Abstract
The classification scheme of electronic phases uses two prominent paradigms: correlations and topology. Electron correlations give rise to superconductivity and charge density waves, while the quantum geometric Berry phase gives rise to electronic topology. The intersection of these two paradigms has initiated an effort to discover electronic instabilities at or near the Fermi level of topological materials. Here we identify the electronic topology of chiral fermions as the driving mechanism for creating van Hove singularities that host electronic instabilities in the surface band structure. We observe that the chiral fermion conductors RhSi and CoSi possess two types of helicoid arc van Hove singularities that we call type I and type II. In RhSi, the type I variety drives a switching of the connectivity of the helicoid arcs at different energies. In CoSi, we measure a type II intra-helicoid arc van Hove singularity near the Fermi level. Chemical engineering methods are able to tune the energy of these singularities. Finally, electronic susceptibility calculations allow us to visualize the dominant Fermi surface nesting vectors of the helicoid arc singularities, consistent with recent observations of surface charge density wave ordering in CoSi. This suggests a connection between helicoid arc singularities and surface charge density waves.
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References
Rajagopal, K. et al. At the Frontier of Particle Physics (ed. Shifman, M.) vol. 3, 2061–2151 (World Scientific, 2001).
v. Löhneysen, H. et al. Fermi-liquid instabilities at magnetic quantum phase transitions. Rev. Mod. Phys. 79, 1015–1075 (2007).
Jérome, D., Rice, T. M. & Kohn, W. Excitonic insulator. Phys. Rev. 158, 462–475 (1967).
Lee, P., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).
Piriou, A. et al. First direct observation of the van Hove singularity in the tunneling spectra of cuprates. Nat. Commun. 2, 221 (2011).
Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010).
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Qi, X. L. & Zhang, S. C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
Zyuzin, A. A. et al. Weyl semimetal with broken time reversal and inversion symmetries. Phys. Rev. B 85, 165110 (2012).
Vafek, O. & Vishwanath, A. Dirac fermions in solids: from high-Tc cuprates and graphene to topological insulators and Weyl semimetals. Annu. Rev. Cond. Matter Phys. 5, 83–112 (2014).
Hasan, M. Z. et al. Topological insulators, topological superconductors and Weyl semimetals. Phys. Scr. T164, 014001 (2015).
Burkov, A. A. Topological semimetals. Nat. Mater. 15, 1145–1148 (2016).
Keimer, B. & Moore, J. E. The physics of quantum materials. Nat. Phys. 13, 1045–1055 (2017).
de Juan, F. et al. Quantized circular photogalvanic effect in Weyl semimetals. Nat. Commun. 8, 15995 (2017).
Hasan, M. Z. et al. Weyl, Dirac and high-fold chiral fermions in topological quantum matter. Nat. Rev. Mater. 6, 784–803 (2021).
Stormer, H. L. Nobel lecture: the fractional quantum Hall effect. Rev. Mod. Phys. 71, 875–889 (1999).
Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020).
Iqbal Bakti Utama, M. et al. Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist. Nat. Phys. 17, 184–185 (2021).
Lisi, S. et al. Observation of flat bands in twisted bilayer graphene. Nat. Phys. 17, 189–193 (2021).
Li, G. et al. Observation of van Hove singularities in twisted graphene layers. Nat. Phys. 6, 109–113 (2010).
Jones, A. J. H. et al. Observation of electrically tunable van Hove singularities in twisted bilayer graphene from nanoARPES. Adv. Mater. 32, 2001656 (2020).
Yuan, N. F. Q., Isobe, H. & Fu, L. Magic of high-order van Hove singularity. Nat. Commun. 10, 5769 (2019).
Jia, Y. et al. Evidence for a monolayer excitonic insulator. Nat. Phys. 18, 87–93 (2022).
Ortiz, B. R. et al. Superconductivity in the Z2 kagome metal KV3Sb5. Phys. Rev. Mater. 5, 034801 (2021).
Jiang, K. et al. Unconventional chiral charge order in kagome superconductor KV3Sb5. Nat. Mater. 20, 1353–1357 (2021).
Jiang, K. et al. Kagome superconductors AV3Sb5 (A = K, Rb, Cs). Natl. Sci. Rev., nwac199 (2022).
Yao, H. & Yang, F. Topological odd-parity superconductivity at type-II two-dimensional van Hove singularities. Phys. Rev. B 92, 035132 (2015).
Qin, W., Li, L. & Zhang, Z. Chiral topological superconductivity arising from the interplay of geometric phase and electron correlation. Nat. Phys. 15, 796–802 (2019).
Chang, G. et al. Topological quantum properties of chiral crystals. Nat. Mater. 17, 978–985 (2018).
Weng, H. et al. Weyl semimetal phase in non-centrosymmetric transition metal monophosphides. Phys. Rev. X 5, 011029 (2015).
Huang, S.-M. et al. A Weyl fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat. Commun. 6, 7373 (2015).
Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).
Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).
Belopolski, I. et al. Criteria for directly detecting topological Fermi arcs in Weyl semimetals. Phys. Rev. Lett. 116, 066802 (2016).
Chang, G. et al. Unconventional chiral fermions and large topological Fermi arcs in RhSi. Phys. Rev. Lett. 119, 206401 (2017).
Tang, P. et al. Multiple types of topological termions in transition metal silicides. Phys. Rev. Lett. 119, 206402 (2017).
Sanchez, D. S. et al. Topological chiral crystals with helicoid arc quantum states. Nature 567, 500–505 (2019).
Rao, Z. et al. Observation of unconventional chiral fermions with long Fermi arcs in CoSi. Nature 567, 496–499 (2019).
Cochran, T. A. et al. A Fermi arc quantum ladder. Preprint at https://arxiv.org/abs/2004.11365 (2020).
Xu, X. et al. Crystal growth and quantum oscillations in the topological chiral semimetal CoSi. Phys. Rev. B 100, 045104 (2019).
Fang, C. et al. Topological semimetals with helicoid surface states. Nat. Phys. 12, 936–941 (2016).
Chang, G. et al. Unconventional photocurrents from surface Fermi arcs in topological chiral semimetals. Phys. Rev. Lett. 124, 166404 (2020).
Pshenay-Severin, D. A. & Burkov, A. T. Electronic structure of B20 (FeSi-type) transition-metal monosilicides. Materials 12, 2710 (2019).
Strocov, V. N. et al. Soft-X-ray ARPES facility at the ADRESS beamline of the SLS: concepts, technical realisation and scientific applications. J. Synchrotron Radiat. 21, 32–44 (2014).
Sanchez, D. S. et al. Helicoid arc van Hove singularities in topological chiral crystals. Preprint at https://arxiv.org/abs/2108.13957 (2021).
Li, G. et al. Chirality locking charge density waves in a chiral crystal. Nat. Commun. 13, 2914 (2022).
Rao, Z. et al. Charge instability of topological Fermi arcs in chiral crystal CoSi. Preprint at https://arxiv.org/abs/2110.07815 (2021).
Gooth, J. et al. Axionic charge-density wave in the Weyl semimetal (TaSe4)2I. Nature 575, 315–319 (2010).
Sehayek, D., Thakurathi, M. & Burkov, A. A. Charge density waves in Weyl semimetals. Phys. Rev. B 102, 115159 (2020).
Chiu, W.-C. et al. Relativistic horizon of interacting Weyl fermions in condensed matter systems. Preprint at https://arxiv.org/abs/2201.04757 (2022).
Faraei, Z. & Jafari, S. A. Induced superconductivity in Fermi arcs. Phys. Rev. B 100, 035447 (2019).
Ozaki, T. et al. OpenMX package. http://www.openmx-square.org/.
Kresse, G. & Furthmueller, G. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).
Perdew, J. P. et al. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
Demchenko, P. et al. Single crystal investigation of the new phase Er0.85Co4.31Si and of CoSi. Chem. Met. Alloys 1, 50–53 (2008).
Zhang, P. et al. A precise method for visualizing dispersive features in image plots. Rev. Sci. Instrum. 82, 043712 (2011).
Kasinathan, D. et al. Superconductivity and lattice instability in compressed lithium from Fermi surface hot spots. Phys. Rev. Lett. 96, 047004 (2006).
Kyung, W. S. et al. Enhanced superconductivity in surface-electron-doped iron pnictide Ba(Fe1.94Co0.06)2As2. Nat. Mater. 15, 1233–1236 (2016).
Kurzhals, P. et al. Electron-momentum dependence of electron-phonon coupling underlies dramatic phonon renormalization in YNi2B2C. Nat. Commun. 13, 228 (2022).
Acknowledgements
Work at Princeton University and Princeton-led synchrotron based ARPES measurements were supported by the U.S. Department of Energy (DOE) under the Basic Energy Sciences programme (grant no. DOE/BES DE-FG-02-05ER46200). This research used resources of the Advanced Light Source, which is a DOE Office of Science User Facility under contract No. DE-AC02-05CH11231. We acknowledge the Paul Scherrer Institut, Villigen, Switzerland for provision of synchrotron radiation beam time at the ADRESS beam line of the Swiss Light Source. G.C. acknowledges support from the National Research Foundation, Singapore under NRF fellowship award no. NRF-NRFF13-2021-0010 and a Nanyang Assistant Professorship grant from Nanyang Technological University. K.M. acknowledges the Department of Atomic Energy (DAE), Government of India for funding support via a young scientist’s research award (YSRA) with grant no. 58/20/03/2021-BRNS/37084. T.A.C. was supported by the National Science Foundation Graduate Research Fellowship Program under grant no. DGE-1656466.
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D.S.S., G.C. and M.Z.H. conceived the project. D.S.S. and T.A.C. conducted the ALS ARPES experiments with close assistance from I.B., Z.C., X.P.Y. and J.D.D. and in consultation with M.Z.H. ALS beamline support was provided by J.D.D. T.A.C. and I.B. conducted the SLS ARPES experiments with close assistance from Z.C. and X.P.Y. and in consultation with D.S.S. and M.Z.H. SLS beamline support was provided by A.C. and V.N.S. Y.L., X.X. and S.J. synthesized and characterized the CoSi samples. W.X. further characterized the CoSi samples. K.M., C.S., H.B. and C.F. synthesized and characterized the RhSi samples. G.C. worked on the theoretical predictions and performed the first-principles/density functional theory calculations. T.H. simulated the electronic susceptibility. D.S.S., T.A.C. and G.C. performed the analysis, interpretation and figure development in consultation with J.-X.Y., X.P.Y., Z.C. and M.Z.H. D.S.S. and T.A.C. wrote the manuscript in consultation with G.C. and M.Z.H. All authors contributed to revising and editing the manuscript. M.Z.H. supervised the project.
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Extended data
Extended Data Fig. 1 Helicoid arc dispersion along closed contours in RhSi.
a, Surface-sensitive ARPES measured Fermi surface map of RhSi. Encircling the \(\bar{{{\Gamma }}}\)- and \(\bar{{{{\rm{M}}}}}\)-pockets are dashed-line loops of different radii. b, Energy-momentum cuts along the inner (left panel; orange dashed- line) and outer (right panel; black dashed-line) circular loops resolve a net number of two left-moving chiral modes, corresponding to a projected chiral charge C = − 2 at the \(\bar{{{{\rm{M}}}}}\)-pockets. The inner and outer loops have radius 0.18 Å−1 and 0.23 Å−1, respectively. c, d Energy-momentum cuts along the inner and outer (panel d) circular loops resolve a net number of two right-moving chiral modes, corresponding to a projected chiral charge C = + 2 at the \(\bar{{{\Gamma }}}\)-pocket. The inner and outer loops have radius 0.3 Å−1 and 0.4 Å−1, respectively. Guides for the eye (green dashed lines) track the chiral modes.
Extended Data Fig. 2 Variation of Ni-doping concentration in RhSi.
a, Surface-sensitive ARPES measured Fermi surface map (E = 0 eV) of 9% Ni-doped RhSi. b, Constant energy contour at energy E = − 0.22 eV for 9% Ni-doped RhSi. Guides for the eye (black dashed lines) track the helicoid arcs. c, Bulk-sensitive ARPES measured energy-momentum cut along the \(\bar{{{\Gamma }}}\)-pocket of RhSi (left panel) and 5% Ni-doped RhSi (right panel). d, Fermi surface map of 5% Ni-doped RhSi. e, f, Energy-momentum cuts along \(\bar{{{{\rm{Y}}}}}\) for two orthogonal directions: \(\bar{{{{\rm{Y}}}}}-\bar{{{{\rm{M}}}}}\) (green dashed line: panel e) and \(\bar{{{{\rm{Y}}}}}-\bar{{{\Gamma }}}\) (purple dashed line: panel f). The (001) surface BZ is annotated by black dashed lines. g, ARPES measured constant-energy contours of Ni0.05Rh0.95Si. The helicoid arcs near the \(\bar{{{{\rm{M}}}}}-\bar{{{{\rm{Y}}}}}-\bar{{{{\rm{M}}}}}\) line approach each other with increasing energy and are on track to touch at the \(\bar{{{{\rm{Y}}}}}\)-point, indicated by the orange dashed parabola. A parabolic function fitted to the chiral modes near the Fermi level provides a guide for the eye to visualize the saddle-shape dispersion bottom band (orange dashed line). The fit suggests that the type-I helicoid arc van Hove energy is about + 0.073 eV above the Fermi level of Ni0.05Rh0.95Si.
Extended Data Fig. 3 Analysis of the helicoid arc van Hove singularity in RhSi.
a, ARPES measured constant energy contours of 9% Ni-doped RhSi using linear vertical s-polarized synchrotron radiation at energies E = (0, − 60, − 130, − 200) meV. Guides for the eye track the surface helicoid arcs at different energies. The helicoid arc van Hove singularity in Ni0.09Rh0.91Si is located at E − EF = − 60 meV. b, Energy-momentum cut along the \(\bar{{{{\rm{M}}}}}-\bar{{{{\rm{Y}}}}}\) direction shows a hole-like dispersion. c, Energy-momentum cut along \(\bar{{{\Gamma }}}-\bar{{{{\rm{Y}}}}}\) shows an electron-like dispersion. d, Momentum distribution curve at the Fermi energy along \(\bar{{{\Gamma }}}-\bar{{{{\rm{Y}}}}}\), shows both branches of the saddle-shape dispersion with separation 0.249 Å−1. e, Raw ARPES data for Fig. 2e with energy-momentum cuts parallel to the ka-direction at kb = ( − 0.82, − 0.74, − 0.62, − 0.50, − 0.42) Å−1.
Extended Data Fig. 4 Analysis of the helicoid arc dispersion in CoSi.
a, b, Surface-sensitive ARPES measured Fermi surface map of CoSi and corresponding 2D curvature plot (panel b). The purple (Cut A) and green (Cut B) dashed lines illustrate the orthogonal paths of interest. c, d, Raw ARPES measured energy-momentum cut along Cut A and corresponding 2D curvature plot (panel d). e, f, Raw ARPES measured energy-momentum cut along Cut B and corresponding 2D curvature plot (panel f). The red circles in panels (d) and (f) obtain from a standard Lorentzian fitting procedure of the photoemission intensity at various energies along the kA and kB direction, respectively. Error bars for the extracted points are ± 0.05 Å−1 ( ± 0.08 Å−1) along the kA (kB) axis.
Extended Data Fig. 5 Energy-distribution curves across the helicoid arc singularity in CoSi.
a, Surface-sensitive ARPES measured Fermi surface map for CoSi. The regions of interest are labeled by colored lines, spanning across the helicoid arc. b, Energy-distribution curves (EDCs) extracted from the regions marked in panel (a). Different EDCs are taken at kb = -0.33 Å−1. The EDC obtained at ka = 0.44 Å−1 (red circles) shows a strong photoelectron intensity peak near E = − 0.03 eV, matching the helicoid arc van Hove energy in CoSi.
Extended Data Fig. 6 Helicoid arc unique dispersion in the (001) surface BZ of CoSi.
a, ARPES measured constant energy contour (top panel) at, within the experimental resolution, the type-II inter-helicoid arc van Hove singularity energy (EVHS). The black dashed lines illustrate the (001) surface Brillouin zone boundary dashed lines. b, Corresponding 2D curvature plot of the data presented in panel (a). Using a standard Lorentzian fitting procedure, the helicoid arc at EVHS is tracked (red circles). c, 2D curvature energy-momentum cuts along orthogonal directions bisecting the inter-helicoid arc van Hove singularity. A saddle-shape dispersion is observed and tracked using a Lorentzian fitting procedure (red circles). d-g, ARPES measured Fermi surface map of the helicoid arcs near the \(\bar{{{{\rm{M}}}}}\)-pocket. The energy-momentum cuts of interest are labeled cut 1 (panel e), cut 2 (panel f), and cut 3 (panel g). The Fermi velocity of the helicoid arc dispersion is extracted along cuts 1, 2, and 3. The grey dots track the dispersion along cuts 1 and 2. A nearly 1D-like dispersion (flat-like band) with an extremely low Fermi velocity obtains along cut 3 (panel g), relative to the high Fermi velocity dispersion along cut 1 (panel e) and cut 2 (panel f).
Extended Data Fig. 7 Constant-energy contours and calculated electronic susceptibility plots.
a, b, Surface-sensitive ARPES measured constant-energy contours of the surface helicoid arcs in CoSi. The solid blue line represents a fit that tracks the trajectory of the helicoid arcs at E = 0 meV (panel a) and E = − 0.01 eV (panel b). The red box indicates the (001) surface Brillouin zone. c, d, Electronic susceptibility χq plot calculated using the ARPES measured constant energy contours at E = 0 eV (panel c) and E = − 0.01 eV (panel d). Up to symmetry-equivalent scattering vectors, the strong peaks represent all the different peaks in the scattering BZ, which are labeled as Q. The Q vectors, nearest and next- nearest to the \(\bar{{{\Gamma }}}\)-point are labeled Q1 and Q2, respectively. The Q1-vector is annotated by the green arrow, potentially connected to the nesting vectors inside the intra-helicoid arc van Hove singularity. The Q2-vector is annotated by the cyan arrow, potentially connected to nesting vectors linking the nearest inter-helicoid arc van Hove singularity. The length and direction of arrows with the same color remains equivalent when comparing panels (a), (b) to panels (c), (d).
Extended Data Fig. 8 Calculated stereogram of the electronic susceptibility for the Fermi surface map of CoSi.
Stereogram of the electronic susceptibility around the \(\bar{{{\Gamma }}}\)-point. Up to symmetry-equivalent scattering vectors, the strong peaks represent different peaks in the q-plots in the scattering BZ, labeled Q. The Q-vectors, nearest and next-nearest to the \(\bar{{{\Gamma }}}\)-point are labeled Q1 and Q2, respectively. The Q1-vector is annotated by the green arrow, potentially connected to the nesting vectors inside the intra-helicoid arc van Hove singularity. The Q2-vector is annotated by the cyan arrow, potentially connected to nesting vectors linking the nearest inter-helicoid arc van Hove singularity. The white box highlights regions of negligible weak intensities.
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Source Data Fig. 1
Source data for Fig. 1d–f.
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Sanchez, D.S., Cochran, T.A., Belopolski, I. et al. Tunable topologically driven Fermi arc van Hove singularities. Nat. Phys. 19, 682–688 (2023). https://doi.org/10.1038/s41567-022-01892-6
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DOI: https://doi.org/10.1038/s41567-022-01892-6
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