Observation of competing, correlated ground states in the flat band of rhombohedral graphite
Imre Hagymási, Mohammad Syahid Mohd Isa, Zoltán Tajkov, Krisztián Márity, Oroszlány László, János Koltai, Assem Alassaf, Péter Kun, Konrád Kandrai, András Pálin… 展开作者
Imre Hagymási, Mohammad Syahid Mohd Isa, Zoltán Tajkov, Krisztián Márity, Oroszlány László, János Koltai, Assem Alassaf, Péter Kun, Konrád Kandrai, András Pálinkás, Péter Vancsó, Levente Tapasztó, Péter Nemes-Incze
In crystalline solids the interactions of charge and spin can result in a variety of emergent quantum ground states, especially in partially filled, topological flat bands such as Landau levels or in 'magic-angle' bilayer graphene. Much less explored is rhombohedral graphite (RG), perhaps the simplest and structurally most perfect condensed matter system to host a flat band protected by symmetry. By scanning tunneling microscopy we map the flat band charge density of 8, 10 and 17 layers and identify a domain structure emerging from a competition between a sublattice antiferromagnetic insulator and a gapless correlated paramagnet. Our density-matrix renormalization group calculations explain the observed features and demonstrate that the correlations are fundamentally different from graphene based magnetism identified until now, forming the ground state of a quantum magnet. Our work establishes RG as a new platform to study many-body interactions beyond the mean-field approach, where quantum fluctuations and entanglement dominate.
Rhombohedral graphite features peculiar electronic properties, including persistence of low-energy surface bands of a topological nature. Here, we study the contribution of electron-hole excitations towards inelastic light scattering in thin films of rhombohedral graphite. We show that, in contrast to the featureless electron-hole contribution towards Raman spectrum of graphitic films with Bernal stacking, the inelastic light scattering accompanied by electron-hole excitations in crystals with rhombohedral stacking produces distinct features in the Raman signal which can be used both to identi…
We use an exact analytical technique [Phys. Rev. B \textbf{101}, 115405 (2020), Phys. Rev. B \textbf{102}, 165117 (2020)] to recover the surface Green's functions for Bernal (ABA) and rhombohedral (ABC) graphite. For rhombohedral graphite we recover the predicted surface flat bands. For Bernal graphite we find that the surface state spectral function is similar to the bilayer one, but the trigonal warping effects are enhanced, and the surface quasiparticles have a much shorter lifetime. We subsequently use the T-matrix formalism to study the quasiparticle interference patterns generated on the…
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…
Topological flat bands emerging at the inversion of stacking order in rhombohedral graphite
Comisión Nacional de Energía Atómica (CNEA)（国家原子能委员会）；Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)（国家科学研究委员会）；Universidad Nacional de San Martín（圣马丁国立大学）；Instituto de Nanociencia y Nanotecnología, CNEA-CONICET, GAIDI, Centro Atómico Bariloche and Instituto Balseiro（纳米科学与纳米技术研究所，CNEA-CONICET，GAIDI，巴里洛切原子中心及巴尔塞罗研究所）；Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，格勒诺布尔理工学院，内耳研究所）
Of the two stable forms of graphite, hexagonal (HG) and rhombohedral (RG), the former is more common and has been studied extensively. RG is less stable, which so far precluded its detailed investigation, despite many theoretical predictions about the abundance of exotic interaction-induced physics. Advances in van der Waals heterostructure technology have now allowed us to make high-quality RG films up to 50 graphene layers thick and study their transport properties. We find that the bulk electronic states in such RG are gapped and, at low temperatures, electron transport is dominated by surf…
Enrichment of rhombohedral stacking by mechanical exfoliation of graphite
Hungarian Research Network, Centre for Energy Research（匈牙利研究网络能源研究中心）；MTA - HUN-REN EK Lendület “Momentum” Topology in Nanomaterials Research Group（MTA-HUN-REN EK Lendulet“动量”纳米材料拓扑研究组）；Óbuda University（奥比乌斯大学）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）；ELTE Eötvös Loránd University（罗兰大学）
The electronic structure including energy bands, band weights, and local density of states (LDOS) of interfaces between hexagonal (AB) and rhombohedral (ABC) graphite has been has been calculated. The full-potential local-orbital code (FPLO) and the generalized gradient approximation (GGA) to the density functional theory has been used. Both of the two existing interface structures host (localized) interface bands, which are located around the K-point in the Brillouin zone, and which give rise to strong peaks in the LDOS at the Fermi energy. All interface bands near the Fermi energy are locali…
Topologically non-trivial states characterized by Berry curvature appear in a number of materials ranging from spin-orbit-coupling driven topological insulators to graphene. In multivalley conductors, such as mono- and bilayer graphene, despite a zero total Chern number for the entire Brillouin zone, Berry curvature with different signs concentrated in different valleys can affect the observable material's transport characteristics. Here we consider thin films of rhombohedral graphite, which appear to retain truly two-dimensional properties up to tens of layers of thickness and host two-dimens…
The band structure of ABC-stacked N-layer graphene comprises topologically corresponding flat surface and gapped bulk subbands, as a consequence of the unique stacking configuration. In this paper, the bulk subbands are for the first times ever obtained for arbitrary N. A non-perturbative effective Hamiltonian closed in the bulk subspace is derived and used. The gapped bulk subbands are shown to evolve towards the zero energy with increasing N and in the infinite limit, they touch linearly along a circle. This outcome is a manifestation of the dimensional crossover to a three-dimensional Dirac…
Tunneling atomic force microscopy (TUNA) was used at ambient conditions to measure the current-voltage ($I$-$V$) characteristics at clean surfaces of highly oriented graphite samples with Bernal and rhombohedral stacking orders. The characteristic curves measured on Bernal-stacked graphite surfaces can be understood with an ordinary self-consistent semiconductor modeling and quantum mechanical tunneling current derivations. We show that the absence of a voltage region without measurable current in the $I$-$V$ spectra is not a proof of the lack of an energy band gap. It can be induced by a surf…
One-way electron mirrors from single-layer stacking shifts in rhombohedral graphite
Hungarian Research Network, HUN-REN Centre for Energy Research, Institute of Technical Physics and Materials Science（匈牙利研究网络，HUN-REN能源研究中心，技术物理与材料科学研究所）；Department of Physics, Institute of Physics, Budapest University of Technology and Economics（布达佩斯技术与经济大学，物理系，物理研究所）；MTA - HUN-REN EK Lendület “Momentum” Topology in Nanomaterials Research Group（匈牙利科学院-HUN-REN EK Lendület “Momentum”纳米材料拓扑研究组）；ELTE, Eötvös Loránd University（厄特沃什·罗兰大学）；Óbuda University（奥比杜斯大学）
Electrostatically stabilized surface flat bands in rhombohedral graphite at zero displacement field
Aalto University School of Science（阿尔托大学理学院）；University of California at Santa Barbara（加州大学圣塔芭芭拉分校）；National High Magnetic Field Laboratory（国家高磁场实验室）；Florida State University（佛罗里达州立大学）
Few layer graphene (FLG) has been recently intensively investigated for its variable electronic properties defined by a local atomic arrangement. While the most natural layers arrangement in FLG is ABA (Bernal) stacking, a metastable ABC (rhombohedral) stacking characterized by a relatively high energy barrier can also occur. When both stacking occur in the same FLG device this results in in-plane heterostructure with a domain wall (DW). We show that ABC stacking in FLG can be controllably and locally turned into ABA stacking by two following approaches. In the first approach, Joule heating wa…
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 …
Competing Orders Driven by Wigner Crystal Phase in Rhombohedral Graphene
Institute of Physics, Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院物理研究所）；SPEC, CEA, CNRS, Université Paris-Saclay（法国原子能和替代能源委员会、国家科学研究中心、萨克雷大学SPEC实验室）；Department of Physics, Florida State University（佛罗里达州立大学物理系）；National High Magnetic Field Laboratory（国家高磁场实验室）；FSU Quantum Initiative, Florida State University（佛罗里达州立大学FSU量子倡议项目）；Research Center for Functional Materials, National Institute for Materials Science（日本物质材料研究机构功能材料研究中心）
Competing Chern states revealed by quasiparticle charging in moiré rhombohedral graphene
Cornell University（康奈尔大学）；Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构与动力学研究所）；Massachusetts Institute of Technology（麻省理工学院）；Florida State University（佛罗里达州立大学）；National Institute for Materials Science（国立材料研究所）
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 …
Novel systems of layered graphene are attracting interest for theories and applications. The stability, band structures of few-layer graphite films, and their dependence on electric field applied along the c-axis are examined within the density functional theory. We predict that those of Bernal type and also rhombohedral type tri- and tetra-layer graphite films exhibit stability. The rhombohedral-type systems including AB-bilayer, show variable band gap induced by perpendicular electric field, whereas the other systems such as the Bernal-type films stay semi-metallic.
Low-energy electronic properties of ABC-stacked graphite are studied by the tight-binding model. There are linear and parabolic bands with and without degeneracy. They show strongly anisotropic dispersions. ABC-stacked grahite is a semimetal due to slight overlapping near the Fermi level beween conduction and valence bands. The interlayer interactions could change the energy dispersion, state degeneracy, and positions of band-crossing and band-edge state. Density of states exhibit a shoulder structure, owing to band-edge states near or at high symmetric points. Low-frequency Coulomb excitation…
We analyze the electronic properties of a simple stacking defect in Bernal graphite. We show that a bound state forms, which disperses as $|\bfk-\bfK|^3$ in the vicinity of either of the two inequivalent zone corners $\bfK$. In the presence of a strong c-axis magnetic field, this bound state develops a Landau level structure which for low energies behaves as $E\nd_n\propto |n B|^{3/2}$. We show that buried stacking faults have observable consequences for surface spectroscopy, and we discuss the implications for the three-dimensional quantum Hall effect (3DQHE). We also analyze the Landau level…
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）
Ferromagnetism is most common in transition metal compounds but may also arise in low-density two-dimensional electron systems, with signatures observed in silicon, III-V semiconductor systems, and graphene moiré heterostructures. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene drive the spontaneous ferromagnetic polarization of the electron system into one or more spin- and valley flavors. Using capacitance measurements on graphite-gated van der Waals heterostructures, we find a cascade of density- and electronic displacement field tuned phase transitions…
Horizontal shifts in the top layer of highly oriented pyrolytic graphite, induced by a scanning tunneling microscope (STM) tip, are presented. Excellent agreement is found between STM images and those simulated using density functional theory. First-principle calculations identify that the low-energy barrier direction of the top layer displacement is toward a structure where none of the carbon pz orbitals overlap, while the high-energy barrier direction is toward AA stacking. Each directional shift yields a real-space surface charge density similar to graphene; however the low-energy barrier d…
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…
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）
Combining mean-field and renormalization group analyses, here we unveil the nature of recently observed superconductivity and parent metallic states in chemically doped rhombohedral trilayer graphene, subject to external electric displacement fields ($D$) [H. Zhou, \emph{et al.}, Nature (London) {\bf 598}, 434 (2021)]. We argue that close to the charge neutrality, on site Hubbard repulsion favors layer antiferromagnet, which when combined with the $D$-field induced layer polarization, produces a spin-polarized, but valley-unpolarized half-metal, conducive to the nucleation of spin-triplet $f$-…
Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
Several experiments have recently found room-temperature ferromagnetism in graphite-like carbon based materials. This paper offers a model explaining such ferromagnetism by using an asymmetric nano-graphene. Our first typical model is C48H24 graphene molecule, which has three dihydrogenated (-CH2) zigzag edges. There are several multiple spin states competing for stable minimum energy in the same atomic topology. Both molecular orbital and density function theory methods indicate that the quartet state(S=3/2) is more stable than that of doublet (S=1/2), which means that larger saturation magne…
A DFT-based investigation of rhombohedral (ABC)-type graphene stacks in finite static electric fields is presented. Electronic band structures and field-induced charge densities are compared with related literature data as well as with own results on (AB) stacks. It is found, that the undoped AB-bilayer has a tiny Fermi line consisting of one electron pocket around the K-point and one hole pocket on the line K-$Γ$. In contrast to (AB) stacks, the breaking of translational symmetry by the surface of finite (ABC) stacks produces a gap in the bulk-like states for slabs up to a yet unknown critica…
Divergent density of states offers the unique opportunity to explore a wide variety of correlated electron physics. In the thinnest limit, this has been predicted and verified in the ultra-flat bands of magic-angle twisted bilayer graphene, the band touching points of few-layer rhombohedral graphite, and the lightly doped rhombohedral trilayer graphene. The simpler and seemingly better understood Bernal bilayer graphene is also susceptible to orbital magnetism-driven phases at charge neutrality, such as layer antiferromagnet and quantum anomalous Hall octet. Here we report the discovery of a c…
Thermodynamic evidence for interaction-driven first-order topological quantum phase transitions
Weizmann Institute of Science（魏茨曼科学研究所）；University of Texas at Dallas（德克萨斯大学达拉斯分校）；Massachusetts Institute of Technology（麻省理工学院）；Florida State University（佛罗里达州立大学）；University of Colorado Denver（科罗拉多大学丹佛分校）；National Institute for Materials Science（国立材料研究所）
In recent times, trilayer graphene has attracted wide attention owing to its stacking and electric field dependent electronic properties. However, a direct and well-resolved experimental visualization of its band structure has not yet been reported. In this work, we present angle resolved photoemission spectroscopy (ARPES) data which show with high resolution the electronic band structure of trilayer graphene obtained on α-SiC(0001) and β-SiC(111) via hydrogen intercalation. Electronic bands obtained from tight-binding calculations are fitted to the experimental data to extract the interatomic…
The theoretical description of sparse matter attracts much interest, in particular for those ground-state properties that can be described by density functional theory (DFT). One proposed approach, the van der Waals density functional (vdW-DF) method, rests on strong physical foundations and offers simple yet accurate and robust functionals. A very recent functional within this method called vdW-DF-cx [K. Berland and P. Hyldgaard, Phys. Rev. B 89, 035412] stands out in its attempt to use an exchange energy derived from the same plasmon-based theory from which the nonlocal correlation energy wa…
Electrons with large kinetic energy have a superconducting instability for infinitesimal attractive interactions. Quenching the kinetic energy and creating a flat band renders an infinitesimal repulsive interaction the relevant perturbation. Thus, flat band systems are an ideal platform to study the competition of superconductivity and magnetism and their possible coexistence. Recent advances in the field of twisted bilayer graphene highlight this in the context of two-dimensional materials. Two dimensions, however, put severe restrictions on the stability of the low-temperature phases due to …
