The dispersion of charge carriers in a metal is distinctly different from that of free electrons owing to their interactions with the crystal lattice. These interactions may lead to quasiparticles mimicking the massless relativistic dynamics of high-energy particle physics1,2,3, and they can twist the quantum phase of electrons into topologically non-trivial knots—producing protected surface states with anomalous electromagnetic properties4,5,6,7,8,9. These effects intertwine in materials known as Weyl semimetals, and in their crystal-symmetry-protected analogues, Dirac semimetals10. The latter show a linear electronic dispersion in three dimensions described by two copies of the Weyl equation (a theoretical description of massless relativistic fermions). At the surface of a crystal, the broken translational symmetry creates topological surface states, so-called Fermi arcs11, which have no counterparts in high-energy physics or conventional condensed matter systems. Here we present Shubnikov–de Haas oscillations in focused-ion-beam-prepared microstructures of Cd3As2 that are consistent with the theoretically predicted ‘Weyl orbits’, a kind of cyclotron motion that weaves together Fermi-arc and chiral bulk states12. In contrast to conventional cyclotron orbits, this motion is driven by the transfer of chirality from one Weyl node to another, rather than momentum transfer of the Lorentz force. Our observations provide evidence for direct access to the topological properties of charge in a transport experiment, a first step towards their potential application.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Katsnelson, M. I., Novoselov, K. S. & Geim, A. K. Chiral tunnelling and the Klein paradox in graphene. Nat. Phys. 2, 620–625 (2006)
Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005)
Vafek, O. & Vishwanath, A. Dirac fermions in solids — from high Tc cuprates and graphene to topological insulators and Weyl semimetals. Annu. Rev. Condens. Matter Phys. 5, 83–112 (2014)
Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007)
Fu, L. & Kane, C. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008)
Roushan, P. et al. Topological surface states protected from backscattering by chiral spin texture. Nature 460, 1106–1109 (2009)
Zhang, T. et al. Experimental demonstration of topological surface states protected by time-reversal symmetry. Phys. Rev. Lett. 103, 266803 (2009)
Pan, Z.-H. et al. Electronic structure of the topological insulator Bi2Se3 using angle-resolved photoemission spectroscopy: evidence for a nearly full surface spin polarization. Phys. Rev. Lett. 106, 257004 (2011)
Park, S. R. et al. Chiral orbital-angular momentum in the surface states of Bi2Se3 . Phys. Rev. Lett. 108, 046805 (2012)
Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012)
Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011)
Potter, A. C., Kimchi, I. & Vishwanath, A. Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5, 5161 (2014)
Adler, S. L. Axial-vector vertex in spinor electrodynamics. Phys. Rev. 177, 2426–2438 (1969)
Bell, J. S. & Jackiw, R. A PCAC puzzle: π0 → γγ in the σ-model. Nuovo Cim. A 60, 47–61 (1969)
Nielsen, H. B. & Ninomiya, M. The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal. Phys. Lett. B 130, 389–396 (1983)
Haldane, F. D. M. Attachment of surface “Fermi arcs” to the bulk Fermi surface: “Fermi-level plumbing” in topological metals. Preprint at http://arXiv.org/abs/1401.0529v1 (2014)
Wang, Z. et al. Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb). Phys. Rev. B 85, 195320 (2012)
Wang, Z., Weng, H., Wu, Q., Dai, X. & Fang, Z. Three-dimensional Dirac semimetal and quantum transport in Cd3As2 . Phys. Rev. B 88, 125427 (2013)
Liang, T. et al. Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2 . Nat. Mater. 4, 3–7 (2014)
Neupane, M. et al. Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2 . Nat. Commun. 5, 3786 (2014)
Liu, Z. K. et al. A stable three-dimensional topological Dirac semimetal Cd3As2 . Nat. Mater. 13, 677–681 (2014)
Yi, H. et al. Evidence of topological surface state in three-dimensional Dirac semimetal Cd3As2 . Sci. Rep. 4, 6106 (2014)
Liu, Z. K. et al. Topological Dirac semimetal, Na3Bi. Science 343, 864–867 (2014)
Borisenko, S. et al. Experimental realization of a three-dimensional Dirac semimetal. Phys. Rev. Lett. 113, 027603 (2014)
Jeon, S. et al. Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2 . Nat. Mater. 13, 851–856 (2014)
He, L. P. et al. Quantum transport evidence for the three-dimensional Dirac semimetal phase in Cd3As2 . Phys. Rev. Lett. 113, 246402 (2014)
Rosenberg, A. J. & Harman, T. C. Cd3As2 — a noncubic semiconductor with unusually high electron mobility. J. Appl. Phys. 30, 1621–1622 (1959)
Analytis, J. G. et al. Two-dimensional surface state in the quantum limit of a topological insulator. Nat. Phys. 6, 960–964 (2010)
Moll, P. J. W. et al. Transition from slow Abrikosov to fast moving Josephson vortices in iron pnictide superconductors. Nat. Mater. 12, 134–138 (2012)
Moll, P. J. W., Zhu, X., Cheng, P., Wen, H.-H. & Batlogg, B. Intrinsic Josephson junctions in the iron-based multi-band superconductor (V2Sr4O6)Fe2As2 . Nat. Phys. 10, 644–647 (2014)
Moll, P. J. W. et al. Field induced density wave in the heavy fermion compound CeRhIn5 . Nat. Commun. 6, 6663 (2015)
Jaroszynski, J. et al. Upper critical fields and thermally-activated transport of Nd(O0.7F0.3)FeAs single crystal. Phys. Rev. B 78, 174523 (2008)
Ooi, S., Mochiku, T. & Hirata, K. Periodic oscillations of Josephson-vortex flow resistance in Bi2Sr2CaCu2O8+y . Phys. Rev. Lett. 89, 247002 (2002)
Moll, P. J. W. et al. High magnetic-field scales and critical currents in SmFeAs(O, F) crystals. Nat. Mater. 9, 628–633 (2010)
Ziegler, J. F. SRIM-2003. Nucl. Instrum. Methods Phys. Res. B 220, 1027–1036 (2004)
Shoenberg, D. Magnetic Oscillations in Metals (Cambridge Univ. Press, 1984)
Wray, L. A. et al. How robust the topological properties of Bi2Se3 surface are: a topological insulator surface under strong Coulomb, magnetic and disorder perturbations. Nat. Phys. 7, 32–37 (2011)
Beenakker, C. W. J. & van Houten, H. Quantum transport in semiconductor nanostructures. Solid State Phys. 44, 1–228 (1991)
de Jong, M. & Molenkamp, L. Hydrodynamic electron flow in high-mobility wires. Phys. Rev. B 51, 13389–13402 (1995)
Thornton, T. J., Roukes, M. L., Scherer, A. & Van De Gaag, B. P. Boundary scattering in quantum wires. Phys. Rev. Lett. 63, 2128–2131 (1989)
Tokumoto, M. et al. Direct observation of spin-splitting of the Shubnikov-de Haas oscillations in a quasi-two-dimensional organic conductor (BEDT-TTF)2KHg(SCN)4 . J. Phys. Soc. Jpn 59, 2324–2327 (1990)
Wallace, P. R. Electronic g-factor in Cd3As2 . Phys. Status Solidi 92, 49–55 (1979)
Ali, M. N. et al. The crystal and electronic structures of Cd3As2, the three-dimensional electronic analogue of graphene. Inorg. Chem. 53, 4062–4067 (2014)
The FIB work was supported by the SCOPE-M centre for electron microscopy at ETH Zurich. We thank P. Gasser, J. Reuteler and B. Batlogg for FIB support, and M. Bachmann for performing magnetoresistance measurements. A.C.P. was supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4307. We also thank S. Teat and K. Gagnon for their help in conducting X-ray diffraction measurements at the Advanced Light Source (ALS) beam line 11.3.1, and N. Tamura for micro-diffraction on beam line 12.3.2. N.T. and the ALS are supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences Division, of the US Department of Energy under contract no. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory and the University of California, Berkeley. Transport experiments, material synthesis and FIB microstructuring were supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4374. Single-crystal X-ray refinements (T.H.) and theoretical support (A.V. and I.K.) were funded by the Quantum Materials FWP, US Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under contract no. DE-AC02- 05CH11231. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231.
The authors declare no competing financial interests.
Extended data figures and tables
a, A typical facetted Cd3As2 single crystal, and b, the powder X-ray diffraction (PXRD) spectrum. Cd3As2 single crystals were produced using the flux growth technique with a 5:1 ratio of Cd flux to Cd3As2. Elemental Cd and As were placed into an aluminium oxide crucible with a quartz wool plug and sealed into a quartz ampoule under vacuum. The ampoule was heated to 825 °C and held at that temperature for two days to ensure a fully homogenized mixture. It was then cooled at a rate of 6 °C per hour to 425 °C, where it was centrifuged to remove excess Cd. Bulk crystals were found trapped in the quartz wool following this procedure, and were confirmed to be Cd3As2 by both PXRD and single-crystal X-ray diffraction. The PXRD data (red trace) can be well fitted by the I41/acd low-temperature phase of Cd3As2 (ref. 43) (black trace), and no parasitic phases were observed.
a, Sketch of the device cross-section before and after the irradiation. Three possible current paths exist in these devices: the crystal bulk (purple), the topological surface states (orange), and the amorphous FIB-induced damage shell (green). b, Device after the heavy irradiation damage. The dimples due to the beam centre impact are well visible across the whole device. The polished back side remained undisturbed by this procedure. c, Comparison of the same device with pristine surfaces and after damaging the surface. The resistance increases after irradiation, as expected for the increased scattering. d, Magnetoresistance of the Cd3As2 microstructure before and after irradiation; and e, the Fourier components of the quantum oscillations.
The temperature dependence of the Shubnikov–de Haas (SdH) amplitudes in the bulk (blue) and at the surface (red) follow the usual Lifshitz–Kosevich behaviour. The fits to the data (lines) yield an effective electron mass in the bulk of 0.044me, in good agreement with previously reported values26. The surface state appears slightly heavier (0.05me).
a, Positions of the nth Landau levels, Bn, calculated for spin-splitting (blue) and experimentally observed values (red). The observed deviation is opposite to the expectation of spin-splitting, yet qualitatively and quantitatively consistent with the non-adiabatic corrections of the Weyl orbit process. b, Calculated Landau level energy spectrum for Dirac systems with and without spin-splitting as described by equation (2).
Shown are Shubnikov–de Haas oscillations of the 150-nm-wide rectangular device, the smallest microstructure fabricated in this study, as a function of 1/field, for different angles between the sample and the magnetic field. Following the notation of the main manuscript, 0° and 180° correspond to a field perpendicular to the surface of the device (‘surf’). The separation between curves along y represents the field angle on a linear scale. Close to the perpendicular field configurations, traces at 5° angle increment were taken, and at 10° increment elsewhere. The appearance of the surface frequency can be well seen in the raw data as strong beating appears around 0°. Also, the characteristic cos(θ)−1 angle dependence of a surface frequency can be easily seen by following the peak positions to higher angles.
Shown are Shubnikov–de Haas oscillations of the triangular (top) and rectangular (bottom) devices, as a function of 1/field for different angles between the sample and the magnetic field. Traces were taken at 5° angle increment. Those angles where the field is perpendicular to a surface are marked by ‘surf’ for both the rectangular and the triangular devices. While the rectangular device shows the characteristic beating, the peak positions in the triangle remain at the same fields.
About this article
Cite this article
Moll, P., Nair, N., Helm, T. et al. Transport evidence for Fermi-arc-mediated chirality transfer in the Dirac semimetal Cd3As2. Nature 535, 266–270 (2016). https://doi.org/10.1038/nature18276
Communications Physics (2021)
Nature Reviews Physics (2021)
Nature Reviews Physics (2021)
Nature Communications (2021)
Nature Communications (2020)