Observation of an isolated flat band in the van der Waals crystal NbOCl$_2$

Abstract

Dispersionless electronic bands lead to an extremely high density of states and suppressed kinetic energy, thereby increasing electronic correlations and instabilities that can shape emergent ordered states, such as excitonic, ferromagnetic, and superconducting phases. A flat band that extends over the entire momentum space and is well isolated from other dispersive bands is, therefore, particularly interesting. Here, the band structure of the van der Waals crystal NbOCl$_2$ is revealed by utilizing photoelectron momentum microscopy. We directly map out an electronic band that is flat throughout the entire Brillouin zone and features a width of only $\sim$100 meV. This band is well isolated from both the conduction and remote valence bands. Moreover, the quasiparticle band gap shows a high tunability upon the deposition of caesium atoms on the surface. By combining the single-particle band structure with the optical transmission spectrum, the optical gap is identified. The fully isolated flat band in a van der Waals crystal provides a qualitatively new testbed for exploring flat-band physics.

Figures (4)

• Figure Fig. 1: $\bm{|}$ NbOCl$_2$ as a potential host of flat bands.a, b, Crystal structure of the van der Waals crystal NbOCl$_2$ from side and top views. c, The surface Brillouin zone with labeled high-symmetry points. d, e, Ideal square lattice of Nb atoms without Peierls distortion (d). The green shadows represent the Nb 4$d_z^2$ orbitals, whose overlap results in a partially flat band as schematically shown in e. f, g, Realistic rectangular lattice of Nb atoms with a Peierls distortion (f) and corresponding ideal flat band as schematically shown in g owing to the band folding and gap opening. The dashed curves are dispersions without gap opening.
• Figure Fig. 2: $\bm{|}$ Observation of an isolated flat band throughout the entire Brillouin zone.a, Dispersion image along the Z-$\Gamma$-Z direction and corresponding integrated energy distribution curve (EDC). The color scale is enhanced above -0.8 eV and the EDC is multiplied by 1000 for better visibility of the weak signal of the CB. The peak width of the flat band is larger than the energy resolution possibly owing to the intrinsic broadening or roughness of the cleaved surface. b, Curvature-filtered dispersion map in 2D momentum space. The color scale indicates photoelectron intensity processed by the 1D curvature filter along the energy direction. c, Full dispersion images along all high-symmetry momentum directions in the entire Brillouin zone. The color scale indicates photoelectron intensity in a and c. d, Extracted dispersion of the flat band across the Brillouin zone from the data in c.
• Figure Fig. 3: $\bm{|}$ Revealing the quasiparticle band gap by caesium deposition.a-d, Dispersion images along the Z-$\Gamma$-Z direction at different caesium deposition stages. A logarithmic color scale is used to clearly show the CB. e, Integrated EDCs across momentum space from the data in a-d. The inset shows a zoom-in around the Fermi level, highlighting the CB. f, Extracted energy positions of the CB and the flat band as a function of deposition time. The thick curves are guides to the eye. g, Band gap extracted from the energy difference between the CB and the flat band. The thick curve is a guide to the eye.
• Figure Fig. 4: $\bm{|}$ Anisotropic optical gap.a, b, Optical extinction spectrum for light polarized along the b-axis (a) and the c-axis (b). c, Optical extinction map as a function of light polarization and photon energy. The corresponding crystal orientations are labeled. d, Schematic band structure with experimentally determined bottom of CB, flat band, and band edge of the remote VBs. The observed optical gap is indicated by the red arrow.