Flat Chern Band in a Two-Dimensional Organometallic Framework

By combining exotic band dispersion with nontrivial band topology, an interesting type of band structure, namely, the flat Chern band, has recently been proposed to spawn high-temperature fractional quantum Hall states. Despite the proposal of several theoretical lattice models, however, it remains doubtful whether such a “romance of flatland” could exist in a real material. Here, we present a first-principles design of a two-dimensional indium-phenylene organometallic framework that realizes a nearly flat Chern band right around the Fermi level by combining lattice geometry, spin-orbit coupling, and ferromagnetism. An effective four-band model is constructed to reproduce the first-principles results. Our design, in addition, provides a general strategy to synthesize topologically nontrivial materials by virtue of organic chemistry and nanotechnology.

Figure 1

(a) The atomic structure of the IPOF. (b) The first Brillouin zone and special $k$ points. (c) (Left) Band structure without SOC from DFT [solid (blue) curves] and the model Hamiltonian Eq. (8) with $t_1=0.7\mathrm{eV}$, $\lambda =0$, $M=0$ [dashed (red) curves]. The insets are the wave function isosurfaces of the two states denoted by arrows. (Right) Atomic-orbital projected density of states.

Figure 2

(a) Band structure with SOC. (b) Band structure with SOC when doping one hole into the unit cell. The solid (blue) curves are DFT results. The dashed (red) curves are from model Hamiltonian Eq. (8) with parameters (a) $t_1=0.7\mathrm{eV}$, $\lambda =0.05\mathrm{eV}$, $M=0$; (b) $t_1=0.7\mathrm{eV}$, $\lambda =0.05\mathrm{eV}$, $M=0.1\mathrm{eV}$. (c) Zoomed-in band plot around the Fermi level. (d) Momentum-resolved edge density of states of a semi-infinite IPOF with SOC and doping. The brightness is proportional to the magnitude of the density of states. (e) Distribution of the Berry curvature $F_{12}(\mathbf{k})$ of the top flat band in the reciprocal space. On the left is the DFT result; on the right is the model result using the same parameters as in (b).