$_2$, achieving excellent agreement with experimental data over a wide photon-energy range. Our results establish a robust and accessible route toward quantitative ARPES modeling, opening the door to systematic studies of orbital textures, many-body effects, and nonequilibrium phenomena within widely used ab initio platforms.

💡 Research Summary

The authors present a versatile first‑principles framework for simulating angle‑resolved photoemission spectroscopy (ARPES) that directly solves the Kohn‑Sham (KS) equations with scattering boundary conditions to obtain the final photoelectron states. By imposing appropriate asymptotic conditions on the KS wavefunctions, the method reproduces the same physics as the traditional one‑step model and the Lippmann‑Schwinger (LS) formalism, but it can be implemented within any standard plane‑wave or real‑space density‑functional theory (DFT) code. The theory is developed for two‑dimensional periodic systems using a Laue expansion, which separates the in‑plane plane‑wave components from the out‑of‑plane real‑space functions. The kinetic operator becomes diagonal in reciprocal‑lattice‑vector (G) space, while the KS potential couples different G‑channels. Open channels (those satisfying 2E > (k+G)²) acquire a propagating wavevector κ(G), and the scattering boundary conditions introduce unknown reflection and transmission coefficients. By constructing the Green’s function of the one‑dimensional differential operator, the KS equation with scattering conditions is recast into an LS integral equation. Numerically, both the LS equation and the KS equation are discretized on a uniform z‑grid with high‑order finite‑difference schemes (up to O(h⁵)). Iterative linear solvers (e.g., GMRES) are employed, and the KS formulation benefits from efficient preconditioning (diagonal or multigrid), leading to convergence 2–3 times faster than the LS approach.

A central focus of the work is the assessment of pseudopotential (PP) accuracy for high‑energy photoelectrons. Using norm‑conserving PPs from the PSEUDO‑DOJO library, the authors compare all‑electron (AE) calculations with PP results for circular‑dichroism ARPES (CD‑ARPES) of monolayer graphene. The PP’s non‑local part, which acts only on s and p angular channels, is shown to be essential for reproducing the experimental CD‑AD patterns at photon energies above ~65 eV; without it, the calculated nodal lines and “leg” features deviate markedly. Up to 100 eV the PP results match AE calculations almost perfectly, confirming that high‑quality PPs can faithfully describe scattering phases of photoelectrons across the VUV–XUV range.

The methodology is further validated on bulk 2H‑WSe₂, where experimental data were obtained with a time‑ and polarization‑resolved extreme‑UV momentum microscope. Two PP variants are tested: (i) a PP that includes semicore states (5s,5p for W and 3d for Se) and (ii) a PP that omits them. The inclusion of semicore states is crucial for correctly reproducing the circular‑dichroism (CD‑AD) and time‑reversal dichroism (TRD‑AD) textures at the three inequivalent K‑points. In particular, the valley‑integrated CD‑AD at K‑point 2 is severely underestimated when semicore states are excluded, leading to an incorrect ordering of dichroism strengths among the K‑points. This demonstrates that semicore electrons significantly affect the scattering phase of the final photoelectron wavefunctions, and that PP designs must capture these effects for quantitative ARPES modeling.

Beyond the technical achievements, the authors discuss the broader implications of having explicit photoelectron wavefunctions. First, matrix‑element effects, multiple‑scattering pathways, and interference patterns can be examined directly, providing physical insight that is obscured in approaches that only yield intensities. Second, the framework is compatible with advanced exchange‑correlation functionals, GW quasiparticle corrections, and time‑dependent DFT, opening the door to systematic studies of orbital textures, many‑body renormalizations, and nonequilibrium dynamics within widely used ab‑initio platforms. Finally, the demonstrated computational efficiency and the ability to use standard PP libraries make the method readily applicable to large‑scale materials screening and to complex heterostructures where experimental ARPES data are increasingly intricate.

In summary, the paper establishes a robust, efficient, and broadly accessible route to quantitative ARPES simulations by solving the Kohn‑Sham equation with scattering boundary conditions. It validates the approach against high‑resolution CD‑ARPES experiments on graphene and WSe₂, elucidates the critical role of pseudopotential non‑locality and semicore states, and highlights the method’s potential for future explorations of electronic structure phenomena that rely on detailed photoemission matrix elements.