We study the mean-field broken symmetry phases of charge neutral multilayer rhombohedral graphene within tight-binding approximations including self-consistent extended Hubbard interactions. We used on-site and inter-site Hubbard interactions obtained from a newly developed first-principles calculation method. Our calculations for systems up to eight layers give rise to electron-hole asymmetries, band flatness, band gaps, and layer anti-ferromagnetic ground states in keeping with available experiments. By including the intersite Hubbard interactions up to the next-nearest neighboring sites, the band gaps are shown to open when the number of layers is larger than three, while the trilayer system maintains its metallic nature with two low energy density of state peaks near the Fermi energy whose separation increases with the range of inter-site Hubbard parameters. Within our framework, the calculated band gaps reflect mean-field ground states with extended Hubbard interactions, in closer agreement with experimental estimates. The tight-binding formulation further enables efficient treatment of large rhombohedral chiral systems, including twisted multilayer graphene.
Graphene layers are known to stack in two stable configurations, namely ABA or ABC stacking, with drastically distinct electronic properties. Unlike the ABA stacking, little has been done to experimentally investigate the electronic properties of ABC graphene multilayers. Here, we report the first magneto optical study of a large ABC domain in a graphene multilayers flake, with ABC sequences exceeding 17 graphene sheets. The ABC-stacked multilayers can be fingerprinted with a characteristic electronic Raman scattering response, which persists even at room temperatures. Tracing the magnetic fie…
We study the electronic structure of multilayer graphenes with a mixture of Bernal and rhombohedral stacking and propose a general scheme to understand the electronic band structure of an arbitrary configuration. The system can be viewed as a series of finite Bernal graphite sections connected by stacking faults. We find that the low-energy eigenstates are mostly localized in each Bernal section, and, thus, the whole spectrum is well approximated by a collection of the spectra of independent sections. The energy spectrum is categorized into linear, quadratic and cubic bands corresponding to sp…
Charge carriers in single and multilayered graphene systems behave as chiral particles due to the particular lattice symmetry of the crystal. We show that the interplay between the meta-material properties of graphene multilayers and the pseudospinorial properties of the charge carriers result in the occurrence of Klein and anti-Klein tunneling for rhombohedral stacked multilayers. We derive an algebraic formula predicting the angles at which these phenomena occur and support this with numerical calculations for systems up to four layers. We present a decomposition of an arbitrarily stacked mu…
There has been a lot of excitement around the observation of superconductivity in twisted bilayer graphene, associated to flat bands close to the Fermi level. Such correlated electronic states also occur in multilayer rhombohedral stacked graphene (RG), which has been receiving increasing attention in the last years. In both natural and artificial samples however, multilayer stacked Bernal graphene (BG) occurs more frequently, making it desirable to determine what is their relative stability and under which conditions RG might be favored. Here, we study the energetics of BG and RG in bulk and …
Layer-Number-Controlled Symmetry Breaking and Surface-State Transport in Rhombohedral Graphene Multilayers
State Key Laboratory of Micro-nano Engineering Science, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute and School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Department of Quantum Matter Physics, University of Geneva（日内瓦大学量子物质物理系）；Department of Physics, University of Seoul（首尔大学物理系）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（国家材料科学研究所电子光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（国家材料科学研究所材料纳米架构研究中心）；Department of Smart Cities, University of Seoul（首尔大学智慧城市系）
Stackings in graphene have a pivotal role in properties to be discussed in the future, as seen in the recently found superconductivity of twisted bilayer graphene. Beyond bilayer graphene, the stacking order of multilayer graphene can be rhombohedral, which shows flat bands near the Fermi level that are associated with interesting phenomena, such as tunable conducting surface states expected to exhibit spontaneous quantum Hall effect, surface superconductivity, and even topological order. However, the difficulty in exploring rhombohedral graphenes is that in experiments, the alternative, hexag…
The low-energy physics of rhombohedral $N$-layer graphene mainly arises on the external layers, where most of the π electrons are located. Their Bloch band structure defines a two-band semimetal; the dispersion relation scales as $\pm q^{N}$ with the momentum norm $q$ in the vicinity of two nonequivalent valleys. In this paper, we address the problem of elastic scattering through a localized impurity located either on the surface of the material or within the bulk, and focus on the quantum interferences it induces on the two external layers. It is apprehended in the framework of a $T$-matrix a…
Multilayer graphene with rhombohedral and Bernal stacking are supposed to be metallic, as predicted by density functional theory calculations using semi-local functionals. However recent angular resolved photoemission and transport data have questioned this point of view. In particular, rhombohedral flakes are suggested to be magnetic insulators. Bernal flakes composed of an even number of layers are insulating, while those composed of an odd number of layers are pseudogapped. Here, by systematically benchmarking with plane waves codes, we develop very accurate all-electron Gaussian basis sets…
Charge imprinting biases topology of correlated insulator in hBN-aligned rhombohedral multilayer graphene
University of Chinese Academy of Sciences（中国科学院大学）；Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院理论科学 kavli 研究所）；ShanghaiTech University（上海科技大学）；Liaoning Academy of Materials（辽宁省材料研究院）
Using a numerical tight-binding approach based on the Chebyshev-Bogoliubov-de Gennes method we describe Josephson junctions made of multilayer graphene contacted by top superconducting gates. Both Bernal (ABA) and rhombohedral (ABC) stacking are considered and we find that the type of stacking has a strong effect on the proximity effect and the supercurrent flow. For both cases the pair amplitude shows a polarization between dimer and non-dimer atoms, being more pronounced for rhombohedral stacking. Even though the proximity effect in non-dimer sites is enhanced when compared to single layer g…
Rhombohedral multilayer graphene is a physical realization of the chiral two-dimensional electron gas that can host zero-line modes (ZLMs), also known as kink states, when the local ap opened by inversion symmetry breaking potential changes sign in real space. Here we study how the variations in the local stacking coordination of multilayer graphene affects the formation of the ZLMs. Our analysis indicates that the valley Hall effect develops whenever an interlayer potential difference is able to open up a band gap in stacking faulted multilayer graphene, and that ZLMs can appear at the domain…
Spin-polarized Superconductivity and High-Chern Insulators in Twisted Rhombohedral Graphene Family
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；State Key Laboratory for Mesoscopic Physics, Frontiers Science Centre for Nano-optoelectronics, School of Physics, Peking University（北京大学物理学院介观物理国家重点实验室纳米光电子前沿科学中心）；Research Center for Electronic and Optical Materials, National Institute for Material Science（日本国立物质材料研究所电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Material Science（日本国立物质材料研究所材料纳米结构研究中心）；Interdisciplinary Institute of Light-Element Quantum Materials and Research Centre for Light-Element Advanced Materials, Peking University（北京大学轻元素量子材料交叉研究院轻元素先进材料研究中心）
We apply the mean-field Hartree Fock theory of gapped electronic states at charge neutrality in bilayer graphene to thin films of rhombohedral graphite with up to thirty layers. For the ground state, the order parameter (the separation of bands at the valley center) saturates to a constant non-zero value as the layer number increases, whereas the band gap decreases with layer number. We consider chiral symmetry breaking disorder in the form of random layer potentials and chiral preserving disorder in the form of random values of the interlayer coupling. The former reduces the magnitude of the …
The crystal structure of solid-state matter greatly affects its electronic properties. For example in multilayer graphene, precise knowledge of the lateral layer arrangement is crucial, since the most stable configurations, Bernal and rhombohedral stacking, exhibit very different electronic properties. Nevertheless, both stacking orders can coexist within one flake, separated by a strain soliton that can host topologically protected states. Clearly, accessing the transport properties of the two stackings and the soliton is of high interest. However, the stacking orders can transform into one a…
The thermodynamic properties of the electron gas in multilayer graphene depend strongly on the number of layers and the type of stacking. Here we analyse how those properties change when we vary the number of layers for rhombohedral stacked multilayer graphene and compare our results with those from a conventional two dimensional electron gas. We show that the highly degenerate zero energy Landau level which is partly filled with electrons and partly with holes has a strong influence on the value of the different thermodynamic quantities.
Multiple Superconducting Phases in Rhombohedral Heptalayer Graphene
State Key Laboratory of Micro-nano Engineering Science, Tsung-Dao Lee lnstitute & School of Physics and Astronomy, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai Jiao Tong University（上海交通大学微纳电子学系、李政道理论与研究学院、人工结构量子控制教育部重点实验室）；National Institute for Materials Science（国立材料研究所）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区（广东）量子科学中心）；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）
Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
Fermi lune and non-reciprocal transport in rhombohedral multilayer graphene
ShanghaiTech University（上海科技大学）；Nanjing University（南京大学）；Southern University of Science and Technology（南方科技大学）；National Institute for Materials Science（物质材料研究机构）；Fudan University（复旦大学）；Peking University（北京大学）；Liaoning Academy of Materials（辽宁省材料科学研究院）
One-Step Epitaxial Access to Rhombohedral Graphene Flat-Band States on Step-Bunched SiC
Institute for Advanced Studies, Wuhan University（武汉大学高等研究院）；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）；School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）
Chiral superconductors and competing states across a Lifshitz transition in rhombohedral pentalayer graphene
Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大东京大学研究院）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；University of Tennessee（田纳西大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；National Institute for Materials Science（物质材料研究机构）；Hefei National Laboratory（合肥国家实验室）；Wuhan University（武汉大学）；Southern University of Science and Technology（南方科技大学）
Multi-layer graphene with rhombohedral stacking is a promising carbon phase possibly displaying correlated states like magnetism or superconductivity due to the occurrence of a flat surface band at the Fermi level. Recently, flakes of thickness up to 17 layers were tentatively attributed ABC sequences although the Raman fingerprint of rhombohedral multilayer graphene is currently unknown and the 2D resonant Raman spectrum of Bernal graphite not understood. We provide a first principles description of the 2D Raman peak in three and four layers graphene (all stackings) as well as in Bernal, rhom…
We investigate the competition between acoustic-phonon-mediated superconductivity and the long-range Coulomb interaction in moiréless graphene multilayers, specifically, Bernal bilayer graphene, rhombohedral trilayer graphene, and ABCA-stacked tetralayer graphene. In these graphene multilayers, the acoustic phonons can realize, through electron-phonon coupling, both spin-singlet and spin-triplet pairings, and the intra-sublattice pairings ($s$-wave spin-singlet and $f$-wave spin-triplet) are the dominant channels. Our theory naturally explains the distinct recent experimental findings in Berna…
The discovery of superconductivity and correlated electronic states in the flat bands of twisted bilayer graphene has raised a lot of excitement. Flat bands also occur in multilayer graphene flakes that present rhombohedral (ABC) stacking order on many consecutive layers. Although Bernal-stacked (AB) graphene is more stable, long-range ABC-ordered flakes involving up to 50 layers have been surprisingly observed in natural samples. Here we present a microscopic atomistic model, based on first-principles density functional theory calculations, that demonstrates how shear stress can produce long-…
Tunable high-Chern-number Chern insulators in rhombohedral tetralayer graphene/hBN moiré superlattices
State Key Laboratory of Micro-nano Engineering Science, Tsung-Dao Lee lnstitute & School of Physics and Astronomy, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai Jiao Tong University（上海交通大学微纳电子工程科学国家重点实验室、李政道研究所及物理与天文学院人工结构与量子控制教育部重点实验室）；Department of Physics, City University of Hong Kong（香港城市大学物理系）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（国家材料研究所电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（国家材料研究所材料纳米结构研究中心）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）；Department of Physics, Hong Kong University of Science and Technology（香港科技大学物理系）
Valley Valves at Domain Walls in Symmetry-Broken Rhombohedral Graphene
Florida State University（佛罗里达州立大学）；National High Magnetic Field Laboratory（国家高磁场实验室）；Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC（马德里材料科学研究所，西班牙国家研究委员会）；IMDEA Nanoscience（IMDEA纳米科学研究所）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；University of Pennsylvania（宾夕法尼亚大学）
