Reexamining Circular Dichroism in Photoemission From a Topological Insulator

TL;DR

CD-ARPES has been used to infer Berry curvature and orbital angular momentum, but extrinsic photoemission matrix elements and surface symmetry breaking complicate this interpretation. By combining wide-range circular-dichroism ARPES on Bi$_2$Se$_3$ with Wannier-ARPES modeling and one-step SPR-KKR simulations, the study shows that bulk CDAD can be as large as surface CDAD because finite inelastic mean free path reveals local atomic OAM despite global inversion symmetry. The photon-energy dependence of CDAD is dominated by inter-atomic interference and final-state effects, with intra-atomic (local OAM) contributions playing a smaller role and Cooper-minimum–driven changes in radial channels modulating the spectra. The work concludes that CD-ARPES is not a robust bulk-versus-surface probe of OAM or Berry curvature, but it provides access to hidden local OAM and photoemission phase information, offering a pathway to quantify attosecond-scale delays in solids and guiding careful modeling of final-state scattering in ARPES analyses.

Abstract

The orbital angular momentum (OAM) of electron states is an essential ingredient for topological and quantum geometric quantities in solids. For example, Dirac surface states with helical spin- and orbital-angular momenta are a hallmark of a 3D topological insulator. Angle-resolved photoemission spectroscopy (ARPES) with variable circular light polarization, known as circular dichroism (CD), has been assumed to be a direct probe of OAM and, by proxy, of the Berry curvature of electronic bands in energy- and momentum-space. Indeed, topological surface states have been shown to exhibit angle-dependent CD (CDAD), and more broadly, CD is often interpreted as evidence of spin-orbit coupling. Meanwhile, it is well-established that CD originates from the photoemission matrix elements, which can have extrinsic contributions related to the experimental geometry and the inherently broken inversion symmetry at the sample surface. Therefore, it is important to broadly examine CD-ARPES to determine the scenarios in which it provides a robust probe of intrinsic material physics. We performed CD-ARPES on the canonical topological insulator $\mathrm{Bi}_2\mathrm{Se}_3$ over a wide range of incident photon energies. Not only do we observe angle-dependent CD in the surface states, as expected, but we also find CD of a similar magnitude in virtually all bulk bands. Since OAM is forbidden by inversion symmetry in the bulk, we conclude this originates from symmetry-breaking in the photoemission process. Comparison with theoretical calculations supports this view and suggests that $\textit{hidden}$ OAM - localized to atomic sites within each unit cell - contributes significantly. Additional effects, including inter-atomic interference and final-state resonances, are responsible for the rapid variation of the CDAD signal with photon energy.

Figures (10)

• Figure 1: (a) Schematic drawing of the experimental geometry of the ARPES experiment. The angle $\alpha$ indicates the incidence direction of the circularly polarized light (purple line) compared to the normal emission of the electrons (red region) towards the slit of the analyzer (black line). The relevant mirror plane of the crystal is shown in blue. (b) Side view of the surface crystal structure of $\mathrm{Bi}_2\mathrm{Se}_3$. (c) Sum ($I^{(+)}+I^{(-)}$) and (d) difference ($I^{(+)}-I^{(-)}$) of ARPES spectra obtained with circularly polarized light, along the $M-\Gamma-M'$ (left) and $K-\Gamma-K$ (right) directions. The spectra were obtained with $45$ eV circularly polarized light.
• Figure 2: CDAD ($I^{(+)}-I^{(-)}$) along the $K-\Gamma-K$ direction of $\mathrm{Bi}_2\mathrm{Se}_3$, obtained with circularly polarized light at $25.5-50$ eV photon energies. The dashed region in the right panel marks the zoomed-in region discussed in Fig.\ref{['fig:intra_inter']} for all photon energies.
• Figure 3: Local OAM and inversion symmetry. (a) Schematic of exponential profile with inelastic mean free path (IMFP) $\lambda$. (b) Calculated local OAM vectors for Bismuth atoms in a $\mathrm{Bi}_2\mathrm{Se}_3$ slab and (c) the zoomed-in image demonstrating inversion-symmetric OAM pairs of Bismuth atoms. Slab band resolved local OAM for (d) Bi3 and (e) Bi4 along the in-coming light direction in the zoomed-in cell. Note that the vectors in (b)-(c) are integrated over the range of the highlighted box in (e).
• Figure 4: (a) Intra-atomic contribution for Bi3 $I_{\mathrm{intra}}^{\mathrm{Bi3}}$ and (b) inter-atomic interference terms between Bi1 and Bi3 $I_{\mathrm{inter}}^{\mathrm{Bi1,Bi3}}$. Signal for three photon energies are shown to demonstrate the photon energy dependence, over the part of the spectrum highlighted in Fig. \ref{['fig:wide_CDAD']}. All the data in this figure is calculated from the bulk bands corresponding to the $k_z$ curve resolved with photon energy $\hbar\omega=$35 eV, with $\mathbf{k_{\parallel}}$ along $K$-$\Gamma$-$K$ direction. See Appendix \ref{['appendix:kz_band']} for detailed discussion.
• Figure 5: Effect of IMFP on surface state CDAD. (a) Experimental CDAD of the Dirac state along the $K$-$\Gamma$-$K$ direction at 25.5 $eV$. This is compared with (b) the one-step model calculated CDAD extracted for different values of the imaginary part of the time-reversed LEED final state to account for different inelastic mean free paths.