Photoemission Spectroscopic Evidence for the Dirac Nodal Line in the Monoclinic Semimetal ${\mathrm{SrAs}}_3$

Topological nodal-line semimetals with exotic quantum properties are characterized by symmetry-protected line-contact bulk band crossings in the momentum space. However, in most of identified topological nodal-line compounds, these topological nontrivial nodal lines are enclosed by complicated topological trivial states at the Fermi energy ($E_F$), which would perplex their identification and hinder further applications. Utilizing angle-resolved photoemission spectroscopy and first-principles calculations, we provide compelling evidence for the existence of Dirac nodal-line fermions in the monoclinic semimetal ${\mathrm{SrAs}}_3$, which possesses a simple nodal loop in the vicinity of $E_F$ without the distraction from complicated trivial Fermi surfaces. Our calculations revealed that two bands with opposite parities were inverted around $Y$ near $E_F$, resulting in the single nodal loop at the $\mathrm{\Gamma }\text{−}Y\text{−}S$ plane with a negligible spin-orbit coupling effect. The band crossings were tracked experimentally and the complete nodal loop was identified quantitatively, which provide a critical experimental support for the existence of nodal-line fermions in the ${\mathrm{CaP}}_3$ family of materials. Hosting simple topological nontrivial bulk electronic states around $E_F$ and without complication from the trivial states, ${\mathrm{SrAs}}_3$ is expected to be a potential platform for topological quantum state investigation and applications.

Figure 1

(a) The side view of the crystal structure of ${\mathrm{SrAs}}_3$. The atomic layers of As and Sr stack alternately along the $c$ axis, and the natural cleavage and mirror symmetry planes are represented by the green and gray planes, respectively. (b) The monoclinic primitive cell of ${\mathrm{SrAs}}_3$. (c) The single-crystal XRD measured on the (001) plane of the conventional lattice of ${\mathrm{SrAs}}_3$. The inset shows the flat and shining cleavage plane. (d) The comparison between the x-ray Laue pattern taken on the cleaved sample (upper) and simulation (lower).

Figure 2

(a) The 3D BZ of the ${\mathrm{SrAs}}_3$ primitive lattice. The nodal loop (red ring) surrounds the $Y$ point on the $\mathrm{\Gamma }\text{−}Y\text{−}S$ plane, i.e., the mirror symmetry plane. The green plane is perpendicular to the $k_y$ ($k_b$) axis. (b) The projected BZ perpendicular to $k_b$. The red line is the projection of the nodal loop. $k_1$ and $k_2$ represent projections of $k_a$ and $k_c$ onto this plane, respectively. (c) The calculated band structure along high-symmetry paths without SOC. (d) The calculated band structure with orbital characters and parity analysis. (e) The schematic of the nodal loop on the $k_x$-$k_y$ plane. (f) The calculated surface state in the projected BZ along the $k_c$ direction ($\overline{\mathrm{\Gamma }}\text{−}\overline{Y}\text{−}\overline{S}$ plane). The drumheadlike surface state is nestled between two solid Dirac cones, which are the projection of the nodal loop. (g),(h) Calculated band structure along different high-symmetry paths in the project BZ along the $k_y$ direction ($\overline{\mathrm{\Gamma }}\text{−}\overline{X}\text{−}\overline{Z}$ plane).

Figure 3

(a),(b) Integrated photoemission intensity maps in the $k_x$-$k_y$ plane taken at $E_F$ and $E_F\text{−}0.6\mathrm{eV}$, respectively. The photon energies used for the $k_y$ dispersion measurement were from 14 to 86 eV. The measurement with low photon energies (14–30 eV) was performed at 13U beam line of NSRL. The measurement with high photon energies (30–86 eV) was performed at Dreamline beam line of SSRF. (c) Corresponding calculated bulk constant energy surface on the $k_x$-$k_y$ plane taken at $E_F\text{−}0.6\mathrm{eV}$. (d),(g) Integrated photoemission intensity maps in the $\mathrm{\Gamma }\text{−}X\text{−}Z$ ($hv=30\mathrm{eV}$) plane and $Y\text{−}M\text{−}N$ ($hv=17\mathrm{eV}$) plane, respectively. (e),(f) Photoemission intensity plots taken along $\mathrm{\Gamma }\text{−}X$ and $\mathrm{\Gamma }\text{−}Z$, respectively. (h),(i) Photoemission intensity plots taken along $Y\text{−}M$ and $Y\text{−}N$, respectively.

Figure 4

(a) Band dispersions along the $\overline{Y}\text{−}\overline{M}$ direction taken with different photon energies, and the calculations are illustrated by white lines for comparison. These blue dots represent nodes. The inset shows the schematic of ARPES cuts crossing the nodal loop along $k_y$ on the $k_x$-$k_y$ plane. Green lines represent ARPES cuts at different $k_y$ positions, which are taken with different photon energies. The red ring stands for the nodal loop. (b) Corresponding EDCs taken at different photon energies. (c) The comparison between nodal loops determined by ARPES (blue dots) and calculations (the red ring).