Topological surface Fermi arcs in the magnetic Weyl semimetal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$

Very recently, the half-metallic compound ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ was proposed to be a magnetic Weyl semimetal (WSM) with Weyl points only 60 meV above the Fermi level $E_F$. Owing to the low charge carrier density and large Berry curvature induced, ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ possesses both a large anomalous Hall conductivity and a large anomalous Hall angle, which provide strong evidence for the existence of Weyl points in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. In this work, we theoretically study the surface topological feature of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ and its counterpart ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{Se}}_2$. By cleaving the sample at the weak Sn-S/Se bonds, one can achieve two different surfaces terminated with Sn and S/Se atoms, respectively. The resulting Fermi-arc-related states can range from the energy of the Weyl points to $E_F-0.1$ eV in the Sn-terminated surface. Therefore, it should be possible to observe the Fermi arcs in angle-resolved photoemission spectroscopy (ARPES) measurements. Furthermore, in order to simulate quasiparticle interference in scanning tunneling microscopy (STM) measurements, we also calculate the joint density of states for both terminals. This work should be helpful for a comprehensive understanding of the topological properties of these two magnetic WSMs and further ARPES and STM measurements.

Figure 1

(a) Rhombohedral lattice structure of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ and ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{Se}}_2$, which exhibit a layered lattice structure in the $xy$ plane. (b) The kagome lattice structure of Co atoms in the $xy$ plane. (c) Band structures of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$, with (black dashed lines) and without (red solid lines for spin up and green solid lines for spin down) SOC. (d) Location of the Weyl points (red and blue represent opposite chiralities) and nodal lines (green) in the 3D Brillouin zone (BZ) and the 2D BZ projected in the (001) direction. (e) Top view along the $z$ direction of BZ with nodal lines and Weyl points. (f) and (g) Energy dispersion along the $k$ path crossing a pair of Weyl points located on the same nodal line for ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ and ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{Se}}_2$, respectively. The Fermi level and energy of the Weyl points are labeled $E_F$ and $E_W$, respectively.

Figure 2

The change in the total energy with the increasing of the angle between the $z$ axis and magnetic momenta of Co atoms. When the magnetic momenta are parallel to the $z$ axis, it is most stable.

Figure 3

The (001) surface states of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ for S and Sn terminals. (a) Sn-terminated surface FS with energy fixed at the Weyl points. (b) Energy dispersion for the Sn-terminated surface along a $k$ path crossing a pair of Weyl points connected by a Fermi arc. (c) Sn-terminated surface FS at the charge-neutral point. (d) Schematic diagram of the FS distribution on the Sn-terminated surface. (e) S-terminated surface FS with energy fixed at the Weyl points. (f) Surface band structure for S-terminated states taken along the same direction as that in (b). (g) S-terminated surface FS at the Fermi energy $E_F$. (h) Schematic diagram of the FS distribution on the S-terminated surface. The color bars for (a)–(c) and (e)–(g) demonstrate the intensity of states. Light (dark) color demonstrates the occupied (unoccupied) states. The dashed curves in (d) and (h) represent surface states that merge into the bulk. The Fermi arcs and trivial FSs are shown in yellow and black, respectively.

Figure 4

The decay of the surface state into the bulk. The wave function at the sample point $K$ in Fig. 3 on the surface state shows its decay into bulk as a function of the number of unit cells. The penetration depth is about 30–40 unit cells.

Figure 5

QPI patterns for an Sn-terminated surface. (a) Surface FSs without those that merge into the bulk states. The independent scattering vectors $q_1-q_6$ are labeled with arrows. (b) QPI patterns taking contributions from all possible scatterings into account. (c) QPI patterns considering only Fermi-arc-related scatterings. (d) The intra-arc scattering of a nontrivial Fermi arc. (e) and (f) Specified interarc scattering patterns between two nontrivial Fermi arcs. (g)–(i) Details of the interarc scattering between a nontrivial Fermi arc and a trivial FS.

Figure 6

QPI patterns for an S-terminated surface. (a) Surface FSs excluding parts that merge into the bulk states. The six Fermi-arc-related independent scattering vectors are labeled $q_1-q_6$. (b) Full QPI pattern taking all possible surface-state scattering channels into account. (c) QPI pattern considering only the scattering from the nontrivial Fermi arcs. (d) Intensity of the $q_1$ arc-arc scattering. (e)–(i) Intensity distributions of the five independent Fermi-arc-related interarc scattering $q_2-q_6$.