Momentum-space signatures of Berry flux monopoles in the Weyl semimetal TaAs

ARTICLE https://doi.org/10.1038/s41467-021-23727-3 OPEN Momentum-space signatures of Berry flux monopoles in the Weyl semimetal TaAs 1234567890():,; M. Ünzelmann1,10, H. Bentmann 1,10 ✉, T. Figgemeier1,10, P. Eck2,10, J. N. Neu3,4, B. Geldiyev1, F. Diekmann5,6, S. Rohlf5,6, J. Buck5,6, M. Hoesch 7, M. Kalläne5,6, K. Rossnagel 5,6,7, R. Thomale2, T. Siegrist3,4, G. Sangiovanni 2, D. Di Sante 2,8,9 & F. Reinert1 Since the early days of Dirac flux quantization, magnetic monopoles have been sought after as a potential corollary of quantized electric charge. As opposed to magnetic monopoles embedded into the theory of electromagnetism, Weyl semimetals (WSM) exhibit Berry flux monopoles in reciprocal parameter space. As a function of crystal momentum, such monopoles locate at the crossing point of spin-polarized bands forming the Weyl cone. Here, we report momentum-resolved spectroscopic signatures of Berry flux monopoles in TaAs as a paradigmatic WSM. We carried out angle-resolved photoelectron spectroscopy at bulksensitive soft X-ray energies (SX-ARPES) combined with photoelectron spin detection and circular dichroism. The experiments reveal large spin- and orbital-angular-momentum (SAM and OAM) polarizations of the Weyl-fermion states, resulting from the broken crystalline inversion symmetry in TaAs. Supported by first-principles calculations, our measurements image signatures of a topologically non-trivial winding of the OAM at the Weyl nodes and unveil a chirality-dependent SAM of the Weyl bands. Our results provide directly bulksensitive spectroscopic support for the non-trivial band topology in the WSM TaAs, promising to have profound implications for the study of quantum-geometric effects in solids. 1 Experimentelle Physik VII and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, Würzburg, Germany. 2 Theoretische Physik I, Universität Würzburg, Würzburg, Germany. 3 Department of Chemical and Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, FL, USA. 4 National High Magnetic Field Laboratory, Tallahassee, FL, USA. 5 Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, Kiel, Germany. 6 Ruprecht Haensel Laboratory, Kiel University and DESY, Kiel, Germany. 7 Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany. 8 Department of Physics and Astronomy, University of Bologna, Bologna, Italy. 9 Center for Computational Quantum Physics, Flatiron Institute, New York, NY, USA. 10These authors contributed equally: M. Ünzelmann, H. Bentmann, T. Figgemeier, P. Eck. ✉email: NATURE COMMUNICATIONS | (2021)12:3650 | https://doi.org/10.1038/s41467-021-23727-3 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-23727-3 T opological semimetals have become a fruitful platform for the discovery of quasiparticles that behave as massless relativistic fermions predicted in high-energy particle physics1–6. A prominent example are Weyl fermions, which are realized at topologically protected crossing points between spin-polarized electronic bands in the bulk band structure of noncentrosymmetric or ferromagnetic semimetals1,2,7–11. Near a Weyl node the momentum-resolved two-band Hamiltonian takes the form H ∝ ±σ ⋅ k, giving rise to the linear energy–momentum dispersion relation of a massless quasiparticle4. The topological structure of the Weyl node, however, is not encoded in the energy spectrum, but rather manifests in the momentum-dependence of the eigenstates, i.e., the electronic wave functions. The pseudospin σ and the Berry curvature Ω wind around the Weyl node, forming a Berry flux monopole in three-dimensional (3D) momentum space12,13. The nontrivial winding of σ stabilizes the Weyl node by a topological invariant, a nonzero Chern number of C = ±1 (ref. 4). Until today, angle-resolved photoelectron spectroscopy (ARPES) experiments have confirmed a number of materials as Weyl semimetals (WSM), based on a comparison of the measured bulk band structure to band calculations and the observation of surface Fermi arcs1,9,10,14,15. Manifestations of the nontrivial topology have also been found, accordingly, in magnetotransport experiments16, by scanning tunneling microscopy17, and via optically induced photocurrents18. The winding of the electronic wave functions in momentum space, however, which characterizes the immediate effect of a Berry flux monopole and thus the topology of the WSM, has so far remained elusive. While the pseudospin σ for a Dirac-Hamiltonian universally shows nontrivial winding, the underlying microscopic degrees of freedom may vary from one system to another19. In two dimensions, examples include the sublattice degree of freedom for graphene and the spin-angular momentum (SAM) for the surface states in topological insulators (TI). Accordingly, the nontrivial Berry-phase properties have been addressed by quasiparticle interference STM imaging and dichroic ARPES in graphene20,21 and by spin-resolved ARPES in TI22. Likewise in 3D WSM, one may expect the relevant degrees of freedom to depend on the considered material system. While previous theories have suggested orbital-sensitive dichroic effects in momentum-resolved spectroscopies, as a probe of topological characteristics in topological semimetals23–25, such approaches have previously not reached application to experimental data. In the present work, we find that the orbital-angular momentum (OAM) L plays a crucial role in the Weyl physics of the paradigmatic WSM TaAs and, like the pseudospin σ, displays a topologically nontrivial winding at the Weyl points. Our experiments are based on soft X-ray (SX) ARPES, which allows for the systematic measurement of bulk band dispersions by virtue of an increased probing depth and excitation into photoelectron final states, with well-defined momentum along kz perpendicular to the surface26, when compared to surface-sensitive ARPES experiments at VUV photon energies. SXARPES has been the key method to probe chiral-fermion dispersions in topological semimetals1,2,5,27–29, but its combination with spin resolution (SR) and circular dichroism (CD) is challenging and not widely explored30. On the other hand, at lower excitation energies SR is routinely used to detect the SAM of electronic states22 and CD has been introduced as a way to address the OAM31–35. We performed SX-ARPES measurements combined with SR and CD to probe the SAM and OAM in the bulk electronic structure of TaAs. Results Bulk band structure of TaAs. TaAs crystallizes in the noncentrosymmetric space group I41md, as shown in Fig. 1a. According to the results of first-principles calculations, its bulk 2 band structure features 12 pairs of Weyl points in the Brillouin zone, which divide into two inequivalent sets, W1 and W2 (refs. 7,8). Here, we focus on the W2 points which are located in kx–ky planes at kz ¼ ± 0:59 2πc , with the length c along z denoting the conventional unit cell. In a (...truncated)