Unusual Dual Flat Bands and two-dimensional Dirac-node Arc State in Kagome Metal Ni3In2S2

Abstract

Kagome materials are at the frontier of condensed matter physics. An ideal kagome lattice features only one geometrically frustrated flat band spanning the entire momentum space and a single Dirac cone at the Brillouin-zone corners. However, for the first time, here we observe unusual flat-band and Dirac physics in the newly discovered "322" kagome material Ni3In2S2 by combining high-resolution synchrotron- and laser-based angle-resolved photoemission spectroscopy with a micro-focused beam, scanning tunneling microscopy, and first-principles calculations. We resolve two distinct electronic flat-band states located in close proximity to the Fermi level: a robust Topological Surface Flat Band at ~40 meV below the Fermi level on the Sulfur-terminated surface, originating from weak topological insulator states, and a kagome lattice-derived flat band at ~100 meV binding energy with an ultranarrow bandwidth (~5 meV). Instead of the single Dirac cone, the Indium-terminated surface hosts a rare two-dimensional Dirac-node arc state, where the gapless Dirac nodes extend along an open one-dimensional line crossing the Brillouin-zone boundary, exhibiting sharp linear dispersion, exceptionally high Fermi velocity, and pronounced circular dichroism. These findings establish Ni3In2S2 as a unique topological kagome metal in which multiple flat-band states of different physical origin coexist with an unusual Dirac-node arc, opening an avenue for discovering flat-band--driven and topology-enabled quantum phenomena.

Figures (4)

• Figure 1: Lattice structure and calculated bulk electronic structure of Ni$_3$In$_2$S$_2$.a Top view of the kagome lattice composed of nickel atoms. b The ideal kagome lattice band dispersion considering only the nearest-neighbor hopping. c A unit cell of Ni$_3$In$_2$S$_2$ with three layers of kagome planes highlighted by the red squares. d Two possible cleaving surfaces corresponding to the In- and S-terminated layers, whose atoms are arranged in a triangular fashion. e Schematic plot of the bulk Brillouin zone of the primitive cell and its projection forming the (001) surface Brillouin zone. f The conventional cell Brillouin zone and projected (001) surface Brillouin zone. g DFT-calculated bulk bands of Ni-3d orbital integrated over all $k_z$ (left panel) and the DOS calculation for bulk states in Ni$_3$In$_2$S$_2$ (right panel). The grey shading bar in (g) highlights the flat band derived from the Ni-based kagome network.
• Figure 2: Signature of TSFB and kagome lattice-derived flat band in Ni$_3$In$_2$S$_2$.a--c For the S-terminated surface (Top to bottom) with ARPES spectra along the $\bar{M}$--$\bar{\Gamma}$--$\bar{K}$--$\bar{M}$ high symmetry directions (a), the corresponding second-derivative image with respect to energy (b), and the calculated band structure with surface states (c). The observed TSFB and kagome lattice-derived flat band are marked by black and red arrows, respectively. d--f Same as (a--c) but for the In-terminated surface. The original spectra for the two surfaces in panels (a) and (d) were both measured using linear horizontal (LH) polarized light with a photon energy of 34 eV at 10 K. g Second-derivative plot with respect to energy of high-resolution laser-based ARPES spectrum along the partial $\bar{\Gamma}$--$\bar{M}$ high symmetry line, obtained at 15 K by using linear vertical (LV) polarized light with a photon energy of 6.994 eV. TSFB and FB features were observed more clearly in the laser data (also indicated by black and red arrows respectively). The kagome flat band distribution in the 2D Brillouin zone is displayed in the inset of (g), which shows an interesting concave triangle. h Sketch of the TSFB in Ni$_3$In$_2$S$_2$, in contrast to the typical Dirac surface state in a seminal topological insulator Bi$_2$Se$_3$, which has an extremely high Fermi velocity. i The schematic diagram of the destructive interference of electron wave functions within the kagome lattice, and the resulting feature of flat band in the momentum space.
• Figure 3: 2D Dirac-node arc state on the In-terminated surface. a Fermi surface and b Constant energy contour at the binding energy of 0.18 eV, with Dirac nodes showing up around the $\bar{M}$ point. They are obtained by integrating the spectral intensity within 10 meV with respect to the $E_F$ and $E_F$ - 0.18 eV, respectively. c Schematic illustration of the 2D Dirac-node-arc structure as revealed by ARPES. d Band dispersions around the $\bar{M}$ point along cuts 1--6, whose locations are indicated by the pink dashed lines in panel (e). e Zoomed-in view of the measured Fermi surface with partial surface Brillouin zone and high symmetry momentum points overlaid. f Quantitative momentum locations shown as green bars of the observed Dirac nodes around the $\bar{M}$ point. g EDCs stacked at the momentum positions of Dirac points in (d), illustrating gapless Dirac dispersions (cuts 3--5) and gapped ones (cuts 1, 2, and 6). h Evolution of the gap size and Dirac point energy with the increasing $k_y$ close to the $\bar{M}$ point. The data in panels (a--h) were acquired at 10 K by using synchrotron-based ARPES with a photon energy of 34 eV. i Band dispersions measured at 15 K by using laser-based ARPES with a photon energy of 6.994 eV. The cuts 7--8 parallel to the $\bar{K}$--$\bar{M}$--$\bar{K}$ direction are marked with green dotted lines in (e).
• Figure 4: Fermi surface and QPI signature of the two types of cleavage surfaces in Ni$_3$In$_2$S$_2$. a, b Experimental Fermi surfaces for the S- (a) and In- (b) terminated surfaces, respectively, measured at 15 K by using laser-based ARPES (6.994 eV). c EDCs obtained by integrating the ARPES data of the entire $\bar{\Gamma}$--$\bar{M}$ path shown in Fig. 2a,d. The data have been divided by the Fermi--Dirac distribution. d, e QPI patterns acquired at +20 meV under zero magnetic field for the S- (d) and In- (e) terminated surfaces. Bragg points are marked by red dots. f Differential conductance spectrum ($dI/dV$) taken on two terminations. g, h Calculated Fermi surface maps with surface states of S- (g) and In- (h) terminated surfaces. i Calculated LDOS on two terminations. The similar arc-like features captured by ARPES and QPI are marked by red arcs in (a, b, d, e).