Accessing bands with extended quantum metric in kagome Cs2Ni3S4 through soft chemical processing

Abstract

Flat bands that do not merely arise from weak interactions can produce exotic physical properties, such as superconductivity or correlated many-body effects. The quantum metric can differentiate whether flat bands will result in correlated physics or are merely dangling bonds. A potential avenue for achieving correlated flat bands involves leveraging geometrical constraints within specific lattice structures, such as the kagome lattice; however, materials are often more complex. In these cases, quantum geometry becomes a powerful indicator of the nature of bands with small dispersions. We present a simple, soft-chemical processing route to access a flat band with an extended quantum metric below the Fermi level. By oxidizing Ni-kagome material Cs₂Ni₃S₄ to CsNi₃S₄, we see a two orders of magnitude drop in the room temperature resistance. However, CsNi₃S₄ is still insulating, with no evidence of a phase transition. Using experimental data, density functional theory calculations, and symmetry analysis, our results suggest the emergence of a correlated insulating state of unknown origin.

Fig. 1.. Structure models for Cs₂Ni₃S₄ from experimental powder x-ray diffraction refinements and calculated band structure.

The stacking direction of the nickel layers sandwiched between double layers of cesium can be seen in (A) along with the stacking direction along the c axis. The slightly distorted kagome lattice is depicted in (B) with color-coded bond lengths. The square-planar Ni-S coordination environment is shown in (C). The Fmmm (D) and P6₃/mmc (E) band structure show the flat bands close to the Fermi level.

Fig. 2.. Reaction schematics and electron images, and EDX spectroscopy comparing the parent compound to CsNi₃S₄.

(A) Proposed chemical reaction for the synthesis of CsNi₃S₄ with the d⁷ Ni(III) and d⁸ Ni(II) labeled within the chemical formula. Scanning electron microscope images of (B) Cs_2–xNi₃S₄ and (C) CsNi₃S₄. A decrease in cesium content is seen in the (D) EDX spectroscopy comparison. Additional electron microscope image of CsNi₃S₄ emphasizing the delamination of the layers is shown in (E). Panel (F) contains the square-planar molecular orbital diagram for a d⁷ and a d⁸ nickel based on the decrease in cesium shown in (D).

Fig. 3.. HRSTEM images of CsNi₃S₄ viewed along the ac plane (zone [100]).

The inset of (A) shows the distance between three layers of Ni. The inset of (B) shows a defect within the crystal containing the double layer of cesium, which “zippers” into a single layer.

Fig. 4.. PXRD of Cs_2–xNi₃S₄ and CsNi₃S₄.

(A) Cs_2–xNi₃S₄ and (B) CsNi₃S₄ with Rietveld calculated pattern, differences between the experimental and calculated, and Bragg positions. Peaks unable to be fit in (B) are marked with a red asterisk. These peaks are most likely due to cesium defects in the system. The (002) stacking peak is indicated in red for both (A) and (B).

Fig. 5.. Structure models for CsNi₃S₄ from experimental PXRD refinements and calculated band structure.

The stacking direction of the nickel layers sandwiched between single cesium layers can be seen in (A) along with the stacking direction along the c axis. On the basis of the results from the Rietveld refinement and HRSTEM, we included a small amount of Cs disorder in the structural models. The slightly distorted kagome lattice is depicted in (B) with color-coded bond lengths. The square-planar Ni-S coordination environment is shown in (C). The PM (paramagnetic), AFM, and FM II band structures (D to H) shows that the Fermi level resides in the flat bands. For the PM phase (D), irreproducible representations at high-symmetry points are marked, and the orange dots indicate Dirac crossings protected by mirror symmetry. Band structures for magnetic structures remain metallic, but adding a Hubbard U [(F) and (H)] widens the gap along most places of the BZ, unless at those points where mirror symmetry protects Dirac nodes.

Fig. 6.. Magnetometry measurements for Cs _2−xNi₃S₄ and CsNi₃S₄.

Magnetic characterization of both Cs _2−xNi₃S₄ (A to D) and CsNi₃S₄ (E and F). Cs _2−xNi₃S₄ has measurements along both the ab plane [(A) and (B)] and the c axis [(C) and (D)]. Insets shown in (B), (D), and (F) are taken at 1.8 K

Fig. 7.. Electronic transport measurements for Cs _2−xNi₃S₄ and CsNi₃S₄.

Panels (A) and (B) show the resistivity measured for the parent compound and CsNi₃S₄, respectively, with insets emphasizing the two orders of magnitude difference in resistivity at high temperatures between both samples.

Fig. 8.. Heat capacity measurements for Cs _2−xNi₃S₄ and CsNi₃S₄.

C_p/T versus T² of (A) Cs _2−xNi₃S₄ and (B) CsNi₃S₄ with linear fittings.