Magnetotransport properties of the single-crystalline nodal-line semimetal candidates $\mathrm{Ca}TX(T=\text{Ag},\text{Cd};X=\text{As},\text{Ge})$

Topological semimetals are characterized by protected crossings between conduction and valence bands. These materials have recently attracted significant interest because of the deep connections to high-energy physics, the novel topological surface states, and the unusual transport phenomena. While Dirac and Weyl semimetals have been extensively studied, the nodal-line semimetal remains largely unexplored due to the lack of an ideal material platform. In this paper, we report the magnetotransport properties of the two nodal-line semimetal candidates CaAgAs and CaCdGe. First, the transport properties of our single crystalline CaAgAs agree with those of CaAgAs polycrystals. They can be explained by the single-band model, consistent with the theoretical proposal that only nontrivial Fermi pockets linked by the topological nodal-line are present at the Fermi level. Second, our CaCdGe sample provides an ideal platform to perform comparative studies because the theoretical calculation shows that it features the same topological nodal line but has a more complicated Fermiology with irrelevant Fermi pockets. As a result, the magnetoresistance of our CaCdGe sample is more than 100 times larger than that of CaAgAs. Through our systematic magnetotransport and first-principles band structure calculations, we show that our CaTX compounds can be used to study, isolate, and control the novel topological nodal-line physics in real materials.

Figure 1

(a) Crystal structure of CaAgAs and CaCdGe. $T{X}_4$ octahedra are shown in blue. Ca atoms are shown in green. (b) and (c) Mirror symmetry protected nodal-lines in CaAgAs and CaCdGe. (b) Schematic of a band structure diagram for the nodal-line feature in CaAgAs and CaCdGe. The conduction and valence bands are made up of the Ag(Cd) $4d$ and As(Ge) $4p$ orbitals, respectively. The band crossings near the $\mathrm{\Gamma }$ point are protected because these two bands have opposite mirror eigenvalues. (c) and (d) First-principles calculated band structures of CaAgAs near the $\mathrm{\Gamma }$ point without SOC (c) and with SOC (e) Wilson loop calculation of the SOC band structure on the $k_z=0$ and $k_z=\pi /2$ planes.

Figure 2

(a) The powder x-ray diffraction patterns of CaCdGe and CaAgAs. The ticks below each pattern indicate the Bragg peak positions determined by the respective crystal structure. The impurity peak marked with an asterisk in the CaCdGe pattern is from Cd while the one in CaAgAs is from CaAs. (Inset) CaCdGe single crystal on a millimeter scale. The crystalline directions are shown. (b) Temperature dependence of the electrical resistivity ${\rho }_{xx}$ for CaCdGe and CaAgAs at $B=0$ T with $I\parallel c$. (c) MR of CaCdGe and CaAgAs single crystals at $T=2$ K with $I\parallel c$ and $B\perp ac$.

Figure 3

CaAgAs single crystal with $I\parallel c$ and B $\perp ac$: (a) Hall resistivity ${\rho }_{yx}$. (b) Field dependent transverse MR. (c) Temperature dependent carrier density and mobility.

Figure 4

CaCdGe single crystal s3 with $I\parallel c$ and $B\perp ac$: (a) transverse magnetoresistivity ${\rho }_{xx}$. (b) Hall resistivity ${\rho }_{yx}$. The symbols correspond to experimental data, while the lines are the curves obtained from the two band model fitting. (c) Temperature dependent carrier densities. (d) Temperature dependent mobilities.

Figure 5

(a) The oscillating part of ${\rho }_{xx},\delta {\rho }_{xx}$, vs $1/B$. (b) FFT spectrum of $\delta {\rho }_{xx}$ for a few representative temperatures. (Inset) Measurement configuration. The magnetic field was normal to the $ac$ plane. (c) Temperature dependence of the normalized amplitude of $\delta {\rho }_{xx}$ denoted as A/A(2K). (d) $1/B$ dependence of the quantity $\ln (\delta {\rho }_{xx}/4{\rho }_0{R}_T)$, where $R_T=\frac{\alpha T{m}^{*}/B}{sinh(\alpha T{m}^{*}/B)}$, used to extract the Dingle temperature.

Figure 6

(a) and (b) Angular dependence of the experimental $F_a^{\mathrm{SdH}}$ (yellow lines; see text) and the calculated $F_{\beta }^{\mathrm{SdH}}$ (black lines; see text) with the measurement geometries in the insets. (c) and (d) The electronic band structure of CaCdGe with SOC: (c) using the LDA/GGA potential and (d) using the MBJ potential. (e) The Fermi pockets associated with (d).