The dispersion of charge carriers in a metal is distinctly different from that of free electrons due to their interactions with the crystal lattice. These interactions may lead to quasiparticles mimicking the massless relativistic dynamics of high-energy particle physics 1-3 , and they can twist the quantum phase of electrons into topologically nontrivial knots -producing protected surface states with anomalous electromagnetic properties 4-9 . 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.
These effects intertwine in materials known asThe bulk electrons in topological semimetals are described by an ultra-relativistic dispersion relation, E(k)=±ħv F σ*k, resembling the Weyl equation for massless spin-1/2 particles. Here σ is a pseudo-spin-1/2 degree of freedom that is energetically locked parallel or anti-parallel to the momentum, k, of the electron, giving electrons definite chirality k ±σ. Applying electromagnetic fields to Weyl or Dirac semimetals induces a pumping of electric charge between Weyl nodes with opposite chirality, a phenomena known in high energy physics as the chiral anomaly [13][14][15] . At the surface of these materials, this anomalous chirality transfer is facilitated by topologically protected surface arcs, the so-called "Fermi arc" surface states, which act as a pipeline connecting opposite chirality Weyl points 11,16 (Fig.1) weaves together the chiral states in the bulk with the topological Fermi-arc states on opposite surfaces into a closed orbit. Its quantization produces a distinctive contribution to the quantum oscillation spectrum that provides an observable signature of the chiral and topological character of these materials. This closed orbit is strikingly different from typical electrons orbiting around a Fermi surface in a metal as the quasiparticle experiences zero Lorentz force on the chiral path segments traversing the bulk.The main result of this study is an additional quantum oscillation frequency observed in microstructures smaller than the mean-free-path that exhibits characteristics of both surface-like and bulk-like states, as naturally expected for Weyl orbits. The microstructures were prepared from Cd 3 As 2 single crystals by FIB etching (Fig.1, see Methods). Down to the smallest thickness of L=150nm, the magnetoresistance at temperatures below 100K shows pronounced Shubnikovde Haas oscillations signaling the low effective mass of the charge carriers and the high crystal quality of the devices (Fig.1b). Quantum oscillations on bulk crystals have reported one single frequency 19,26 , arising from an essentially spherical 3D Fermi surface in agreement with ARPES and STM experiments. This single bulk frequency (F B ) is also consistently observed in all of the studied parent ...