- Open Access
Reexamining circular dichroism in photoemission from a topological insulator
Phys. Rev. Research 7, 033027 – Published 7 July, 2025
DOI: https://doi.org/10.1103/g9d4-qls9
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 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 “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.
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References (71)
- Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Experimental observation of the quantum Hall effect and Berry's phase in graphene, Nature (London) 438, 201 (2005).
- I. Sodemann and L. Fu, Quantum nonlinear Hall effect induced by berry curvature dipole in time-reversal invariant materials, Phys. Rev. Lett. 115, 216806 (2015).
- J. Ahn, G.-Yu Guo, N. Nagaosa, and A. Vishwanath, Riemannian geometry of resonant optical responses, Nat. Phys. 18, 290 (2022).
- B. Yan and S.-C. Zhang, Topological materials, Rep. Prog. Phys. 75, 096501 (2012).
- I. Souza and D. Vanderbilt, Dichroic -sum rule and the orbital magnetization of crystals, Phys. Rev. B 77, 054438 (2008).
- D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
- R. Resta, Electrical polarization and orbital magnetization: The modern theories, J. Phys.: Condens. Matter 22, 123201 (2010).
- J. Ma and D. A. Pesin, Chiral magnetic effect and natural optical activity in metals with or without Weyl points, Phys. Rev. B 92, 235205 (2015).
- R. Takahashi and N. Nagaosa, Berry curvature and orbital angular momentum of electrons in angle-resolved photoemission spectroscopy, Phys. Rev. B 91, 245133 (2015).
- R. Resta, Magnetic circular dichroism versus orbital magnetization, Phys. Rev. Res. 2, 023139 (2020).
- J. H. Ryoo and C.-H. Park, Hidden orbital polarization in diamond, silicon, germanium, gallium arsenide and layered materials, NPG Asia Mater. 9, e382 (2017).
- Y. Yen, J. A. Krieger, M. Yao, I. Robredo, K. Manna, Q. Yang, E. C. McFarlane, C. Shekhar, H. Borrmann, S. Stolz, R. Widmer, O. Gröning, V. N. Strocov, S. S. P. Parkin, C. Felser, M. G. Vergniory, M. Schüler, and N. B. M. Schröter, Controllable orbital angular momentum monopoles in chiral topological semimetals, Nat. Phys. 20, 1912 (2024).
- S. S. Brinkman, X. L. Tan, B. Brekke, A. C. Mathisen, Ø. Finnseth, R. J. Schenk, K. Hagiwara, M.-J. Huang, J. Buck, M. Kalläne, M. Hoesch, K. Rossnagel, K.-H. Ou Yang, M.-T. Lin, G.-J. Shu, Y.-J. Chen, C. Tusche, and H. Bentmann, Chirality-driven orbital angular momentum and circular dichroism in CoSi, Phys. Rev. Lett. 132, 196402 (2024).
- M. Kang, S. Kim, Y. Qian, P. M. Neves, L. Ye, J. Jung, D. Puntel, F. Mazzola, S. Fang, C. Jozwiak, A. Bostwick, E. Rotenberg, J. Fuji, I. Vobornik, J.-H. Park, J. G. Checkelsky, B.-J. Yang, and R. Comin, Measurements of the quantum geometric tensor in solids, Nat. Phys. 21, 110 (2025).
- Y.-G. Choi, D. Jo, K.-H. Ko, D. Go, K.-H. Kim, H. G. Park, C. Kim, B.-C. Min, G.-M. Choi, and H.-W. Lee, Observation of the orbital Hall effect in a light metal Ti, Nature (London) 619, 52 (2023).
- D. Go, D. Jo, C. Kim, and H.-W. Lee, Intrinsic spin and orbital Hall effects from orbital texture, Phys. Rev. Lett. 121, 086602 (2018).
- T. G. Rappoport, First light on orbitronics as a viable alternative to electronics, Nature (London) 619, 38 (2023).
- N. Gedik and I. Vishik, Photoemission of quantum materials, Nat. Phys. 13, 1029 (2017).
- B. Lv, T. Qian, and H. Ding, Angle-resolved photoemission spectroscopy and its application to topological materials, Nat. Rev. Phys. 1, 609 (2019).
- J. A. Sobota, Y. He, and Z.-X. Shen, Angle-resolved photoemission studies of quantum materials, Rev. Mod. Phys. 93, 025006 (2021).
- Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Observation of a large-gap topological-insulator class with a single Dirac cone on the surface, Nat. Phys. 5, 398 (2009).
- Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, Experimental realization of a three-dimensional topological insulator, , Science 325, 178 (2009).
- J. A. Sobota, S. L. Yang, A. F. Kemper, J. J. Lee, F. T. Schmitt, W. Li, R. G. Moore, J. G. Analytis, I. R. Fisher, P. S. Kirchmann, T. P. Devereaux, and Z.-X. Shen, Direct optical coupling to an unoccupied Dirac surface state in the topological insulator , Phys. Rev. Lett. 111, 136802 (2013).
- S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia et al., Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349, 613 (2015).
- L. X. Yang, Z. K. Liu, Y. Sun, H. Peng, H. F. Yang, T. Zhang, B. Zhou, Y. Zhang, Y. F. Guo, M. Rahn, D. Prabhakaran, Z. Hussain, S.-K. Mo, C. Felser, B. Yan, and Y. L. Chen, Weyl semimetal phase in the non-centrosymmetric compound TaAs, Nat. Phys. 11, 728 (2015).
- D. F. Liu, A. J. Liang, E. K. Liu, Q. N. Xu, Y. W. Li, C. Chen, D. Pei, W. J. Shi, S. K. Mo, P. Dudin, T. Kim, C. Cacho, G. Li, Y. Sun, L. X. Yang, Z. K. Liu, S. S. P. Parkin, C. Felser, and Y. L. Chen, Magnetic Weyl semimetal phase in a Kagomé crystal, Science 365, 1282 (2019).
- A. Rossi, V. Ivanov, S. Sreedhar, A. L. Gross, Z. Shen, E. Rotenberg, A. Bostwick, C. Jozwiak, V. Taufour, S. Y. Savrasov, and I. M. Vishik, Electronic structure and topology across in magnetic Weyl semimetal , Phys. Rev. B 104, 155115 (2021).
- M. Schüler, T. Pincelli, S. Dong, T. P. Devereaux, M. Wolf, L. Rettig, R. Ernstorfer, and S. Beaulieu, Polarization-modulated angle-resolved photoemission spectroscopy: Toward circular dichroism without circular photons and Bloch wave-function reconstruction, Phys. Rev. X 12, 011019 (2022).
- F. de Juan, A. Grushin, T. Morimoto, and J. Moore, Quantized circular photogalvanic effect in Weyl semimetals, Nat. Commun. 8, 15995 (2016).
- M. Schüler, U. De Giovannini, H. Hübener, A. Rubio, M. A. Sentef, and P. Werner, Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy from two-dimensional materials, Sci. Adv. 6, eaay2730 (2020).
- O. Pozo, C. Repellin, and A. G. Grushin, Quantization in chiral higher order topological insulators: Circular dichroism and local chern marker, Phys. Rev. Lett. 123, 247401 (2019).
- T. Figgemeier, M. Ünzelmann, P. Eck, J. Schusser, L. Crippa, J. N. Neu, B. Geldiyev, P. Kagerer, J. Buck, M. Kalläne, M. Hoesch, K. Rossnagel, T. Siegrist, L.-K. Lim, R. Moessner, G. Sangiovanni, D. Di Sante, F. Reinert, and H. Bentmann, Imaging orbital vortex lines in three-dimensional momentum space, Phys. Rev. X 15, 011032 (2025).
- O. Fedchenko, K. Medjanik, S. Chernov, D. Kutnyakhov, M. Ellguth, A. Oelsner, B. Schönhense, T. R. F. Peixoto, P. Lutz, C.-H. Min, F. Reinert, S. Däster, Y. Acremann, J. Viefhaus, W. Wurth, J. Braun, J. Minár, H. Ebert, H. J. Elmers, and G. Schönhense, 4D texture of circular dichroism in soft-x-ray photoemission from tungsten, New J. Phys. 21, 013017 (2019).
- S. R. Park, C. H. Kim, J. Yu, J. H. Han, and C. Kim, Orbital-angular-momentum based origin of Rashba-type surface band splitting, Phys. Rev. Lett. 107, 156803 (2011).
- S. Cho, J.-H. Park, S. Huh, J. Hong, W. Kyung, B.-G. Park, J. D. Denlinger, J. H. Shim, C. Kim, and S. R. Park, Studying local Berry curvature in by circular dichroism photoemission utilizing crystal mirror plane, Sci. Rep. 11, 1684 (2021).
- Y. H. Wang, D. Hsieh, D. Pilon, L. Fu, D. R. Gardner, Y. S. Lee, and N. Gedik, Observation of a warped helical spin texture in photoemission spectroscopy, Phys. Rev. Lett. 107, 207602 (2011).
- E. Razzoli, T. Jaouen, M.-L. Mottas, B. Hildebrand, G. Monney, A. Pisoni, S. Muff, M. Fanciulli, N. C. Plumb, V. A. Rogalev, V. N. Strocov, J. Mesot, M. Shi, J. H. Dil, H. Beck, and P. Aebi, Selective probing of hidden spin-polarized states in inversion-symmetric bulk , Phys. Rev. Lett. 118, 086402 (2017).
- S. Beaulieu, J. Schusser, S. Dong, M. Schüler, T. Pincelli, M. Dendzik, J. Maklar, A. Neef, H. Ebert, K. Hricovini, M. Wolf, J. Braun, L. Rettig, J. Minár, and R. Ernstorfer, Revealing hidden orbital pseudospin texture with time-reversal dichroism in photoelectron angular distributions, Phys. Rev. Lett. 125, 216404 (2020).
- J. Schusser, H. Orio, M. Ünzelmann, J. Heßdörfer, M. P. T. Masilamani, F. Diekmann, K. Rossnagel, and F. Reinert, Towards robust dichroism in angle-resolved photoemission, Commun. Phys. 7, 270 (2024).
- X. Zhang, Q. Liu, J.-W. Luo, A. J. Freeman, and A. Zunger, Hidden spin polarization in inversion-symmetric bulk crystals, Nat. Phys. 10, 387 (2014).
- J. M. Riley, F. Mazzola, M. Dendzik, M. Michiardi, T. Takayama, L. Bawden, C. Graneroød, M. Leandersson, T. Balasubramanian, M. Hoesch, T. K. Kim, H. Takagi, W. Meevasana, P. Hofmann, M. S. Bahramy, J. W. Wells, and P. D. C. King, Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor, Nat. Phys. 10, 835 (2014).
- J. Tu, X. B. Chen, X. Z. Ruan, Y. F. Zhao, H. F. Xu, Z. D. Chen, X. Q. Zhang, X. W. Zhang, J. Wu, L. He, Y. Zhang, R. Zhang, and Y. B. Xu, Direct observation of hidden spin polarization in , Phys. Rev. B 101, 035102 (2020).
- S. Cho, J.-H. Park, J. Hong, J. Jung, B. S. Kim, G. Han, W. Kyung, Y. Kim, S.-K. Mo, J. D. Denlinger, J. H. Shim, J. H. Han, C. Kim, and S. R. Park, Experimental observation of hidden berry curvature in inversion-symmetric bulk , Phys. Rev. Lett. 121, 186401 (2018).
- S. R. Park, J. Han, C. Kim, Y. Y. Koh, C. Kim, H. Lee, H. J. Choi, J. H. Han, K. D. Lee, N. J. Hur, M. Arita, K. Shimada, H. Namatame, and M. Taniguchi, Chiral orbital-angular momentum in the surface states of , Phys. Rev. Lett. 108, 046805 (2012).
- F. Vidal, M. Eddrief, B. Rache Salles, I. Vobornik, E. Velez-Fort, G. Panaccione, and M. Marangolo, Photon energy dependence of circular dichroism in angle-resolved photoemission spectroscopy of Dirac states, Phys. Rev. B 88, 241410 (2013).
- M. P. Seah and W. A. Dench, Quantitative electron spectroscopy of surfaces: A standard data base for electron inelastic mean free paths in solids, Surf. Interface Anal. 1, 2 (1979).
- H. Ebert, D. Ködderitzsch, and J. Minár, Calculating condensed matter properties using the KKR-Green's function method–recent developments and applications, Rep. Prog. Phys. 74, 096501 (2011).
- S. Beaulieu, M. Schüler, J. Schusser, S. Dong, T. Pincelli, J. Maklar, A. Neef, F. Reinert, M. Wolf, L. Rettig, J. Minár, and R. Ernstorfer, Unveiling the orbital texture of 1T- using intrinsic linear dichroism in multidimensional photoemission spectroscopy, npj Quantum Mater. 6, 93 (2021).
- Y. Yen, G. Parusa, and M. Schüler, First-principle tight-binding approach to angle-resolved photoemission spectroscopy simulations: importance of light-matter gauge and ubiquitous interference effects, arXiv:2402.14496.
- S. Moser, A toy model for dichroism in angle resolved photoemission, J. Electron Spectrosc. Relat. Phenom. 262, 147278 (2023).
- R. P. Day, B. Zwartsenberg, I. S. Elfimov, and A. Damascelli, Computational framework chinook for angle-resolved photoemission spectroscopy, npj Quantum Mater. 4, 54 (2019).
- G. Zhang, H. Qin, J. Teng, J. Guo, Q. Guo, X. Dai, Z. Fang, and K. Wu, Quintuple-layer epitaxy of thin films of topological insulator , Appl. Phys. Lett. 95, 053114 (2009).
- J. R. Yates, X. Wang, D. Vanderbilt, and I. Souza, Spectral and Fermi surface properties from Wannier interpolation, Phys. Rev. B 75, 195121 (2007).
- T. Heider, G. Bihlmayer, J. Schusser, F. Reinert, J. Minár, S. Blügel, C. M. Schneider, and L. Plucinski, Geometry-induced spin filtering in photoemission maps from surface states, Phys. Rev. Lett. 130, 146401 (2023).
- D. Wawrzik, J. I. Facio, and J. van den Brink, Surface induced electronic Berry curvature in bulk Berry curvature free materials, Mater. Today Phys. 33, 101027 (2023).
- S. Moser, An experimentalist's guide to the matrix element in angle resolved photoemission, J. Electron Spectrosc. Relat. Phenom. 214, 29 (2017).
- M. R. Scholz, J. Sánchez-Barriga, J. Braun, D. Marchenko, A. Varykhalov, M. Lindroos, Y. J. Wang, H. Lin, A. Bansil, J. Minár, H. Ebert, A. Volykhov, L. V. Yashina, and O. Rader, Reversal of the circular dichroism in angle-resolved photoemission from , Phys. Rev. Lett. 110, 216801 (2013).
- J. Braun, J. Minár, and H. Ebert, Correlation, temperature and disorder: Recent developments in the one-step description of angle-resolved photoemission, Phys. Rep. 740, 1 (2018).
- J. Schusser, H. Bentmann, M. Ünzelmann, T. Figgemeier, C.-H. Min, S. Moser, J. N. Neu, T. Siegrist, and F. Reinert, Assessing nontrivial topology in Weyl semimetals by dichroic photoemission, Phys. Rev. Lett. 129, 246404 (2022).
- H. Boban, M. Qahosh, X. Hou, T. Sobol, E. Beyer, M. Szczepanik, D. Baranowski, S. Mearini, V. Feyer, Y. Mokrousov, K. Jin, T. Wichmann, J. Martinez-Castro, M. Ternes, F. Stefan Tautz, F. Lüpke, Claus M. Schneider, Jürgen Henk, and L. Plucinski, Scattering makes a difference in circular dichroic angle-resolved photoemission, arXiv:2410.19652.
- J. Erhardt, C. Schmitt, P. Eck, M. Schmitt, P. Keßler, K. Lee, T. Kim, C. Cacho, I. Cojocariu, D. Baranowski, V. Feyer, L. Veyrat, G. Sangiovanni, R. Claessen, and S. Moser, Bias-free access to orbital angular momentum in two-dimensional quantum materials, Phys. Rev. Lett. 132, 196401 (2024).
- Z. Tao, C. Chen, T. Szilvási, M. Keller, M. Mavrikakis, H. Kapteyn, and M. Murnane, Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids, Science 353, 62 (2016).
- S. Heinrich, T. Saule, M. Högner, Y. Cui, V. S. Yakovlev, I. Pupeza, and U. Kleineberg, Attosecond intra-valence band dynamics and resonant-photoemission delays in W(110), Nat. Commun. 12, 3404 (2021).
- R. Borrego-Varillas, M. Lucchini, and M. Nisoli, Attosecond spectroscopy for the investigation of ultrafast dynamics in atomic, molecular and solid-state physics, Rep. Prog. Phys. 85, 066401 (2022).
- P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos et al., QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. I. Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto et al., Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
- J. W. Cooper, Photoionization from outer atomic subshells. A model study, Phys. Rev. 128, 681 (1962).
- A. Damascelli, Probing the electronic structure of complex systems by ARPES, Phys. Scr. 2004, 61 (2004).
- R. P. Day, I. S. Elfimov, and A. Damascelli, Looking beyond the surface with angle-resolved photoemission spectroscopy, Phys. Rev. B 108, 045106 (2023).
- J. Minár, J. Braun, S. Mankovsky, and H. Ebert, Calculation of angle-resolved photo emission spectra within the one-step model of photo emission–recent developments, J. Electron Spectrosc. Relat. Phenom. 184, 91 (2011).