Flat bands and nontrivial topology are two important topics in condensed matter physics. It is important to find material systems with both flat bands and nontrivial topology to realize novel physical effects. Recently, Professor Shuyun Zhou from the Department of Physics at Tsinghua University and collaborators reported the topological flat bands in rhombohedral graphite (RG). They found that RG is a topological nodal line semimetal, and its flat band topological surface state is protected by the bulk topological Dirac nodal lines. Moreover, through the exotic behavior of the flat band upon electron doping, they revealed the electron correlation effect in RG. This result titled "Correlated topological flat bands in rhombohedral graphite" was published online in the "Proceedings of the National Academy of Sciences" (PNAS) on October 16, 2024.
In RG, the carbon atomic layers translate along the C-C bond between adjacent layers, forming the rhombohedral stacking structure (ABC stacking) as shown in Figure 1a. This special structure makes the electronic structure of few-layer RG highly tunable by electric field, and it exhibits novel physical properties such as fractional quantum anomalous Hall effect. The electronic density of states near the Fermi energy is exponentially related to the momentum in RG (the exponential index is determined by the number of layers), leading to even flatter bands and higher density of states in bulk RG than that of few-layer RG. In addition, the nearest neighbor interaction of RG is analogous to the one-dimensional Su-Schrieffer-Heeger (SSH) topology model. Therefore, RG is expected to achieve both flat bands and nontrivial topological physics. Although this system has rich physics, its electronic band structure is not explored, and the physics of flat band and correlation in such system remains largely elusive.
Figure 1: Crystal structure and topological flat band surface states of RG. (a) The side view of RG atomic structure, where t0 and γ0 are the parameters of the in-plane and out-of-plane nearest neighbor hopping parameters. The lower left corner is the schematic of one-dimensional SSH model. (b) ARPES detected topological flat bands (indicated by red arrows) and bulk Dirac cones (indicated by black arrows). (c) Schematic drawing of the Dirac nodal line formed by the node of bulk Dirac cone and the "drum-dead" topological surface state.
With great effort, Shuyun Zhou’s group prepared successfully high-quality RG samples, and then performed Angle-resolved photoemission spectroscopy (ARPES/NanoARPES) measurements. Together with their collaborators, this team revealed for the first time the topological flat band electronic structure and correlation effects in RG. They found that the bulk states exhibit a Dirac cone band structure (indicated by the black arrow in Figure 1b) and nodes of the Dirac cone form a helical nodal line in the kx-ky-kz three-dimensional momentum space (Figure 1c), indicating that RG is a topological nodal line semimetal. Moreover, a clear flat band (indicated by the red arrow in Figure 1b) was observed near the Fermi energy. By combining the experimental and theoretical results, they found that the flat band corresponds to the surface state of the topological nodal line semimetal, known as the "drum-head" surface state (see Figure 1c), and the topological surface state is protected by the bulk topological Dirac nodal lines.
More interestingly, the topological flat band exhibits exotic behavior upon surface electron doping (Figure 2). The flat band shows splitting after doping, and the bandwidth of the lower flat band increases significantly upon increasing electron doping (red arrow), while the bandwidth and energy of the upper flat band near the Fermi energy remain almost unchanged (orange arrow). The Hartree-Fock calculations reveal the existence of electron correlation effect in RG, but the pinning of flat band near the Fermi energy indicates that correlation effect beyond the mean field theory needs to be considered.
These results reveal the topological flat bands and correlation effects in RG, and lay an important foundation for further exploring the novel physical properties of the coexistence of nontrivial topology and correlation.
Figure 2: Evolution of flat band upon surface electron doping. (a-c) Evolution of the flat band electronic structure of RG upon surface electron doping. (d-f) Schematic drawing of the band evolution.
Professor Shuyun Zhou from the Department of Physics at Tsinghua University is the corresponding author. Hongyun Zhang, a "Shuimu-Tsinghua Scholar" from the Department of Physics at Tsinghua University, and Qian Li, a graduated PhD at 2024, are the co-first authors of the paper. Collaborators include Professor Biao Lian from Princeton University, Professor Wenhui Duan, Professor Hong Yao, Professor Pu Yu and Professor Yong Xu from the Department of Physics at Tsinghua University, Professor Peizhe Tang from Beihang University, etc. This study was carried out at beamline BL403 at the Advanced light source, beamline BL03U at the Shanghai Synchrotron Radiation Facility, the ANTARES NanoARPES beamline at Synchrotron SOLEIL in France, and in-house facility at Tsinghua University. This research work has been supported by the National Key Research and Development Program of the Ministry of Science and Technology (2021YFA1400100), the Key Project of the National Natural Science Foundation of China, the Basic Science Center Project, the "Shuimu-Tsinghua Scholar" Program and the Postdoctoral Surface Project of Tsinghua University.
Link of the paper：https://www.pnas.org/doi/10.1073/pnas.2410714121
