Observation of Chiral Fermions with a Large Topological Charge and Associated Fermi-Arc Surface States in CoSi

Topological semimetals materialize a new state of quantum matter where massless fermions protected by a specific crystal symmetry host exotic quantum phenomena. Distinct from well-known Dirac and Weyl fermions, structurally chiral topological semimetals are predicted to host new types of massless fermions characterized by a large topological charge, whereas such exotic fermions are yet to be experimentally established. Here, by using angle-resolved photoemission spectroscopy, we experimentally demonstrate that a transition-metal silicide CoSi hosts two types of chiral topological fermions, a spin-1 chiral fermion and a double Weyl fermion, in the center and corner of the bulk Brillouin zone, respectively. Intriguingly, we found that the bulk Fermi surfaces are purely composed of the energy bands related to these fermions. We also find the surface states connecting the Fermi surfaces associated with these fermions, suggesting the existence of the predicted Fermi-arc surface states. Our result provides the first experimental evidence for the chiral topological fermions beyond Dirac and Weyl fermions in condensed-matter systems, and paves the pathway toward realizing exotic electronic properties associated with unconventional chiral fermions.

Figure 1

(a) Schematic band dispersions in 3D $E\text{−}k$ space for the spin-$1/2$ Weyl fermion (left), spin-1 chiral fermion (middle), and double Weyl fermion (right). (b),(c) Crystal structure and bulk or surface BZs of CoSi, respectively. Blue and red dots in (c) represent the $\mathit{k}$ points where the band-crossing points exist for the spin-1 chiral fermion and double Weyl fermion, respectively. (d) Calculated bulk-band structure near $E_F$ of CoSi along high-symmetry cuts in the bulk BZ obtained by our first-principles band-structure calculations. Note that the calculated band structure is essentially the same as that previously reported [25]. (e) Plot of the normal-emission ARPES intensity as a function of $k_z$ (corresponding to the out-of-plane $\mathrm{\Gamma }X$ cut). The inner potential was set to be $V_0=20\mathrm{eV}$ from the periodicity of the band dispersion. (f) Corresponding calculated band structure along the $\mathrm{\Gamma }X$ cut. (g) ARPES intensity along the $\overline{\mathrm{\Gamma }}\overline{X}$ cut measured with $h\nu =170\mathrm{eV}$. (h) Bulk BZ in the $k_y\text{−}{k}_z$ plane together with measured cut at $h\nu =170\mathrm{eV}$. The BZ size is based on the experimental lattice constant of $a=4.438\AA$.

Figure 2

(a) ARPES-intensity mapping at $E_F$ plotted as a function of $k_x$ and $k_y$ measured at $h\nu =170\mathrm{eV}$. Intensity at $E_F$ was obtained by integrating the spectral intensity within $\pm 10\mathrm{meV}$ of $E_F$. Calculated FS is overlaid by the blue curve. (b) ARPES intensity and (c) its second-derivative intensity measured along the cut $A$ in (a) ($\mathrm{\Gamma }M$ cut). The second-derivative plot in (c) is based on the EDC divided by the Fermi-Dirac (FD) function at $T=25\mathrm{K}$ convoluted with the resolution function. Note that this division is useful to avoid the appearance of a false flat band at $E_F$ originating from the background with a finite FD cutoff. Red dashed curves in (c) represent the calculated band structure along the $\mathrm{\Gamma }M$ line. (d)–(g) ARPES intensity measured along the cuts $B–E$ in (a), respectively. Red open circles are the energy position of bands determined by tracing the peak position of the EDCs divided by the FD function at $T=25\mathrm{K}$ convoluted with the resolution function, while the blue dashed curves are a guide to the eyes to trace the experimental band dispersion obtained by assuming symmetric band dispersions with respect to the $\mathrm{\Gamma }M$ line (vertical dashed line). (h) Schematic band dispersion for the spin-1 chiral fermion at $\mathrm{\Gamma }$, together with the measured cuts (cuts $B–D$).

Figure 3

(a) ARPES-intensity mapping at $E_F$ plotted as a function of $k_x$ and $k_y$ around the $R$ point measured at $h\nu =136\mathrm{eV}$ ($k_z\sim \pi$ plane). Calculated Fermi surface is shown with a blue curve. (b) Calculated band structure (left), ARPES intensity (middle), and the second-derivative of the ARPES intensity (right), measured along cut $A$ in (a) which crosses the $R$ point. ARPES intensity along cut $A$ (parallel to the analyzer slit; tilted from the high-symmetry line due to sample alignment) was obtained by simultaneously collecting fine angular images of photoelectrons. (c) Second derivative of the ARPES intensity along $\mathrm{\Gamma }R$ and $RM$ cuts, together with the calculated band structure (red dashed curves). (d) Corresponding raw EDCs whose peak position is indicated by black dots. (e) Schematic band dispersion for a double Weyl fermion at the $R$ point.

Figure 4

(a) FS mapping of CoSi at $h\nu =56-72\mathrm{eV}$. (b) Measured cuts in $k_x-k_z$ ($k_y-k_z$) plane. (c), (d) ARPES intensity and second-derivative intensity of MDCs, respectively, measured along cut $A$ in (a) (red line) at $h\nu =67\mathrm{eV}$. White arrow in (c) indicates the $E_F$ crossing point of surface states. (e) Same as (c) but measured along cut $B$ in (a). (f) Same as (d) but measured at $h\nu =61\mathrm{eV}$. (g) Experimental band dispersions extracted from the second derivative of MDCs at various $h\nu$’s.