Magnetoresistance signature of two-dimensional electronic states in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$

Two-dimensional (2D) Dirac bands and flat bands are characteristics of a kagome lattice. However, experimental studies on their electrical transport are few, because three-dimensional (3D) bulk bands of kagome materials, consisting of stacked 2D kagome layers, dominate the transport. We report a magnetoresistance (MR) study of a kagome material, ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. Based on analysis of the temperature, magnetic field, and field angle dependence of the resistivity, we obtain a complete anatomy of MR. Besides a magnon MR, a chirality-dependent MR, and a chiral-anomaly-induced MR, the most intriguing feature is an orbital MR that scales only with the out-of-plane field, which strongly indicates its 2D nature. We attribute it to the Dirac band of the kagome lattice.

Figure 1

Temperature dependence of the resistivity and MR. (a) Crystal structure of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. (b) Temperature-dependent resistivity of two different samples. Their optical images are shown in the inset. The macroscopic shapes and the crystal directions of samples are indicated. Both scale bars are $200\mu \mathrm{m}$. (c) MR of B07 under an out-of-plane field at different temperatures. (d) Temperature dependence of the coefficient of the quadratic term in MR.

Figure 2

Magnon MR at different field angles. (a) MR of B07 at different angles at 150 K. (b) Hall resistivity at different angles at 150 K. (c) In-plane magnetic field related MR component. The inset shows a schematic of the current and magnetic field direction. (d) MR of B04 at 210 K.

${}^{*}$: the field direction is ${10}^{\circ }$ out of plane.

Figure 3

Positive MR for B04 at 20 K. The field is rotated from the $z$ axis towards the current. (a) MR at different angles. (b) In-plane magnetic field related MR.

Figure 4

Positive MR at 20 K under a transverse field. The field is rotated from the $z$ axis towards the $y$ axis. (a) MR of B04 at plus and minus angles. (b) MR of B04 as a function of the out-of-plane field after $\theta$-symmetrizing. (c) MR of B07 at different angles. (d) MR of B07 as a function of the in-plane field after removing $M{R}_{\mathrm{orb}}$.