48 49 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 0 / 2 1 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 0 / 2 1 Structures and Surfaces Group Beamline I05 Visualising the handedness and topological charge of electrons in chiral crystals Related publication: Schröter N. B. M., Stolz S., Manna K., De Juan F.,VergnioryM. G., Krieger J. A., Pei D., SchmittT., Dudin P., KimT. K., Cacho C., Bradlyn B., Borrmann H., Schmidt M.,Widmer R., StrocovV. N. & Felser C. Observation and control of maximal Chern numbers in a chiral topological semimetal. Science (80-. ). 369 , 179–183 (2020). DOI: 10.1126/science.aaz3480 Publication keywords: Topology; Chern number; ARPES; Chirality; Fermi-arcs; Surface-state; Handedness; New fermions; Rarita-Schwinger;Weyl- fermion C hirality refers to objects that - like our hands - do not coincide with their mirror image. Chirality can also manifest itself in crystals, for instance, where atoms wind around each other to forma helix. Recent research showed that chiral crystals can host‘exotic’topological phenomena in their electronic structure. However, we do not yet knowhow large they could become in real materials andwhether the chirality of the crystal structure is related to the electrons surrounding the atoms. An international teamof researchers investigated two crystals of the chiral crystal palladiumgallium (PdGa). Theyweremirror copies of each other, meaning that in one crystal the gallium atoms formed a right-handed helix and in the other a left-handed one. The team performed high-resolution spectroscopic measurements to resolve the fine details of the electronic structure in the crystals using Diamond Light Source’s Angle-Resolved Photoemission Spectroscopy (ARPES) beamline, I05. They observed that the chirality of the atomic structure imprints a handedness to the wavefunction of the electrons. Due to the very high- resolution and quality of the data, they resolved an energy splitting in the surface electronic structure. This splitting indicates that the topological charges in these materials can reach the maximum value allowed in any metallic crystal. That this is possible in a real material has never been shown before. These materials may lend themselves to useful applications, such as efficient photodetectors in the infrared- and terahertz-spectrum. Topological semimetals have attracted much attention over the past five years because their electronic band structure can host quasiparticles that mimic the behaviour of elementary particles predicted in high-energy physics that have so far remained elusive as free particles, such as Weyl-fermions in topological Weyl-semimetals. These materials are called topological because the two-band crossing in their electronic band structure that forms the Weyl- fermion is protected by a topological invariant known as the “Chern-number” (C), which is closely related to the quantised Hall conductance that is observed in the quantum Hall effect, and which is also called the topological charge of theWeyl-fermion.Weyl-fermions have a Chern number with magnitude |C|=1 and can occur in non-centrosymmetric or magnetic crystals. Recently it has been predicted that chiral crystals, which possess neither mirror- nor inversion-symmetries, could host new fermionic quasiparticles that can be considered as a generalisation of Weyl-fermions and have no equivalent as elementary particles 1 . It is expected that these quasiparticles could realise the largest possible topological charge in any metallic crystal with a maximal magnitude of 4. Finding materials with such a large Chern number is important because many of the exotic phenomena predicted for topological semimetals are directly proportional to |C|, such as the number of Fermi-arc surface states, the number of chiral Landau levels at large magnetic fields, or the strength of quantised photocurrents. Moreover, since the sign of the topological charge embodies the electronic wave function with a handedness, it would be interesting to see how the structural chirality of the atoms is linked to the chirality of the electronic structure. Although there have been many recent photoemission studies that detected the presence of new fermionic excitations in chiral crystals 2,3,4 , the magnitude of their topological charge, as well as the connection between the atomic and electronic chirality of these materials has not been investigated in detail until now. Previous efforts have been hindered by two factors: on the one hand, preparing clean and flat surfaces of the studied crystals has been difficult, which meant that spectroscopic signatures were washed out. On the other hand, at least some of the previously studied materials contained light atoms with weak spin-orbit coupling, which made it difficult to resolve small energy splitting of interest. In the present work, both of these limitations were overcome by working with crystals of palladium gallium (PdGa), an intermetallic catalyst with strong spin-orbit coupling for which established methods exist to produce clean and flat surfaces in ultra-high vacuum. Moreover, by using a chiral seed crystal during crystal growth, it is possible to grow two mirror copies (called enantiomers) of the same crystal structure; in one of them, the gallium atoms form a left-handed helix along the (111) direction, in the other one this helix is right-handed (Fig. 1a). Low-energy electron diffraction (LEED) patterns from clean surfaces of both crystals revealed the structural chirality of the surface atoms through the observation of a characteristic S-shaped intensity modulation of the diffraction pattern that is mirrored between the two enantiomers (Fig. 1b). By performing high-resolution Angle-Resolved Photoelectron Spectroscopy (ARPES) at beamline I05, the surface electronic structure of the PdGa crystals was studied. These measurements revealed the presence of long Fermi-arc surface states that are connecting the and high symmetry points across the full diagonal of the surface Brillouin zone (Fig. 2a). Complimentary soft X-ray ARPES measurements at the Swiss Light Source of the Paul Scherrer Institute confirmed that new fermionic Rarita-Schwinger and Weyl-1 excitations are located at the corresponding Γ and R points of the bulk Brillouin zone, which are referred to as multifold fermions. Interestingly, the propagation direction of the Fermi-arcs is reversed between the two enantiomers (Fig. 2b), which implies that the handedness of the electronic structure (represented by the sign of the Chern numbers) is directly linked to the chirality of the host structure. Structural chirality can therefore be considered as a control parameter to manipulate the topological properties of these crystals, such as the direction of topological photocurrents. Moreover, by making use of the high instrumental resolution of the ARPES endstation I05 at Diamond, a spin-orbit induced splitting of the Fermi-arcs was revealed (Fig. 3), which means that a total of four Fermi-arcs connecting the multifold fermions were observed. This finding implies that the topological charge of the multifold fermions realises the largest magnitude that can exist in any metallic material in nature. This is the first time that such a maximal Chern number has been observed experimentally, but it can be expected that similar topological properties are shared by many other chiral crystals. The hunt for more exotic topological phenomena in chiral compounds, such as the quantised circular photogalvanic effect 5 , has therefore only just begun. References: 1. Bradlyn B. et al. Beyond Dirac andWeyl fermions: Unconventional quasiparticles in conventional crystals. Science (80-. ). 353 , aaf5037 (2016). DOI: 10.1126/science.aaf5037 2. Rao Z. et al. Observation of unconventional chiral fermions with long Fermi arcs in CoSi. Nature 567 , 496–499 (2019). DOI: 10.1038/s41586- 019-1031-8 3. Takane D. et al. Observation of Chiral Fermions with a Large Topological Charge and Associated Fermi-Arc Surface States in CoSi. Phys. Rev. Lett. 122 , 76402 (2019). DOI: 10.1103/PhysRevLett.122.076402 4. Schröter N. B. M. et al. Chiral topological semimetal with multifold band crossings and long Fermi arcs. Nat. Phys. 15 , 759–765 (2019). DOI: 10.1038/s41567-019-0511-y 5. De Juan F. et al. Quantized circular photogalvanic effect inWeyl semimetals. Nat. Commun. 8 , 15995 (2017). DOI: 10.1038/ncomms15995 Funding acknowledgement: N.B.M.S. was supported by Microsoft. K.M. and C.F. acknowledge nancial support from the European Research Council (ERC) Advanced Grant nos. 291472 “Idea Heusler”and 742068“TOP-MAT”, and Deutsche Forschungsgemeinschaft (project ID 258499086 and FE 633/30-1). M.G.V. acknowledges support from DFG INCIEN2019-000356 from Gipuzkoako Foru Aldundia. S.S. and R.W. acknowledge funding from the Swiss National Science Foundation under SNSF project number 159690. D.P. acknowledges support from the Chinese Scholarship Council. J.A.K. acknowledges support from the Swiss National Science Foundation (SNF-grant no. 200021_165910). Corresponding author: Dr Niels B. M. Schröter, Swiss Light Source, Paul Scherrer Institute and Max Planck Institute for Microstructure Physics,
[email protected] Figure 1: (a) Illustration of the crystal structure of the two enantiomers of PdGa. In enantiomer A, the Ga atoms (red spheres) form a left-handed helix along the (111) direction of the cubic unit cell, whilst the Pd atoms (blue sphere) form a right-handed helix. The direction of the helices is reversed in enantiomer B, for which the crystal structure forms a mirror copy of the structure in A; (b) Low-energy electron diffraction patterns for both enantiomers. The red dashed lines indicate the S-shaped intensity modulation, which is mirrored for the two enantiomers. Figure 2: (a) Fermi surface of the two enantiomers of PdGa measured at beamline I05. The red arrows indicate the Fermi-arc surface states that are connecting the bulk pockets at the and points; (b) Band dispersions along a line cut at k x =0.39 A -1 . Red arrows indicate Fermi-arcs that have a reversed propagation direction for the two enantiomers. Figure 3: (a) Zoom-in of the Fermi-surface of enantiomer A. Red arrows indicate a splitting of the Fermi-arcs. Red dashed arrow indicates the direction of the line-cut shown in (b); (b) Band dispersion along the direction shown in (a). Blue dashed lines show the direction of the momentum distribution curve (MDC) and the energy distribution curve (EDC), shown in the inset on top and on the right, respectively. The red arrows indicate the position of the two bands, and the magnitude of the band splitting.