The electronic structure of multilayer graphenes depends strongly on the number of layers as well as the stacking order. Here we explore the electronic transport of purely ABA-stacked trilayer graphenes in a dual-gated field-effect device configuration. We find that both the zero-magnetic-field transport and the quantum Hall effect at high magnetic fields are distinctly different from the monolayer and bilayer graphenes, and that they show electron-hole asymmetries that are strongly suggestive of a semimetallic band overlap. When the ABA trilayers are subjected to an electric field perpendicular to the sheet, Landau level splittings due to a lifting of the valley degeneracy are clearly observed.
Layer stacking and crystal lattice symmetry play important roles in the band structure and the Landau levels of multilayer graphene. ABA-stacked trilayer graphene possesses mirror-symmetry-protected monolayer-like and bilayer-like band structures. Broken mirror symmetry by a perpendicular electric field therefore induces hybridization between these bands and various quantum Hall phases emerge. We experimentally explore the evolution of Landau levels in ABA-stacked trilayer graphene under electric field. We observe a variety of valley and orbital dependent Landau level evolutions. These evoluti…
The band structure and the optical conductivity of an ABA (Bernal-type) stacked graphene trilayer are calculated. It is shown that, under appropriate doping, a strong resonant peak develops in the optical conductivity, located at the frequency corresponding to approximately 1.4 times the interlayer hopping energy and caused by the 'nesting' of two nearly parabolic bands in the electronic spectrum. The intensity of this resonant absorption can be controlled by adjusting the gate voltage. The effect is robust with respect to increasing temperature.
We present the solutions of the energy spectrum of charge carriers confined in quantum ring in ABA-stacked trilayer graphene subjected to a perpendicular magnetic field. The calculations were performed in the context of the continuum model by solving the Dirac equation for a zero width ring geometry, i.e. freezing out the carrier radial motion. We show that the obtained energy spectrum exhibits different symmetries with respect to the magnetic field and other parameters. The application of a potential shift the energy spectrum vertically while the application of a magnetic field breaks all sym…
We investigate the proximity spin-orbit and exchange couplings in ABA and ABC trilayer graphene encapsulated within monolayers of semiconducting transition-metal dichalcogenides and the ferromagnetic semiconductor Cr$_2$Ge$_2$Te$_6$. Employing first-principles calculations we obtain the electronic structures of the multilayer stacks and extract the relevant proximity-induced orbital and spin interaction parameters by fitting the low-energy bands to model Hamiltonians. We also demonstrate the tunability of the proximity effects by a transverse electric field. Using the model Hamiltonians we als…
The tight-binding model is closely associated with the modified random-phase approximation to thoroughly explore the electron-electron interactions in trilayer AB-stacked graphene. The intralayer and interlayer atomic/Coulomb interactions dominate the collective and electron-hole excitations. The unusual energy bands are directly reflected in the diverse transferred momentum-frequency phase diagrams. There exist three kinds of plasmon modes during the variation of the doping level, being accompanied with the complicated intraband and interband single-particle excitations. The excitation behavi…
Crystal symmetry plays a central role in governing a wide range of fundamental physical phenomena. One example is the nonlinear optical second harmonic generation (SHG), which requires inversion symmetry breaking. Here we report a unique stacking-induced SHG in trilayer graphene, whose individual monolayer sheet is centrosymmetric. Depending on layer stacking sequence, we observe a strong optical SHG in Bernal (ABA) stacked non-centrosymmetric trilayer, while it vanishes in rhombohedral (ABC) stacked one which preserves inversion symmetry. This highly contrasting SHG due to the distinct stacki…
Bernal-stacked multilayer graphene is a versatile platform to explore quantum transport phenomena and interaction physics due to its exceptional tunability via electrostatic gating. For instance, upon applying a perpendicular electric field, its band structure exhibits several off-center Dirac points (so-called Dirac gullies) in each valley. Here, the formation of Dirac gullies and the interaction-induced breakdown of gully coherence is explored via magnetotransport measurements in high-quality Bernal-stacked (ABA) trilayer graphene. In the absence of a magnetic field, multiple Lifshitz transi…
The sequence of the zeroth Landau levels (LLs) between filling factors $ν$=-6 to 6 in ABA-stacked trilayer graphene (TLG) is unknown because it depends sensitively on the non-uniform charge distribution on the three layers of ABA-stacked TLG. Using the sensitivity of quantum Hall data on the electric field and magnetic field, in an ultraclean ABA-stacked TLG sample, we quantitatively estimate the non-uniformity of the electric field and determine the sequence of the zeroth LLs. We also observe anticrossings between some LLs differing by 3 in LL index, which result from the breaking of the cont…
ABC-stacked trilayer graphene has exhibited a variety of correlated phenomena owing to its relatively flat bands and gate-tunable bandgap. However, convenient methods are still lacking for identifying ABC graphene with nanometer-scale resolution. Here we demonstrate that the scanning near-field optical microscope (SNOM) working in ambient conditions can provide quick recognition of ABC trilayer graphene with no ambiguity and excellent resolution (~20 nm). The recognition is based on the difference in their near-field infrared (IR) responses between the ABA and ABC trilayers. We show that in mo…
We report on quantum capacitance measurements of high quality, graphite- and hexagonal boron nitride encapsulated Bernal stacked trilayer graphene devices. At zero applied magnetic field, we observe a number of electron density- and electrical displacement-tuned features in the electronic compressibility associated with changes in Fermi surface topology. At high displacement field and low density, strong trigonal warping gives rise to emergent Dirac gullies centered near the corners of the hexagonal Brillouin and related by three fold rotation symmetry. At low magnetic fields of $B=1.25$~T, th…
ABA-stacked trilayer graphene (TLG), the simplest system consisting of both massless and massive Dirac fermions, is expected to exhibit many interesting broken-symmetry quantum Hall states and interaction-induced phenomena. However, difficulties in microscopically identifying the stacking order of the TLG and limited spectroscopic resolution have stymied experimental probes of these interesting states and phenomena in scanning tunneling microscopy (STM) studies. Here we studied the detailed features of the electronic structure in the ABA TLG by using high-resolution STM measurements. Landau-le…
We present a comparative measurement of the G-peak oscillations of phonon frequency, Raman intensity and linewidth in the Magneto-Raman scattering of optical E2g phonons in mechanically exfoliated ABA- and ABC-stacked trilayer graphene (TLG). Whereas in ABA-stacked TLG, we observe magnetophonon oscillations consistent with single-bilayer chiral band doublets, the features are flat for ABC-stacked TLG up to magnetic fields of 9 T. This suppression can be attributed to the enhancement of band chirality that compactifies the spectrum of Landau levels and modifies the magnetophonon resonance prope…
There is an increasing interest in the electronic properties of few layer graphene as it offers a platform to study electronic interactions because the dispersion of bands can be tuned with number and stacking of layers in combination with electric field. However, electronic interaction becomes important only in very clean devices and so far the trilayer graphene experiments are understood within non-interacting electron picture. Here, we report evidence of strong electronic interactions and quantum Hall ferromagnetism (QHF) seen in ABA trilayer graphene (ABA-TLG). Due to high mobility $\sim$5…
We report a nano-infrared (IR) imaging study of trilayer graphene (TLG) with both ABA (Bernal) and ABC (rhombohedral) stacking orders using the scattering-type scanning near-field optical microscope (s-SNOM). With s-SNOM operating in the mid-IR region, we mapped in real space the surface plasmon polaritons (SPPs) of ABA-TLG and ABC-TLG, which are tunable with electrical gating. Through quantitative modeling of the plasmonic imaging data, we found that the plasmon wavelength of ABA-TLG is significantly larger than that of ABC-TLG, resulting in a sizable impedance mismatch and hence a strong pla…
Small-twist-angle bilayer graphene supports strongly correlated insulating states and superconductivity. Twisted few-layer graphene systems are likely to open up new directions for strong correlation physics in moiré superlattices. We derive and study moiré band models that describe the electronic structure of graphene trilayers in which one of the three layers is twisted by a small angle relative to perfect AAA, ABA, or ABC stacking arrangements. We find that the electronic structure depends very strongly on the starting stackings arrangement and on which layer is twisted. We identify ABA sta…
Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene
Indian Institute of Science（印度科学研究所）；National Institute for Materials Science（物质材料研究机构）；Physical Research Laboratory（物理研究实验室）；Institute of Mathematical Sciences（数学科学研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）
研究 ABA 三层石墨烯零朗道能级中偶数分母分数量子霍尔态，通过实验观察到特定分数态及相关子态，确定其出现在特定位移场窗口与朗道能级交叉处，发现是朗道能级混合及反演对称性破缺所致，拓展了该领域并建立了可调平台。
We construct a continuum model of twisted trilayer graphene using {\it ab initio} density-functional-theory calculations, and apply it to address twisted trilayer electronic structure. Our model accounts for moiré variation in site energies, hopping between outside layers and within layers. We focus on the role of a mirror symmetry present in ABA graphene trilayers with a middle layer twist. The mirror symmetry is lost intentionally when a displacement field is applied between layers, and unintentionally when the top layer is shifted laterally relative to the bottom layer. We use two band stru…
We study the electronic transport through np and npn junctions for AAA-stacked trilayer graphene. Two kinds of gates are considered where the first is a single gate and the second is a double gate. After obtaining the solutions for the energy spectrum, we use the transfer matrix method to determine the three transmission probabilities for each individual cone $τ=0, \pm 1$. We show that the quasiparticles in AAA-stacked trilayer graphene are not only chiral but also labeled by an additional cone index $τ$. The obtained bands are composed of three Dirac cones that depend on the chirality indexes…
Tunable topological narrow bands in twisted bilayer-trilayer graphene
Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University（教育部人工微纳结构重点实验室和武汉大学物理科学与技术学院）；IMDEA Nanoscience（IMDEA纳米科学研究所）；School of Artificial Intelligence, Wuhan University（武汉大学人工智能学院）；Wuhan Institute of Quantum Technology（武汉量子技术研究院）
Northeast Normal University（东北师范大学）；Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences（中国科学院长春光学精密机械与物理研究所）；University of Science and Technology Beijing（北京科技大学）；Zhengzhou University（郑州大学）
The celebrated phenomenon of quantum Hall effect has recently been generalized from transport of conserved charges to that of other approximately conserved state variables, including spin and valley, which are characterized by spin- or valley-polarized boundary states with different chiralities. Here, we report a new class of quantum Hall effect in ABA-stacked graphene trilayers (TLG), the quantum parity Hall (QPH) effect, in which boundary channels are distinguished by even or odd parity under the systems mirror reflection symmetry. At the charge neutrality point and a small perpendicular mag…
The lower-symmetry trilayer AAB-stacked graphene exhibits rich electronic properties and thus diverse Coulomb excitations. Three pairs of unusual valence and conduction bands create nine available interband excitations for the undoped case, in which the imaginary (real) part of the polarizability shows 1D square root asymmetric peaks and 2D shoulder structures (pairs of antisymmetric peaks and logarithm type symmetric peaks). Moreover, the low frequency acoustic plasmon, being revealed as a prominent peak in the energy loss spectrum, can survive in a narrow gap system with the large-density-of…
Bloch states of electrons in honeycomb two-dimensional crystals with multi-valley band structure and broken inversion symmetry have orbital magnetic moments of a topological nature. In crystals with two degenerate valleys, a perpendicular magnetic field lifts the valley degeneracy via a Zeeman effect due to these magnetic moments, leading to magnetoelectric effects which can be leveraged for creating valleytronic devices. In this work, we demonstrate that trilayer graphene with Bernal stacking, (ABA TLG) hosts topological magnetic moments with a large and widely tunable valley g-factor, reachi…
We developed the generalized tight-binding model to study the magneto-electronic properties of AAB-stacked trilayer graphene. Three groups of Landau levels (LLs) are characterized by the dominating subenvelope function on distinct sublattices. Each LL group could be further divided into two sub-groups in which the wavefunctions are, respectively, localized at 2/6 (5/6) and 4/6 (1/6) of the total length of the enlarged unit cell. The unoccupied conduction and the occupied valence LLs in each sub-group behave similarly. For the first group, there exist certain important differences between the t…
Starting with twisted bilayer graphene, graphene-based moiré materials have recently been established as a new platform for studying strong electron correlations. In this paper, we study twisted graphene monolayers on trilayer graphene and demonstrate that this system can host flat bands when the twist angle is close to the magic-angle of 1.16$^\circ$. When monolayer graphene is twisted on ABA trilayer graphene, the flat bands are not isolated, but are intersected by a Dirac cone with a large Fermi velocity. In contrast, graphene twisted on ABC trilayer graphene (denoted AtABC) exhibits a gap …
