Trilayer Graphene Research Articles

Magnetic Field-Stabilized Wigner Crystal States in a Graphene Moiré Superlattice.

ABC-stacked trilayer graphene on boron nitride (ABC-TLG/hBN) moiré superlattices provides a tunable platform for exploring Wigner crystal states in which the electron correlation can be controlled by electric and magnetic fields. Here we report the observation of magnetic field-stabilized Wigner crystal states in a ABC-TLG/hBN. We show that correlated insulating states emerge at multiple fractional and integer fillings corresponding to ν = 1/3, 2/3, 1, 4/3, 5/3, and 2 electrons per moiré lattice site under a magnetic field. These correlated insulating states can be attributed to generalized Mott states for the integer fillings and generalized Wigner crystal states for the fractional fillings. The generalized Wigner crystal states are stabilized by a vertical magnetic field and are strongest at one magnetic flux quantum per three moiré superlattices. The ν = 2 insulating state persists up to 30 T, which can be described by a Mott-Hofstadter transition at a high magnetic field.

Recent Advancements in Applications of Graphene to Attain Next-Level Solar Cells

This paper presents an intensive review covering all the versatile applications of graphene and its derivatives in solar photovoltaic technology. To understand the internal working mechanism for the attainment of highly efficient graphene-based solar cells, graphene’s parameters of control, namely its number of layers and doping concentration are thoroughly discussed. The popular graphene synthesis techniques are studied. A detailed review of various possible applications of utilizing graphene’s attractive properties in solar cell technology is conducted. This paper clearly mentions its applications as an efficient transparent conducting electrode, photoactive layer and Schottky junction formation. The paper also covers advancements in the 10 different types of solar cell technologies caused by the incorporation of graphene and its derivatives in solar cell architecture. Graphene-based solar cells are observed to outperform those solar cells with the same configuration but lacking the presence of graphene in them. Various roles that graphene efficiently performs in the individual type of solar cell technology are also explored. Moreover, bi-layer (and sometimes, tri-layer) graphene is shown to have the potential to fairly uplift the solar cell performance appreciably as well as impart maximum stability to solar cells as compared to multi-layered graphene. The current challenges concerning graphene-based solar cells along with the various strategies adopted to resolve the issues are also mentioned. Hence, graphene and its derivatives are demonstrated to provide a viable path towards light-weight, flexible, cost-friendly, eco-friendly, stable and highly efficient solar cell technology.

Chemical Potential Characterization of Symmetry-Breaking Phases in a Rhombohedral Trilayer Graphene.

Rhombohedral trilayer graphene has recently emerged as a natural flat-band platform for studying interaction-driven symmetry-breaking phases. The displacement field (D) can further flatten the band to enhance the density of states, thereby controlling the electronic correlation that tips the energy balance between spin and valley degrees of freedom. To characterize the energy competition, chemical potential measurement─a direct thermodynamic probe of Fermi surfaces─is highly demanding to be conducted under a constant D. In this work, we characterize D-dependent isospin flavor polarization, where electronic states with isospin degeneracies of one and two can be identified. We also developed a method to measure the chemical potential at a fixed D, allowing for the extraction of energy variation during phase transitions. Furthermore, symmetry breaking could also be invoked in Landau levels, manifesting as quantum Hall ferromagnetism. Our work opens more opportunities for the thermodynamic characterization of displacement-field tuned van der Waals heterostructures.

Magic-angle twisted symmetric trilayer graphene as a topological heavy-fermion problem

Magic-angle twisted symmetric trilayer graphene as a topological heavy-fermion problem

Hydrogen-modulation method for wafer-scale few-layer single-crystal graphene growth

Single-crystal few-layer graphene films have potential applications in microelectronic and optoelectronic devices. Considerable efforts have been taken to prepare large-area bilayer graphene through chemical vapor deposition, but the growth of uniform graphene films with increased layers remains challenging. Herein, a hydrogen-modulation method for growing wafer-scale few-layer single-crystal graphene through chemical vapor deposition was proposed. By controlling the hydrogen flow rate at different stages, the dissolution amount and segregation process of carbon atoms in a CuNi substrate can be regulated separately. The hydrogen-modulation method fully exploits the effect of the dissolution–segregation mechanism, and the number of graphene layers can be controlled by modulating the hydrogen flow rate. Through the proposed method, the coverages of bilayer and trilayer graphene can reach more than 99% and 95%, respectively. The stacking and uniformity of few-layer graphene were evaluated by Raman and microstructure characterization, and bilayer and trilayer graphene were confirmed as AB and ABA stacks, respectively. Transmission line test structure and field effect transistor were prepared to verify the electrical properties of bilayer graphene. Results show that the square resistance of bilayer graphene is significantly lower than that of single-layer graphene, and it can also achieve high on-state current on field effect transistor.

Controlled alignment of supermoiré lattice in double-aligned graphene heterostructures

The supermoiré lattice, built by stacking two moiré patterns, provides a platform for creating flat mini-bands and studying electron correlations. An ultimate challenge in assembling a graphene supermoiré lattice is in the deterministic control of its rotational alignment, which is made highly aleatory due to the random nature of the edge chirality and crystal symmetry. Employing the so-called “golden rule of three”, here we present an experimental strategy to overcome this challenge and realize the controlled alignment of double-aligned hBN/graphene/hBN supermoiré lattice, where the twist angles between graphene and top/bottom hBN are both close to zero. Remarkably, we find that the crystallographic edge of neighboring graphite can be used to better guide the stacking alignment, as demonstrated by the controlled production of 20 moiré samples with an accuracy better than ~ 0.2°. Finally, we extend our technique to low-angle twisted bilayer graphene and ABC-stacked trilayer graphene, providing a strategy for flat-band engineering in these moiré materials.

Spontaneous isospin polarization and quantum Hall ferromagnetism in a rhombohedral trilayer graphene superlattice

Moiré superlattices in van der Waals heterostructures have recently attracted enormous interests, due to the highly controllable electronic correlation that gives rise to superconductivity, ferromagnetism, and nontrivial topological properties. To gain a deep understanding of such exotic properties, it is essential to clarify the broken symmetry between spin and valley flavors which universally exists in these ground states. Here in a rhombohedral trilayer graphene crystallographically aligned with a hexagonal boron nitride, we report various kinds of symmetry-breaking transition tuned by displacement fields (D) and magnetic fields: (i) While it is well known that a finite D can enhance correlation to result in correlated insulators at fractional fillings of a flat band, we find the correlation gap emerges before the flavor is fully filled at a positive D, but the sequence is reversed at a negative D. (ii) Around zero D, electronic correlation can be invoked by narrow Landau levels, leading to quantum Hall ferromagnetism that lifts all the degeneracies including not only spin and valley but also orbital degrees of freedom. Our result unveils the complication of transitions between symmetry-breaking phases, shedding light on the mechanisms of various exotic phenomena in strongly correlated systems.

Quantum Monte Carlo study of superconductivity in rhombohedral trilayer graphene under an electric field

By using the constrained-phase quantum Monte Carlo method, we performed a systematic study of the ground state of the half filled Hubbard model for a trilayer honeycomb lattice. We analyze the effect of the perpendicular electric field on the electronic structure, magnetic property, and pairing correlations. It is found that the antiferromagnetism is suppressed by the perpendicular electric field, especially the long-range parts, and the dominant magnetic fluctuations are still antiferromagnetic. The electronic correlation drives a $d+id$ superconducting pairing to be dominant over other pairing patterns among various electric fields and interaction strengths. We also found that the $d+id$ pairing correlation is greatly enhanced as the on-site Coulomb interaction is increased. Our intensive numerical results may unveil the nature of the recently observed superconductivity in rhombohedral trilayer graphene under an electric field.

Collective Excitations in Chiral Stoner Magnets.

We argue that spin- and valley-polarized metallic phases recently observed in graphene bilayers and trilayers support chiral edge modes that allow spin waves to propagate ballistically along system boundaries without backscattering. The chiral edge behavior originates from the interplay between the momentum-space Berry curvature in Dirac bands and the geometric phase of a spin texture in position space. The edge modes are weakly confined to the edge, featuring dispersion that is robust and insensitive to the detailed profile of magnetization at the edge. This unique character of edge modes reduces their overlap with edge disorder and enhances the mode lifetime. The mode propagation direction reverses upon reversing valley polarization, an effect that provides a clear testable signature of geometric interactions in isospin-polarized Dirac bands.

Anomalous Interfacial Electron-Transfer Kinetics in Twisted Trilayer Graphene Caused by Layer-Specific Localization.

Interfacial electron-transfer (ET) reactions underpin the interconversion of electrical and chemical energy. It is known that the electronic state of electrodes strongly influences ET rates because of differences in the electronic density of states (DOS) across metals, semimetals, and semiconductors. Here, by controlling interlayer twists in well-defined trilayer graphene moirés, we show that ET rates are strikingly dependent on electronic localization in each atomic layer and not the overall DOS. The large degree of tunability inherent to moiré electrodes leads to local ET kinetics that range over 3 orders of magnitude across different constructions of only three atomic layers, even exceeding rates at bulk metals. Our results demonstrate that beyond the ensemble DOS, electronic localization is critical in facilitating interfacial ET, with implications for understanding the origin of high interfacial reactivity typically exhibited by defects at electrode-electrolyte interfaces.

Multilayer graphene with a superlattice potential

Bernal stacked bilayer graphene subject to a superlattice potential can realize topological and stacked flat bands [Ghorashi et al., Phys. Rev. Lett. 130, 196201 (2023)]. In the present work, we extend the study of a superlattice potential on graphene heterostructures to trilayer and quadrilayer graphene. Comparing Bernal- and chirally stacked multilayers reveals that the latter are more suitable for realizing stacks of many flat bands. On the other hand, Bernal-stacked graphene heterostructures can realize topological flat bands. Imposing two simultaneous superlattice potentials enhances the viability of both regimes.

Ising superconductivity induced from spin-selective valley symmetry breaking in twisted trilayer graphene

We show that the e-e interaction induces a strong breakdown of valley symmetry for each spin channel in twisted trilayer graphene, leading to a ground state where the two spin projections have opposite sign of the valley symmetry breaking order parameter. This leads to a spin-valley locking in which the electrons of a Cooper pair are forced to live on different Fermi lines attached to opposite valleys. Furthermore, we find an effective intrinsic spin-orbit coupling explaining the protection of the superconductivity against in-plane magnetic fields. The effect of spin-selective valley symmetry breaking is validated as it reproduces the experimental observation of the reset of the Hall density at 2-hole doping. It also implies a breakdown of the symmetry of the bands from C6 to C3, with an enhancement of the anisotropy of the Fermi lines which is at the origin of a Kohn-Luttinger (pairing) instability. The isotropy of the bands is gradually recovered, however, when the Fermi level approaches the bottom of the second valence band, explaining why the superconductivity fades away in the doping range beyond 3 holes per moiré unit cell in twisted trilayer graphene.

Transformer spin-triplet superconductivity at the onset of isospin order in bilayer graphene

The quest for unconventional superconductivity governed by Coulomb repulsion between electrons rather than phonon attraction received new momentum with the advent of moir\'e graphene. Initially, delineating the phonon and Coulomb-repulsion-based pairing mechanisms has proven to be a challenging task, however the situation has changed after recent discovery of superconductivity in non-twisted graphene bilayers and trilayers. Superconductivity occurring at the phase boundaries of spin and valley polarized orders calls for non-phonon scenarios, yet the specific pairing mechanisms remain to be understood. Here we analyze a striking example -- superconductivity in graphene bilayers occurring at the onset of valley-polarized order induced by a magnetic field. We describe an attraction-from-repulsion mechanism for pairing mediated by a quantum-critical mode, which fully explains the observed phenomenology. While it is usually notoriously difficult to infer the pairing mechanism from the observed superconducting phases, this case presents a rare exception, allowing for a fairly unambiguous identification of the origin of the pairing glue. A combination of factors such as the location of superconducting phase at the onset of isospin-polarized phase, a threshold in a magnetic field, above which superconductivity occurs, and its resilience at high magnetic fields paints a clear picture of a triplet superconductivity driven by quantum-critical fluctuations.

Local probes and superconductivity in magic angle twisted bilayer and trilayer graphene

Local probes and superconductivity in magic angle twisted bilayer and trilayer graphene

Periodic electron oscillation in coupled two-dimensional lattices

We study the time evolution of electron wavepacket in the coupled two-dimensional (2D) lattices with mirror symmetry, utilizing the tight-binding Hamiltonian framework. We show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal directions. The frequency of this oscillation is determined by the strength of the interlayer hopping. Additionally, we provide numerical evidence that a damped periodic oscillation occurs in the coupled 2D disordered lattices with degree of disorder W, with the decay time being inversely proportional to the square of W and the frequency change being proportional to the square of W, which is similar to the case in the coupled 1D disordered lattices. Our numerical results further confirm that the periodic and damped periodic electron oscillations are universal, independent of lattice geometry, as demonstrated in AA-stacked bilayer and tri-layer graphene systems. Unlike the Bloch oscillation driven by electric fields, the periodic oscillation induced by interlayer coupling does not require the application of an electric field, has an ultrafast periodicity much shorter than the electron decoherence time in real materials, and can be tuned by adjusting the interlayer coupling. Our findings pave the way for future observation of periodic electron oscillation in material systems at the atomic scale.

Epitaxial growth of trilayer graphene moiré superlattice

The graphene-based moiré superlattice has been demonstrated as an exciting system for investigating strong correlation phenomenon. However, the fabrication of such moiré superlattice mainly relies on transfer technology. Here, we report the epitaxial growth of trilayer graphene (TLG) moiré superlattice on hexagonal boron nitride (hBN) by a remote plasma-enhanced chemical vapor deposition method. The as-grown TLG/hBN shows a uniform moiré pattern with a period of ∼ 15 nm by atomic force microscopy (AFM) imaging, which agrees with the lattice mismatch between graphene and hBN. By fabricating the device with both top and bottom gates, we observed a gate-tunable bandgap at charge neutral point (CNP) and displacement field tunable satellite resistance peaks at half and full fillings. The resistance peak at half-filling indicates a strong electron–electron correlation in our grown TLG/hBN superlattice. In addition, we observed quantum Hall states at Landau level filling factors ν = 6, 10, 14, …, indicating that our grown trilayer graphene has the ABC stacking order. Our work suggests that epitaxy provides an easy way to fabricate stable and reproducible two-dimensional strongly correlated electronic materials.

Wave-packet scattering at a normal-superconductor interface in two-dimensional materials: A generalized theoretical approach

A wave-packet time evolution method, based on the split-operator technique, is developed to investigate the scattering of quasiparticles at a normal-superconductor interface of arbitrary profile and shape. As a practical application, we consider a system where low-energy electrons can be described as Dirac particles, which is the case for most two-dimensional materials, such as graphene and transition-metal dichalcogenides. However, the method is easily adapted for other cases such as electrons in few-layer black phosphorus or any Schr\"odinger quasiparticles within the effective mass approximation in semiconductors. We employ the method to revisit Andreev reflection in mono-, bi-, and trilayer graphene, where specular- and retro-reflection cases are observed for electrons scattered by a steplike superconducting region. The effect of opening a zero-gap channel across the superconducting region on the electron and hole scattering is also addressed, as an example of the versatility of the technique proposed here.

Superconductivity and correlated phases in non-twisted bilayer and trilayer graphene

The discovery of a very rich phase diagram in twisted bilayer graphene [1,2] renewed the interest into the properties of other systems based on graphene. An unexpected finding has been the observation of superconductivity in non-twisted graphene bilayers and trilayers [3-5]. In this perspective, we give an overview of the search for uncommon phases in non-twisted graphene systems. We first describe results related to the topic before the aforementioned experiments [3-5] were published. Then, we address the new experimental findings which have triggered the recent interest in the problem. Lastly, we analyze the already numerous theory works studying the underlying physical processes [6].

Superconductivity from electronic interactions and spin-orbit enhancement in bilayer and trilayer graphene

What drives superconductivity in non-moir\'e graphene? Here, an electron-electron mechanism is applied to the continuum framework of Bernal bilayer and rhombohedral trilayer graphene. Within a Kohn-Luttinger-like approach, the internal screening of the long-range Coulomb potential leads to an effective attraction between carriers, enabling the formation of Cooper pairs. The calculations provide a filling-dependent critical temperature that is remarkably enhanced due to Ising spin-orbit coupling, and determine the spin-triplet valley-singlet symmetry of the superconducting order parameter, in line with recent experimental advances.

Strong correlations in ABC-stacked trilayer graphene: Moiré is important

Recent experiments uncovering ferromagnetism and superconductivity in multilayer graphene have questioned the importance of moir\'e potentials in determining the myriad phenomena in two-dimensional materials. In this work, using Hartree-Fock analysis with a careful treatment of periodic potentials, the authors demonstrate that moir\'e potentials indeed crucially affect the strong correlation physics, with their impact as beyond that of a weak perturbation. In short: moir\'e is important.