We investigate the occurrence of magnetic and charge density wave instabilities in rhombohedral-stacked multilayer (three to eight layers) graphene by first principles calculations including exact exchange. Neglecting spin-polarization, an extremely flat surface band centered at the special point ${\bf K}$ of the Brillouin zone occurs at the Fermi level. Spin polarization opens a gap in the surface state by stabilizing an antiferromagnetic state. The top and the bottom surface layers are weakly ferrimagnetic in-plane (net magnetization smaller than $10^{-3}μ_B$), and are antiferromagnetic coupled to each other. This coupling is propagated by the out-of-plane antiferromagnetic coupling between the nearest neighbors. The gap is very small in a spin-polarized generalized gradient approximation, while it is proportional to the amount of exact exchange in hybrid functionals. For trilayer rhombohedral graphene it is $38.6$ meV in PBE0, in agreement with the $42$ meV gap found in experiments. We study the temperature and doping dependence of the magnetic gap. At electron doping of $n \sim 7 \times 10^{11}$ cm$^{-2}$ the gap closes. Charge density wave instabilities with $\sqrt{3}\times\sqrt{3}$ periodicity do not occur.
In rhombohedral-stacked few-layer graphene, the very flat energy bands near the charge neutrality point are unstable to electronic interactions, giving rise to states with spontaneous broken symmetries. Using transport measurements on suspended rhombohedral-stacked tetralayer graphene, we observe an insulating ground state with a large interaction-induced gap up to 80 meV. This gapped state can be enhanced by a perpendicular magnetic field, and suppressed by an interlayer potential, carrier density, or a critical temperature of ~ 40 K.
The crystallographic stacking order in multilayer graphene plays an important role in determining its electronic properties. It has been predicted that a rhombohedral (ABC) stacking displays a conducting surface state with flat electronic dispersion. In such a flat band, the role of electron-electron correlation is enhanced possibly resulting in high Tc superconductivity, charge density wave or magnetic orders. Clean experimental band structure measurements of ABC stacked specimens are missing because the samples are usually too small in size. Here, we directly image the band structure of larg…
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-…
The discovery of interfacial ferroelectricity in two-dimensional rhombohedral (3R)-stacked semiconductors opens up a new pathway for achieving ultrathin computing-in-memory devices. However, exploring ferroelectricity switching in natural 3R crystals is difficult due to lack of co-existing 3R stacking domains. Here, we present that MoS2 homoepitaxial patterns with 3R polytypic domains can manifest switchable ferroelectricity at room-temperature. Based on the diffusion limited aggregation theory, such MoS2 patterns are formed under the low Mo chemical potential and low temperature with respect …
Rhombohedral-stacked few-layer graphene (FLG) has been receiving an ever-increasing attention owing to its peculiar electronic properties that could lead to enticing phenomena such as superconductivity and magnetic ordering. Up to now, experimental studies on such material have been mainly limited by the difficulty in isolating it in thickness exceeding 3 atomic layers with device-compatible size. In this work, rhombohedral graphene with thickness up to 9 layers and areas up to ~50 micrometers square is grown via chemical vapor deposition (CVD) on suspended Cu foils and transferred onto target…
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…
Van der Waals (vdW) materials have greatly expanded our design space of heterostructures by allowing individual layers to be stacked at non-equilibrium configurations, for example via control of the twist angle. Such heterostructures not only combine characteristics of the individual building blocks, but can also exhibit emergent physical properties absent in the parent compounds through interlayer interactions. Here we report on a new family of emergent, nanometer-thick, semiconductor 2D ferroelectrics, where the individual constituents are well-studied non-ferroelectric monolayer transition …
We investigate electrical conduction and breakdown behavior of 3D nano-carbon-stacked multilayer graphene (s-MLG) system with complete interlayer decoupling. The s-MLG is prepared by transferring and stacking large-area CVD-grown graphene monolayers, followed by wire patterning and plasma etching. Raman spectroscopy was used to confirm the layer number. The D-band peak indicates low defect level in the samples. Electrical current stressing induced doping is performed to shift the charge-neutrality Dirac point and decrease the graphene/metal contact resistance, improving the overall electrical …
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 …
Single-layer $\it{h}$-BN is known to have edges with unique magnetism, however, in the commonly fabricated multilayer $\text{AA}^{\prime}$-$\it{h}$-BN, edge relaxations occur that create interlayer bonds and eliminate the unpaired electrons at the edge. Recently, a robust method of growing the unconventional Bernal-stacked $\it{h}$-BN (AB-$\it{h}$-BN) has been reported. Here, we use theoretical approaches to investigate the nitrogen-terminated zigzag edges in AB-$\it{h}$-BN that can be formed in a controlled fashion using a high-energy electron beam. We find that these "open" edges remain inta…
We report the synthesis of AB-stacked multilayer graphene via ambient pressure chemical vapor deposition on Cu foils, and demonstrate a method to construct suspended multilayer graphene devices. In four-terminal geometry, such devices were characterized by hot carrier transport at temperatures down to 240 mK and in magnetic fields up to 14 T. The differential conductance (dI/dV) shows a characteristic dip at longitudinal voltage bias V=0 at low temperatures, indicating the presence of hot electron effect due to a weak electron-phonon coupling. Under magnetic fields, the magnitude of the dI/dV …
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 …
Hexagonal La$_2$Ni$_7$ and rhombohedral Y$_2$Ni$_7$ are weak itinerant antiferromagnet (wAFM) and ferromagnet (wFM), respectively. The crystal structure and magnetic properties of $A_2B_7$ intermetallic compounds ($A$ = La, Y, $B$ = Ni) have been investigated combining X-ray powder diffraction and magnetic measurements. The La$_{2-x}$Y$_x$Ni$_7$ intermetallic compounds with $0 \leq x \leq 1$ crystallize in the Ce$_{2}$Ni$_7$-type hexagonal structure with Y preferentially located in the [$AB_2$] units. The compounds with larger Y content ($1.2 \leq x < 2$) crystallize in both hexagonal and rhom…
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…
When single-layer h-BN is subjected to a high-energy electron beam, triangular pores with nitrogen edges are formed. Because of the broken sp2 bonds, these pores are known to possess magnetic states. We report on the magnetism and electronic structure of triangular pores as a function of their size. Moreover, in the Bernal-stacked h-BN (AB-h-BN), multilayer pores with parallel edges can be created, which is not possible in the commonly fabricated multilayer AA'-h-BN. Given that these pores can be manufactured in a well-controlled fashion using an electron beam, it is important to understand th…
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）
Chirally stacked $N$-layer graphene is a semimetal with $\pm p^N$ band-touching at two nonequivalent corners in its Brillioun zone. We predict that an off-resonant circularly polarized light (CPL) drives chirally stacked $N$-layer graphene into a Floquet Chern Insulators (FCIs), a.k.a. quantum anomalous Hall insulators, with tunable high Chern number $C_F=\pm N$ and large gaps. A topological phase transition between such a FCI and a valley Hall (VH) insulator with high valley Chern number $C_v=\pm N$ induced by a voltage gate can be engineered by the parameters of the CPL and voltage gate. We …
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 intrinsic resistance peak (ridge) structures were recently found to appear in the carrier density dependence plot of the resistance of the AB-stacked multilayer graphene with even numbers of layers.The ridges are due to topological changes in the Fermi surface. Here, these structures were studied in AB-stacked multilayer graphene with odd numbers of layers (5 and 7 layers) by performing experiments using encapsulated high-quality graphene samples equipped with top and bottom gate electrodes.The intrinsic resistance peaks that appeared on maps plotted with respect to the carrier density and…
The electronic band structure of ABC-stacked multilayer graphene is studied within an effective mass approximation. The electron and hole bands touching at zero energy support chiral quasiparticles characterized by Berry's phase N pi for N-layers, generalizing the low-energy band structure of monolayer and bilayer graphene. We investigate the trigonal-warping deformation of the energy bands and show that the Lifshitz transition, in which the Fermi circle breaks up into separate parts at low energy, reflects Berry's phase N pi. It is particularly prominent in trilayers, N=3, with the Fermi circ…
Multilayer graphene (MLG) grown by chemical vapor deposition (CVD) is a promising material for electronic and optoelectronic devices. Understanding the stacking configuration and interlayer coupling of MLGs is technologically relevant and of importance for the device applications. Here, we reported a kind of twisted MLGs (tMLGs), which are formed by stacking one graphene monolayer on the top of AB-stacked MLG by rotating a certain angle between them. The twist angle of tMLGs are identified by the twist-related modes, R and R'. With increasing the total layer number of N, the observed interlaye…
Trilayer graphene (TLG) exhibits rich novel electronic properties and extraordinary quantum Hall phenomena owning to enhanced electronic interactions and tunable chirality of its quasiparticles. Here, we report direct observation of chirality transition of quasiparticles at stacking solitons of TLG via spatial-resolved Landau level spectroscopy. The one-dimensional stacking solitons with width of the order of 10 nm separate adjacent Bernal-stacked TLG and rhombohedral-stacked TLG. By using high field tunneling spectra of scanning tunneling microscopy, we measured Landau quantization in both th…
Rhombohedral stacked multilayer graphene displays the occurrence of a magnetic surface state at low temperatures. Recent angular resolved photoemission experiments demonstrate the robustness of the magnetic state in long sequences of ABC graphene. Here, by using first-principles calculations, we show that field-effect doping of these graphene multilayers induces a perfect half-metallic behaviour with 100% of spin current polarization already at dopings attainable in conventional field effect transistors with solid state dielectrics. Our work demonstrates the realisability of a new kind of spin…
Combining both vertical and in-plane two-dimensional (2D) heterostructures opens up the possibility to create an unprecedented architecture using 2D atomic layer building blocks. The thermal transport properties of such mixed heterostructures, critical to various applications in nanoelectronics, however, have not been thoroughly explored. Herein, we construct two configurations of multilayer in-plane graphene/hexagonal boron nitride (Gr/h-BN) heterostructures (i.e. mixed heterostructures) via weak van der Waals (vdW) interactions and systematically investigate the dependence of their interfaci…
Motivated by the observation of two distinct superconducting phases in the moiréless ABC-stacked rhombohedral trilayer graphene, we investigate the electron-acoustic-phonon coupling as a possible pairing mechanism. We predict the existence of superconductivity with the highest $T_c\sim 3$K near the Van Hove singularity. Away from the Van Hove singularity, $T_c$ remains finite in a wide range of doping. In our model, the $s$-wave spin-singlet and $f$-wave spin-triplet pairings yield the same $T_c$, while other pairing states have negligible $T_c$. Our theory provides a simple explanation for th…
Enhanced Emission from Boron-Vacancy Center in Rhombohedral Boron Nitride
Isfahan University of Technology（伊斯法罕理工大学）；HUN-REN Wigner Research Centre for Physics（匈牙利科学院维格纳物理研究中心）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
We calculate the temperature dependent long-range magnetic coupling in the presence of dilute concentrations of random magnetic impurities in chiral multilayer two-dimensional semimetals, i.e., undoped intrinsic multilayer graphene. Assuming a carrier-mediated indirect RKKY exchange interaction among the well-separated magnetic impurities with the itinerant carriers mediating the magnetic interaction between the impurities, we investigate the magnetic properties of intrinsic multilayer graphene using an effective chiral Hamiltonian model. We find that due to the enhanced density of states in t…
We study the electronic structure of multilayer graphene using a $π$-orbital continuum model with nearest-neighbor intralayer and interlayer tunneling. Using degenerate state perturbation theory, we show that the low-energy electronic structure of arbitrarily stacked graphene multilayers consists of chiral pseudospin doublets with a conserved chirality sum.
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…
Most studies on moiré superlattices formed from a stack of h-BN and graphene have focused on single layer graphene; graphene with multiple layers is less understood. Here, we show that a moiré superlattice of multilayer graphene shows new features arising from the anisotropic Fermi surface affected by the superlattice structure. The moiré superlattice of a h-BN/AB-stacked tetralayer graphene heterostructure exhibited resistivity peaks showing a complicated dependence on the perpendicular electric field. The peaks were not due to secondary Dirac cones forming, but rather opening of the energy g…
Graphene, defined as a single atomic plane of graphite, is a semimetal with small overlap between the valence and the conduction bands. The stacking of graphene up to several atomic layers can produce diverse physical properties, depending on the stacking way. The bilayer graphene is also a semimetal, adopting the AB-stacked (or Bernal-stacked) structure or the rare AA-stacked structure. The trilayer or a few layer graphene (FLG) can be semimetal or semiconductor, depending on whether it takes Bernal (ABA) stacking or rhombohedral (ABC) stacking. We will give a perspective on the recent two mi…
Chiral superconductivity from parent Chern band and its non-Abelian generalization
University of Maryland, College Park（马里兰大学帕克分校）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Johns Hopkins University（约翰斯·霍普金斯大学）；University of Pittsburgh（匹兹堡大学）
We examine how the misorientation of a few stacked graphene layers affects the electronic structure of carbon nanosystems. We present {\it ab initio} calculations on bi- and trilayer systems to demonstrate that the massless Fermion behavior typical of single layered graphene is also found in incommensurate multilayered graphitic systems. We also investigate the consequences of this property on experimental fingerprints, such as Raman spectroscopy and scanning tunneling microscopy (STM). Our simulations reveal that STM images of turbostratic few layer graphite are sensitive to the layer arrange…
