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 structure and chiral surface states of rhombohedral graphite, and show that, when doped, it should exhibit multiple 3DQHE plateaus at modest fields.
In graphite crystals, layers of graphene reside in three equivalent, but distinct, stacking positions typically referred to as A, B, and C projections. The order in which the layers are stacked defines the electronic structure of the crystal, providing an exciting degree of freedom which can be exploited for designing graphitic materials with unusual properties including predicted high-temperature superconductivity and ferromagnetism. However, the lack of control of the stacking sequence limits most research to the stable ABA form of graphite. Here we demonstrate a strategy to control the stac…
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）
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）
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…
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…
The magnetic properties of disordered graphene and irradiated graphite are systematically studied using a combination of mean-field Hubbard model and first-principles calculations. By considering large-scale disordered models of graphene, I conclude that only single-atom defects can induce ferromagnetism in graphene-based materials. The preserved stacking order of graphene layers is shown to be another necessary condition for achieving a finite net magnetic moment of irradiated graphite. Ab initio calculations of hydrogen binding and diffusion and of interstitial-vacancy recombination further …
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）
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…
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 report markedly different transport properties of ABA- and ABC-stacked trilayer graphenes. Our experiments in double-gated trilayer devices provide evidence that a perpendicular electric field opens an energy gap in the ABC trilayer, while it causes the increase of a band overlap in the ABA trilayer. In a perpendicular magnetic field, the ABA trilayer develops quantum Hall plateaus at filling factors of ν= 2, 4, 6... with a step of Δν= 2, whereas the inversion symmetric ABC trilayer exhibits plateaus at ν= 6 and 10 with 4-fold spin and valley degeneracy.
Transport measurements indicate strong oscillations in the Hall-,$R_{xy}$, and the diagonal-, $R_{xx}$, resistances and exhibit Hall plateaus at the lowest temperatures, in three-dimensional Highly Oriented Pyrolytic Graphite (HOPG). At the same time, a comparative Shubnikov-de Haas-oscillations-based Berry's phase analysis indicates that graphite is unlike the GaAs/AlGaAs 2D electron system, the 3D n-GaAs epilayer, semiconducting $Hg_{0.8}Cd_{0.2}Te$, and some other systems. Finally, we observe the transport data to follow $B\times dR_{xy}/dB \approx - ΔR_{xx}$. This feature is consistent wit…
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.
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 …
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 …
A systematic review is made for the AA-, AB- and ABC-stacked graphites. The generalized tight-binding model, accompanied with the effective-mass approximation and the Kubo formula, is developed to investigate electronic and optical properties in the presence/absence of a uniform magnetic field. The unusual electronic properties cover the stacking-dependent Dirac-cone structures, the significant energy widths along the stacking direction, the Landau subbands (LSs) crossing the Fermi level, the $B_0$-dependent LS energy spectra with crossings and anti-crossings, and the monolayer- or bilayer-lik…
Measurements of basal plane longitudinal rho_b(B) and Hall rho_H(B) resistivities were performed on highly oriented pyrolytic graphite (HOPG) samples in pulsed magnetic field up to B = 50 T applied perpendicular to graphene planes, and temperatures 1.5 K < T < 4.2 K. At B > 30 T and for all studied samples, we observed a sign change in rho_H(B) from electron- to hole-like. For our best quality sample, the measurements revealed the enhancement in rho_b(B) for B > 34 T (T = 1.8 K), presumably associated with the field-driven charge density wave or Wigner crystallization transition. Besides, well…
We derive an effective two-dimensional Hamiltonian to describe the low energy electronic excitations of a graphite bilayer, which correspond to chiral quasiparticles with a parabolic dispersion exhibiting Berry phase $2π$. Its high-magnetic-field Landau level spectrum consists of almost equidistant groups of four-fold degenerate states at finite energy and eight zero-energy states. This can be translated into the Hall conductivity dependence on carrier density, $σ_{xy}(N)$, which exhibits plateaus at integer values of $4e^{2}/h$ and has a ``double'' $8e^{2}/h$ step between the hole and electro…
A detailed magnetoresistance study of bulk and microflake samples of highly oriented pyrolytic graphite with a thickness of 25 $μ$m to 23~nm reveals that the usually observed field-induced metal-insulator and electronic phase transitions vanish in thinner samples. The observed suppression is accompanied by orders of magnitude decrease of the magnetoresistance and of the amplitude of the Shubnikov-de-Haas oscillations. The overall behavior is related to the decrease in the quantity of two-dimensional interfaces between crystalline regions of the same and different stacking orders present in gra…
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…
We calculated the optical properties of an $N$-layer graphene by formulating the dynamical conductivity of each layer. This is the conductivity when an electromagnetic field is localized at a particular layer and differs from the standard conductivity calculated assuming a uniform field throughout all layers. By combining these conductivities with a transfer matrix method, we took into account the spatial variation of the electromagnetic field caused by internal reflections. The results obtained from the two conductivities show that similar peak structures originating from the interlayer elect…
In a multi-layer electronic system, stacking order provides a rarely-explored degree of freedom for tuning its electronic properties. Here we demonstrate the dramatically different transport properties in trilayer graphene (TLG) with different stacking orders. At the Dirac point, ABA-stacked TLG remains metallic while the ABC counterpart becomes insulating. The latter exhibits a gap-like dI/dV characteristics at low temperature and thermally activated conduction at higher temperatures, indicating an intrinsic gap ~6 meV. In magnetic fields, in addition to an insulating state at filling factor …
The direct experimental probing of locally varying lattice parameters and anisotropic lattice deformations in atomic multilayers is extremely challenging. Here, we develop a new combined numerical/graphical method for the analysis of irregular moiré superstructures measured by scanning tunneling microscopy (STM) on a small-twist-angle ($\sim$0.6$^{\circ}$) graphene on highly oriented pyrolytic graphite (gr/HOPG). We observe distorted moiré patterns with a spatially varying period in annealed gr/HOPG. The nanoscale modulation of the moiré period observed by STM reflects a locally strained (and …
We calculate the electronic structure of AA'AA'...-stacked alternating twist N-layer (tNG) graphene for N = 3, 4, 5, 6, 8, 10, 20 layers and bulk alternating twist (AT) graphite systems where the lattice relaxations are modeled by means of molecular dynamics simulations. We show that the symmetric AA'AA'... stacking is energetically preferred among all interlayer sliding geometries for progressively added layers up to N=6. Lattice relaxations enhance electron-hole asymmetry, and reduce the magic angles with respect to calculations with fixed tunneling strengths that we quantify from few layers…
The advent of black phosphorus field-effect transistors (FETs) has brought new possibilities in the study of two-dimensional (2D) electron systems. In a black phosphorus FET, the gate induces highly anisotropic 2D electron and hole gases. Although the 2D hole gas in black phosphorus has reached high carrier mobilities that led to the observation of the integer quantum Hall effect, the improvement in the sample quality of the 2D electron gas (2DEG) has however been only moderate; quantum Hall effect remained elusive. Here, we obtain high quality black phosphorus 2DEG by defining the 2DEG region…
Domain walls, topological defects that define the frontier between regions of different stacking in multilayer graphene, have proved to host exciting physics. The ability of tuning these topological defects in-situ in an electronic transport experiment brings a wealth of possibilities in terms of fundamental understanding of domain walls as well as for electronic applications. Here, we demonstrate through a MEMS (micro-electromechanical system) actuator and magnetoresistance measurements the effect of domain walls in multilayer graphene quantum Hall effect. Reversible and controlled uniaxial s…
