Evidence of a topological edge state in a superconducting nonsymmorphic nodal-line semimetal

Topological materials host fascinating low dimensional gapless states at the boundary. As a prominent example, helical topological edge states (TESs) of two-dimensional topological insulators and their stacked three-dimensional equivalent, weak topological insulators (WTIs), have sparked research enthusiasm due to their potential application in the next generation of electronics/spintronics with low dissipation. Here, we propose the layered superconducting material CaSn as a WTI with nontrivial $Z_2$ as well as nodal-line semimetal protected by crystalline nonsymmorphic symmetry. Our systematic angle-resolved photoemission spectroscopy (ARPES) investigation on the electronic structure exhibits excellent agreement with the calculation. Furthermore, scanning tunneling microscopy/spectroscopy (STM/STS) at the surface step edge shows signatures of the expected TES. These integrated evidences from ARPES, STM/STS measurement, and corresponding ab initio calculation strongly support the existence of TES in the nonsymmorphic nodal-line semimetal CaSn, which may become a versatile material platform to realize multiple exotic electronic states as well as topological superconductivity.

Figure 1

General characterizations of CaSn. (a) Real-space illustration of the surface state in the strong 3D topological insulator (i), weak 3D topological insulator (ii) and 2D topological insulator (iii). Spin-up (black arrows) and spin-down (red arrows) electrons move in opposite directions. (b) Schematic illustration of the crystal structure of CaSn, showing two adjacent CaSn layers. (c) Optical image of the high-quality CaSn single crystal (i). X-ray diffraction patterns from the (001) (ii), (010) (iii), (100) (iv) surface of CaSn. (d) Three-dimensional Brillouin zone with calculations of surface-projected energy contours on the (001) side surface and (010) top surface. (e) Magnetization and resistance as functions of temperature, show a sharp superconducting transition at $T_{\mathrm{C}}=4.1\mathrm{K}$. (f) Magnetic moment as a function of magnetic field measured at 2.5 K (black), 3.8 K (red), and 5 K (blue). Inset: Hysteresis loop of magnetization curve at 2.5 K with a large magnetic field range.

Figure 2

Overall electronic structures across the 3D Brillouin zone. (a) The 3D BZ shows the Fermi surfaces on the $k_x-k_y$, $k_x-k_z$, and $k_y-k_z$ planes with high symmetry momenta labeled. (b) The measured band dispersions (i) and corresponding calculated bulk structures (ii) along the high-symmetry directions Z-Γ-X-A-Z [indicated by the green lines at $k_{\mathrm{y}}=0$ plane in (a)], Z-T ($k_{\mathrm{y}}$ direction along the BZ boundary), and $T\text{−}Y\text{−}{X}_1\text{−}{A}_1\text{−}T$ (indicated by the red lines at $k_{\mathrm{y}}=\pi$ plane). (c) Evolution of Dirac band dispersions along $k_{\mathrm{y}}$ (Z-T direction). Stack plot of the six cuts with $k_{\mathrm{y}}$ values ranging from 0 to π/b. Dirac nodal lines are indicated by the black arrows.

Figure 3

ARPES measurement on topologically dark (010) surface. (a) The experiment geometry of ARPES measurement on the top surface of a weak 3D topological insulator. (b) The 3D intensity plot of ARPES data on the naturally cleaved (010) surface. (c) Photoemission intensity (left panel) and corresponding ab initio calculation (right panel) along the high symmetry $\overline{X}\overline{A}$ (i), $\overline{\mathrm{\Gamma }}\overline{Z}$ (ii), $\overline{Z}\overline{A}$ (iii), $\overline{\mathrm{\Gamma }}\overline{X}$ (iv) directions. (d) Measured (left panel) and calculated (right panel) constant energy contours (CECs) with five different binding energies $E_b=0\mathrm{eV}$ (i), 0.4 eV (ii), 0.8 eV (iii), 1.2 eV (iv), and 1.6 eV (v), respectively. The experimental plot has been symmetrized with respect to the $k_{\mathrm{x}}=0$ plane according to the crystal symmetry. The raw data of ARPES measurement are presented in Fig. S10 [25].

Figure 4

STM/STS measurements of the edge states. (a) Typical STS measured at the step edge (red curve) and a location away from the edge (blue curve). Inset: Schematics of CaSn (010) termination with a step edge. (b) STM topographic (i), 80 nm × 80 nm, with sample bias $V\mathrm{s}=400\mathrm{mV}$, tunneling current $I\mathrm{s}=200\mathrm{pA}$. (ii)–(v) The corresponding dI/dV mapping of the imaged area (i) at different sample bias. (c) (i) STM topography appended with the line profiles along the dashed red arrow, showing a step of 5.6 Å. (ii) Differential conductance along the dotted red line in (i) within a bias range −1.2 to +0.4 V.