Evidence of Weyl fermions in $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$

Layered honeycomb lattice antiferromagnetic $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ has been studied intensively recently as a Kitaev spin liquid candidate. Here we present strong evidence that this material host realistic Weyl fermions derived from Cl $2p$ electrons. Our theoretical analysis suggests the existence of quadratic Weyl fermions without spin-orbit coupling and linear Weyl fermion with spin-orbit coupling. Angle-resolved photoemission spectroscopy with systematic photon energy-dependent measurements demonstrates that this Weyl cone possesses linear dispersion at bulk Brillouin zone center along all the three reciprocal directions and hyperbolic dispersion off center. Our work reveals the rich topological physics lying in the band structure of Kitaev QSL candidates and will stimulate further investigation not only limited to $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ but also honeycomb iridate family of materials.

Figure 1

Crystal structure and magnetic, electronic properties of $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$. (a) The crystal structure of $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ with a space group of $C2/m, \beta \approx 108.8^{\circ }$. (b) Crystal structure of $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ with a space group of $P{3}_{1}12$. (c) Constant energy contours (CECs) at binding energy $E_B=3\mathrm{eV}$ and 5.5 eV measure by ARPES at 300 K. Red lines indicate the 2D BZ. (d) Single-crystal x-ray diffraction result taken at 300 K. The inset shows a typical single-crystal photo on a millimeter grid. (e) Low-temperature specific heat $C/T$ without magnetic field. (f) The magnetic susceptibility ($\chi$) vs. temperature ($T$) and the corresponding differential for $H//ab$ at various magnetic fields $H=0.1\mathrm{T},1.0\mathrm{T}$, and 9.0 T, respectively.

Figure 2

General valence band structure of $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ measured at 300 K. (a) Photon energy-dependent ARPES measured spectra along $k_z$. (b) The 3D Brillouin zone of $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ corresponding to the space group of $P{3}_{1}12$. (c–h) ARPES spectra (left panels) and corresponding 2D curvature spectra (right panels) along different high symmetry lines. The measurement geometry is $p$-polarization for (c–f) and s-polarization for (g–h).

Figure 3

Comparison of band structure from ARPES and slab calculation. (a) ARPES spectra. (b) 2D curvature plot of ARPES spectra. (c) Calculated dispersion based on a slab of 7 monolayer $\mathrm{Ru}{\mathrm{Cl}}_3$ with the false color representing its projection on Cl $p_x$ orbital. (d) The 3D representation of the energy dispersion near the Weyl point within the $k_x-k_y$ plane, which is extracted from the DFT results. (e) The Wilson loop obtained by Eq. (S3) [92], where the $\mathrm{\Phi }$ ranges from 0 to $2\pi$ and $\theta$ varies from 0 to $\pi$ to enclose a crossing point. Filled black circles in panels (a) and (c) are guide for the eye.

Figure 4

Evidence of linear Weyl cone. (a) Cl $2p$ top valence bands (2D curvature) measured with different photon energies, corresponding to different $k_z$ values. Red circles indicate the band peak positions while yellow dashed lines are the fitted dispersions using linear and hyperbolic line shape. (b) Schematic of the Weyl cone in $E-k_z-k_y$ space. Red planes indicate the photoemission measurement planes corresponding to the spectra in panel (a). (c) Fitted dispersion along $k_x, k_y$ and $k_z$ directions. Left panel: the hole band maximum evolution with $k_z$, with the red circles represent the band maximum shown in panels of panel (a). Middle panel: hole band dispersion along $k_y$, corresponding to the spectra shown in panel (a) with $k_z=4.0\times 2\pi /c$. Right panel: hole band dispersion along $k_x$, corresponding to the spectra shown in Fig. 2.