Nontrivial topology in the layered Dirac nodal-line semimetal candidate ${\mathrm{SrZnSb}}_2$ with distorted Sb square nets

Dirac states hosted by Sb/Bi square nets are known to exist in the layered antiferromagnetic ${\mathrm{AMnX}}_2$ (A = CaSr/Ba/Eu/Yb, X=Sb/Bi) material family with the space group to be $P4/nmm$ or $I4/mmm$. In this paper, we present a comprehensive study of quantum transport behaviors, angle-resolved photoemission spectroscopy (ARPES), and first-principles calculations on ${\mathrm{SrZnSb}}_2$, a nonmagnetic analog to ${\mathrm{AMnX}}_2$, which crystalizes in the $pnma$ space group with distorted square nets. From the quantum oscillation measurements up to 35 T, three major frequencies including $F_1=103\mathrm{T}, F_2=127\mathrm{T}$, and $F_3=160\mathrm{T}$ are identified. The effective masses of the quasiparticles associated with these frequencies are extracted, namely, $m_1^{*}=0.1 {\mathrm{m}}_e, m_2^{*}=0.1 {\mathrm{m}}_e$, and $m_3^{*}=0.09 {\mathrm{m}}_e$, where ${\mathrm{m}}_e$ is the free electron mass. From the three band Lifshitz-Kosevich fit, the Berry phases accumulated along the cyclotron orbit of the quasiparticles are $0.06\pi , 1.2\pi$, and $0.74\pi$ for $F_1, F_2$, and $F_3$, respectively. Combined with the ARPES data and the first-principles calculations, we reveal that $F_2$ and $F_3$ are associated with the two nontrivial Fermi pockets at the Brillouin zone edge while $F_1$ is associated with the trivial Fermi pocket at the zone center. In addition, the first-principles calculations further suggest the existence of a Dirac nodal line in the band structure of ${\mathrm{SrZnSb}}_2$.

Figure 1

(a) Crystal structure of ${\mathrm{SrZnSb}}_2$. (b) Reciprocal lattice plane views at 293 K (top) and 105 K (bottom). (c) In-plane resistivity ${\rho }_{xx}$ (red) and out-of-plane resistivity ${\rho }_{zz}$ (blue) as a function of temperature from 2 K to 300 K. Inset is an optical image of a piece of ${\mathrm{SrZnSb}}_2$ single crystal placed on a millimeter grid paper.

Figure 2

(a) Field dependence of magnetic torque $\tau$ for ${\mathrm{SrZnSb}}_2$ at different temperatures with magnetic field nearly parallel with out-of-plane direction. (b) The oscillatory part of the magnetic torque $\mathrm{\Delta }\tau$. (c) The FFT spectra for $\mathrm{\Delta }\tau$ between 5 T and 15 T at different temperatures. Three major oscillation frequencies are indicated. Inset: multipeak Gaussian fit of the FFT spectra to obtain the intensity of the three frequencies (only 2 K data is shown). (d) The temperature dependence of the FFT amplitude for the three frequencies and the fits to the thermal damping term of LK formula (solid lines).

Figure 3

(a) Field dependence of the magnetic torque measured with different field orientations. (b) The angular dependence of the dHvA oscillation frequency $F\left(\theta \right)$ and the fits to $F\left(\theta \right)=F_0/\left|cos\theta \right|$. The background is the 2D color plot for angle dependent FFT spectra of the dHvA oscillations. (c) Magnetoresistance of ${\mathrm{SrZnSb}}_2$ measured with different field orientations. Inset: A schematic diagram of the measurement geometry. (d) The angular dependence of resistivity at $B=9T$ and the $\left|cos\theta \right|$ fit.

Figure 4

(a) Field dependence of in-plane resistivity ${\rho }_{xx}$ of ${\mathrm{SrZnSb}}_2$ measured up to 35 T at different temperatures. Inset: The comparison of the FFT spectra made between 10 T and 35 T, 20 T to 35 T, and 10 T to 25 T at 2 K. (b) Hall resistivity ${\rho }_{xy}$ up to 35 T measured simultaneously with ${\rho }_{xx}$. (c) The oscillatory part of resistivity $▵{\rho }_{xx}$ (black dots) at $T=2.1\mathrm{K}$ and the fit to LK formula with two known frequencies, namely $F_1$ and $F_2$. (d) The fit of SdH oscillations at $T=2.1\mathrm{K}$ to LK formula including three frequencies, which are $F_1, F_2$, and $F_3$. (e) shows the two-band LK fits of the SdH oscillations at higher temperatures, $T=10\mathrm{K}$, resulting in similar Berry phases to those of SdH oscillations at $T=2.1\mathrm{K}$. (f), (g), and (h) are the trials to fit the SdH oscillations at $T=2.1\mathrm{K}$ to two-band LK formula with fixed Berry phase(s) for $F_1$ and/or $F_2$. (f) The Berry phases are both fixed to be 0 for $F_1$ and $F_2$. (g) Only the Berry phase of $F_2$ is fixed to be 0, and it's a free fitting parameter for $F_1$. (h) Only the Berry phase of $F_1$ is fixed to be 0, and it's a free fitting parameter for $F_2$.

Figure 5

(a),(b) Band structure of ${\mathrm{SrZnSb}}_2$ without SOC (a) and with SOC (b). The Dirac nodes are circled by red dashed lines. The Fermi level has been adjusted based on the ARPES data. (c) The curvature method processed energy band spectra along $Z-\mathrm{\Gamma }-Z$ line observed in ARPES and the fit with the bands obtained by DFT calculations. (d),(e) Fermi surface of ${\mathrm{SrZnSb}}_2$ from the side (d) and top (e) view. (f)–(i) Individual $\alpha , \beta , \gamma$, and $\delta$ Fermi pockets. The maximum and minimum cross section areas of each pocket are circled by the dashed lines.