Two-dimensionality of metallic surface conduction in Co3Sn2S2 thin films

Two-dimensional (2D) surface of the topological materials is an attractive channel for the electrical conduction reflecting the linearly-dispersive electronic bands. By applying a reliable systematic thickness t dependent measurement of sheet conductance, here we elucidate the dimensionality of the electrical conduction paths of a Weyl semimetal Co3Sn2S2. Under the ferromagnetic phase, the 2D conduction path clearly emerges in Co3Sn2S2 thin films, indicating a formation of the Fermi arcs projected from Weyl nodes. Comparison between 3D conductivity and 2D conductance provides the effective thickness of the surface conducting region being estimated to be approximately 20 nm, which is rather thicker than 5 nm in topological insulator Bi2Se3. This large value may come from the narrow gap at Weyl point and relatively weak spin-orbit interaction of the Co3Sn2S2. The emergent surface conduction will provide a pathway to activate quantum and spintronic transport features stemming from a Weyl node in thin-film-based devices.


Introduction
The surface of the films forms interface with substrate or capping layer, which usually plays an active role for the electrical conduction in addition to the bulk region. Various origins for the interface conduction in trivial semiconductors have been explored as charge discontinuity at oxide interface 1 , charge transfer 2 , dipoles effect 3 and electric polarization effect 4,5 . The effective thickness of the two-dimensional (2D) conductive channel is basically dominated by charge accumulation based on Poisson equation. Besides these interface effects, the emergent topological materials hold intrinsic surface conducting channels that are a Dirac surface state in three-dimensional (3D) topological insulator (TI) (ref. 6) and Fermi arc in Dirac and Weyl semimetals 7,8 . The surface conduction in the topological materials exhibits the 3 intriguing features of linearly-dispersive electronic bands such as spin-momentum locking 9,10 , quantum anomalous Hall effect 11,12 and magnetoresistance oscillation at the Weyl orbits 13,14 .
As another important feature, the surface states of TIs suddenly disappear by hybridization between two surfaces of top and bottom in ultrathin films. While the dominant factor of the penetration function along thickness direction has been experimentally 15,16 and theoretically 17 investigated, the critical thickness for 3D-TIs is about 5 nm for Bi2Se3 (ref. 15) and 2 nm for Bi2Te3 (ref. 16). However, surface conduction in Weyl semimetal (WSM) has been rarely explored in thin films. Recently, a Co-kagome magnet of Co3Sn2S2, crystal structure of which is shown in Fig. 1a, has been extensively investigated as a Dirac semimetal (DSM) at paramagnetic phase and a WSM at ferromagnetic phase [18][19][20][21][22][23] . Large anomalous Hall conductivity has been focused with perpendicular magnetic anisotropy owing to large contribution of Berry curvature in the Weyl nodes 18 . By tilting the symmetric line of the two Weyl nodes from z-axis, surface Fermi arc has been observed by spectroscopies [21][22][23] . The contribution of the projected Weyl nodes would be detected in electrical conduction for ultrathin films with suppressed bulk conduction though it has not been apparently obtained in bulk Co3Sn2S2.
The electrical conduction in thin films at zero magnetic field is generally expected to follow the Ohm's law based on the 3D uniform conductivity (Ω -1 cm -1 ) in whole region of the film; = = , where G is the conductance of the sample, I current, V applied voltage, W width, L length, and t thickness of the channel. The sheet conductance is experimentally calculated by = = . When the surface or interface contributes to the electrical conduction in the films, the sheet conductance of the film sums up the tdependent conductance in bulk region Gbulk = and the t-independent 2D surface conductance , = + as shown in Fig. 1b and 1c, where is the 4 3D conductivity of the bulk region. Experimentally, t dependence of the 2D sheet conductance can separately elucidate the conduction path at 3D bulk and 2D surface. However, it is often difficult to achieve the electrical conduction in the ultrathin layers because the island-like grains initially disconnect each other. This is so-called a dead layer at the interface, which is usually evaluated by the t-dependent conductance measurement. To accurately evaluate the bulk conductivity of the thin films, therefore, the t-dependent measurement is reliable with elimination of the additional conduction at the surface and/or with accurate thickness contributing conduction except for a dead layer. In this study, we applied this analysis to the Co3Sn2S2 thin films to elucidate the dimensionality of the conduction channels at bulk and surface separately. The films holding WSM phase are intensively discussed in thickness 23 -61 nm. The metallic conduction of the films at the WSM phase strongly relates on the superior surface conduction.

Results
Temperature dependent resistivity ρxx of two Co3Sn2S2 films with thicknesses of 41 and 40 nm is shown in Fig. 2a with a reference ρxx of bulk crystal 18 24,25 . Since metallic conduction is more pronounced in the WSM phase, here we define the residual resistivity ratio (RRR = ρxx (T = 300 K) / ρxx (T = 2 K)) to characterize the metallicity of the films. This RRR is a good measure to classify the films into two groups while the structural qualities of these films are comparable 5 in the inspection by x-ray diffraction 25 . In Fig. 2b, the RRR for all the films measured in this study is summarized to classify the films into Groups A (blue) and B (red), in which the border for classification is RRR ~ 4. Typical ρxx values for the film #1 of Group A and the film #2 of Group B with comparable t ~ 40 nm represent large and small RRR in Fig. 2a, respectively. In comparison with the reference ρxx of bulk crystal with large RRR ~ 8.5, ρxx of #1 at low temperature is comparable to that of the bulk but the ρxx of both the films at high temperature is largely different.
Thickness t dependence of sheet conductance (Gs = 1/Rs, where Rs is sheet resistance) at T = 300 K and 2 K is plotted as a function of t in Fig. 2c  Although the error bar is large in Fig. 4b, the t-independent 2D conduction region is estimated to be roughly 20 nm constant against t-variation. This value is rather thicker than that of 3D-TI for example 5 nm of Bi2Se3 (ref. 15). The distribution of surface Fermi arc along z-direction may be related to the broadness of the projection of Weyl nodes with narrow gap 17 . In addition, the weaker spin-orbit coupling of Co3Sn2S2 compared to 3D-TIs such as Bi2Se3 and Bi2Te3 may induce the weak confinement of surface state, resulting in the large effective thickness (refs. 15,17). While we here assume uniform to estimate the averaged effective thickness, the penetration function of the surface conduction region should be more carefully considered to be rapid decay along z-direction as like 3D-TIs (refs. 17,30). In this study, apparent detection of the t-independent conductance reveals the possibility of surface Fermi arc conduction in the Co3Sn2S2 thin films.

Discussion
Here we discuss the origin for the appearance of t-independent surface conduction in the films. The robust t-independent current path is experimentally detected by the analysis of sheet conductance of the films. The thickness of the films is enough thick to form uniform crystalline structure and to hold a feature of WSM with large anomalous Hall conductivity 25 .

The top and bottom surfaces of the films form the interface with a capping layer of SiOx and
Al2O3 substrate, respectively. Such interface between oxide insulator and sulfide metal is likely to be basically inactive for the electrical conduction. Other extrinsic defect formation contributing to the metallic electrical conduction can be excluded. As intrinsic origins, the surface projected Fermi arc is possibly located at the inert interface. Moreover, the appearance of surface conduction below TC should be noticeable to the Weyl nodes stemming from WSM 8 phase. However, the origin for different values of RRR in two groups is not obvious from the structural quality. In fact, the analyzed value of for both group is comparable. As shown in Fig. 2b,

Film preparation
Co3Sn2S2 thin films were prepared by radio-frequency sputtering. The growth procedure is following and detail information can be found in previous studies 24,25 . Firstly, a Co3Sn2S2 film was deposited on Al2O3 (0001) substrate at 400 o C. Then, a SiOx capping layer was deposited on the Co3Sn2S2 film. The film was annealed at 800 o C in vacuum for 1 hour.
The crystal structures and composition were characterized by x-ray diffraction and energydispersive x-ray spectroscopy. The t (23 -61nm) was controlled by the deposition duration, which was confirmed by the Laue fringe in x-ray diffraction patterns.

Electrical transport measurement
Electrical measurements were carried out in physical properties measurements system (PPMS, Quantum Design) (ref. 25). The films were scratched to make Hall-bar shape with indium contact electrodes. In the previous studies, the large anomalous Hall conductivity was observed in all films, indicating that the WSM phase is materialized.