ABA Trilayer Graphene Research Articles

Topological confinement states in ABA trilayer graphene with antiparallel electric field

Topological confinement states in ABA trilayer graphene with antiparallel electric field

Electric-Field-Tunable Edge Transport in Bernal-Stacked Trilayer Graphene.

This Letter presents a nonlocal study on the electric-field-tunable edge transport in h-BN-encapsulated dual-gated Bernal-stacked (ABA) trilayer graphene across various displacement fields (D) and temperatures (T). Our measurements revealed that the nonlocal resistance (R_{NL}) surpassed the expected classical Ohmic contribution by a factor of at least 2 orders of magnitude. Through scaling analysis, we found that the nonlocal resistance scales linearly with the local resistance (R_{L}) only when the D exceeds a critical value of ∼0.2 V/nm. Additionally, we observed that the scaling exponent remains constant at unity for temperatures below the bulk-band gap energy threshold (T<25 K). Further, the value of R_{NL} decreases in a linear fashion as the channel length (L) increases. These experimental findings provide evidence for edge-mediated charge transport in ABA trilayer graphene under the influence of a finite displacement field. Furthermore, our theoretical calculations support these results by demonstrating the emergence of dispersive edge modes within the bulk-band gap energy range when a sufficient displacement field is applied.

Emergence of symmetric and asymmetric Dirac points under periodic electric and vector potentials in ABA-trilayer graphene superlattice.

We have theoretically investigated the impact of both periodic electric and vector potentials on the low energy spectrum of ABA-trilayer graphene superlattice. Finite energy Dirac points appear in the energy spectrum due to the application of the vector potential. These extra Dirac points are symmetric about k y = 0 plane for equal barrier and well widths. For different barriers and well widths, one Dirac point shifts away and the second Dirac point shifts towards the k y = 0 plane. The extra Dirac points are not only generated from the original Dirac point but also emerge from the valleys developed in the energy spectrum. The application of both electric and vector potentials with identical barrier and well widths breaks the symmetry of the spectrum about the Fermi level. When the electric and vector potentials are asymmetric with all three layers having the same electric potentials, the energy spectrum becomes asymmetric about the Fermi level, and this asymmetric behavior of both potentials annihilates the original Dirac point from the spectrum. When all the layers have different electric potentials and both electric and vector potentials are asymmetric, the spectrum becomes asymmetric again, but this time the asymmetry of the spectrum occurs across the k y = 0 plane.

Band structure and extra Dirac points in the energy spectrum of ABA-Trilayer graphene superlattice

Band structure and extra Dirac points in the energy spectrum of ABA-Trilayer graphene superlattice

Spontaneous Gully-Polarized Quantum Hall States in ABA Trilayer Graphene.

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. At zero magnetic field, multiple Lifshitz transitions indicating the formation of Dirac gullies are identified. In the quantum Hall regime, the emergence of Dirac gullies is evident as an increase in Landau level degeneracy. When tuning both electric and magnetic fields, electron-electron interactions can be controllably enhanced until, beyond critical electric and magnetic fields, the gully degeneracy is eventually lifted. The arising correlated ground state is consistent with a previously predicted nematic phase that spontaneously breaks the rotational gully symmetry.

Proximity spin-orbit and exchange coupling in ABA and ABC trilayer graphene van der Waals heterostructures

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 also study mixed spin-orbit/exchange coupling encapsulation, which allows to tailor the spin interactions very efficiently by the applied field. We also summarize the spin-orbit physics of bare ABA, ABC, and ABB trilayers, and provide, along with the first-principles results of the electronic band structures, density of states, spin splittings, and electric-field tunabilities of the bands, qualitative understanding of the observed behavior and realistic model parameters as a resource for model simulations of transport and correlation physics in trilayer graphene.

Band Structure and Extra Dirac Points in the Energy Spectrum of Aba-Trilayer Graphene Superlattice

Band Structure and Extra Dirac Points in the Energy Spectrum of Aba-Trilayer Graphene Superlattice

Distinguishing viscous, ballistic, and diffusive current flows in anisotropic metals

We show that in anisotropic Fermi liquids where momentum-conserving scattering is much faster than momentum-relaxing scattering processes, local imaging of the electric current flow patterns can cleanly distinguish between ballistic, viscous and ohmic flow patterns simultaneously (using a single image). We propose using multi-layer graphene-based heterostructures, including ABA trilayer graphene, as a natural experimental platform where an anisotropic ballistic-to-viscous crossover may be visible in near-term experiments. Such experiments could lead to more direct measurements of momentum-conserving scattering lengths in electronic Fermi liquids.

Growing twisted bilayer graphene at small angles

Growing twisted bilayer graphene at small angles

Frank-van der Merwe growth in bilayer graphene

Frank-van der Merwe growth in bilayer graphene

Flat bands, electron interactions, and magnetic order in magic-angle mono-trilayer graphene

Starting with twisted bilayer graphene, graphene-based moir\'e 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 $1.{16}^{\ensuremath{\circ}}$. 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 between flat and remote bands. Since ABC trilayer graphene and twisted bilayer graphene are known to host broken-symmetry phases, we further investigate the ostensibly similar magic-angle AtABC system. We study the effect of electron-electron interactions in AtABC using both Hartree theory and an atomic Hubbard theory to calculate the magnetic phase diagram as a function of doping, twist angle, and perpendicular electric field. Our analysis reveals a rich variety of magnetic orderings, including ferromagnetism and ferrimagnetism, and demonstrates that a perpendicular electric field makes AtABC more susceptible to magnetic ordering.

Unusual electronic excitations in ABA trilayer graphene

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 behaviors are greatly diversified by the number of layers. The theoretical predictions require the high-resolution experimental examinations.

Topological properties in ABA trilayer graphene under the irradiation of light**Project supported by the National Natural Science Foundation of China (Grant No. 61604106) and Shandong Provincial Natural Science Foundation, China (Grant No. ZR2014FL025).

We study ABA trilayer graphene under irradiation of a circularly polarized light. In high-frequency regime, the effective low-energy Hamiltonian is obtained based on the Floquet theory. With increasing circularly polarized light intensity, the band structure shows a band gap closing and reopening, which happen twice. The process of the band gap closing and reopening is accompanied with a topological phase transition. We investigate the Chern numbers and the anomalous Hall conductivities to confirm the topological phase transition. The interplay between light-induced circularity-dependent effective potential and effective sublattice potential is discussed.

Gate-Controlled Conductance in ABA-Stacked Trilayer Graphene

In this work, we theoretically consider the electron transport across a junction on monolayer, Bernal-stacked AB bilayer and ABA trilayer graphene. The electronic transmissions through the electrostatic barrier in trilayer and bilayer graphene are computed within the scattering matrix using Landauer–Buttiker formula. We theoretically evaluate the total conductance. We study the effect of gate potential on the band structures. Our findings show that the effect of the gate potential could open an energy gap and the charge current can be controlled by tuning the gate potential in the middle region that acts as a barrier. Trilayer graphene is chosen as better appropriate candidate for industrial applications. Our findings show that the charge current can be controlled by tuning the gate potential in the middle region trilayer graphene that acts as a barrier.

High-resolution tunneling spectroscopy of ABA-stacked trilayer graphene

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-level (LL) crossings of the massless and massive Dirac fermions, and effective mass renormalization of the massive Dirac fermions were observed, indicating strong electron-electron interactions in the ABA TLG. Most unexpectedly, we observed unconventional splittings of the lowest LLs for both the massless and massive Dirac fermions in high perpendicular magnetic fields. These splittings of the LLs, which are beyond the description of tight-binding calculations, reveal unexplored broken-symmetry quantum Hall states in the ABA TLG induced by many-body effects.

Selective fabrication of free-standing ABA and ABC trilayer graphene with/without Dirac-cone energy bands

Graphene is a single-layer carbon sheet with a honeycomb structure, and bilayer graphene consists of two graphene sheets with AB stacking. In trilayer graphene, the third graphene sheet has two possible stacking sequences, A or C, when it is overlaid on bilayer graphene. It has been theoretically predicted that trilayer graphene exhibits a variety of novel electronic properties with/without a Dirac-cone band, depending on the stacking sequence. In this regard, trilayer graphene has a high potential for widening the capability of graphene-based electronic devices. However, the difficulty of selective fabrication has hindered the progress of research. Here, we report the first success in the selective fabrication of quasi-free-standing trilayer graphene with ABA or ABC stacking grown epitaxially on hydrogen-terminated silicon carbide. Angle-resolved photoemission spectroscopy (ARPES) clearly demonstrated that our trilayer graphene with ABA stacking has a massless Dirac-like band near the Fermi level, while that with ABC stacking shows a parabolic non-Dirac-like band dispersion.

Embedded trilayer graphene flakes under tensile and compressive loading

The mechanical response of embedded ABA trilayer graphene flakes loaded in tension and compression on polymer beams is monitored by simultaneous Raman measurements through the strain sensitivity of the G or 2D peaks. A characteristic peculiarity of the investigated flake is that it contains a trilayer and bilayer part. The Bernal stacked bilayer was used as a strain sensor aiming to assess the efficiency of the load transfer from the polymer matrix through shear to the individual graphene layers. For the trilayer graphene in tension, both peaks are redshifted and splitting of the G peak is reported for the first time. In compression, the studied sample was an almost isolated trilayer, in which both peaks are blue-shifted up to a critical compressive strain. This critical strain is found to be one fourth of the value found in the case of single layer graphene despite the higher bending rigidity that trilayer exhibits over the much thinner monolayer.

Plasmons and their interaction with electrons in trilayer graphene

The interaction between electrons and plasmons in trilayer graphene is investigated within the Overhauser approach resulting in the 'plasmaron' quasi-particle. This interaction is cast into a field theoretical problem, nd its effect on the energy spectrum is calculated using improved Wigner-Brillouin perturbation theory. The plasmaron spectrum is shifted with respect to the bare electron spectrum by $\Delta E(\mathbf{k})\sim 50\div200\,{\rm meV}$ for ABC stacked trilayer graphene and for ABA trilayer graphene by $\Delta E(\mathbf{k})\sim 30\div150\,{\rm meV}$ ($\Delta E(\mathbf{k})\sim 1\div5\,{\rm meV}$) for the hyperbolic linear) part of the spectrum. The shift in general increases with the electron concentration $n_{e}$ and electron momentum. The dispersion of plasmarons is more pronounced in \textit{ABC} stacked than in ABA tacked trilayer graphene, because of the different energy band structure and their different plasmon dispersion.

Local spectroscopy of the electrically tunable band gap in trilayer graphene

The stacking order in trilayer graphene plays a critical role in determining the existence of an electric field tunable band gap. We present spatially resolved tunneling spectroscopy measurements of dual gated Bernal (ABA) and rhombohedral (ABC) stacked trilayer graphene devices. We demonstrate that while ABA trilayer graphene remains metallic, ABC trilayer graphene exhibits a widely tunable band gap as a function of electric field. However, we find that charged impurities in the underlying substrate cause substantial spatial fluctuations of the gap size. Our work elucidates the microscopic behavior of trilayer graphene and its consequences for macroscopic devices.

Broken Symmetry Quantum Hall States in Dual-Gated ABA Trilayer Graphene

ABA-stacked trilayer graphene is a unique 2D electron system with mirror reflection symmetry and unconventional quantum Hall effect. We present low-temperature transport measurements on dual-gated suspended trilayer graphene in the quantum Hall (QH) regime. We observe QH plateaus at filling factors ν = -8, -2, 2, 6, and 10, which is in agreement with the full-parameter tight binding calculations. In high magnetic fields, odd-integer plateaus are also resolved, indicating almost complete lifting of the 12-fold degeneracy of the lowest Landau level (LL). Under an out-of-plane electric field E(perpendicular), we observe degeneracy breaking and transitions between QH plateaus. Interestingly, depending on its direction, E(perpendicular) selectively breaks the LL degeneracies in the electron-doped or hole-doped regimes. Our results underscore the rich interaction-induced phenomena in trilayer graphene.