Bilayer Graphene Superlattices Research Articles

Thermoelectricity in bilayer graphene superlattices

Low-dimensional thermoelectricity is based on the redistribution-accumulation of the electron density of states by reducing the dimension of thermoelectric structures. Superlattices are the archetype of these structures due to the formation of energy minibands and minigaps. Here, we study for the first time the thermoelectric response of gated bilayer graphene superlattices (GBGSLs). The study is based on the four-band effective Dirac Hamiltonian, the hybrid matrix method and the Landauer-Büttiker formalism. We analyze the Seebeck coefficient, the power factor, figure of merit, output power and efficiency for different temperatures and different superlattice structural parameters. We pay special attention to the impact of not only minibands and minigaps on the thermoelectric properties, but also to intrinsic resonances in bilayer graphene structures such as Breit-Wigner, Fano and hybrid resonances. In particular, we analyze the interplay between minibands and Fano resonances as a possible mechanism to improve the thermoelectric response of GBGSLs. We also compute the density of states to know if the redistribution-accumulation of electron states is implicated in the thermoelectric response of GBGSLs.

Tailoring Dirac Fermions by In-Situ Tunable High-Order Moiré Pattern in Graphene-Monolayer Xenon Heterostructure

We report an experimental study of a high-order moiré pattern formed in graphene-monolayer xenon heterostructure. The moiré period is insitu tuned from few nanometers to +∞, by adjusting the lattice constant of the xenon monolayer through annealing. Using angle-resolved photoemission spectroscopy, we observe that Dirac node replicas move closer and finally overlap with a gap opening, as the moiré pattern expands to +∞ and evolves into a Kekulé distortion. A moiré Hamiltonian coupling Dirac fermions from different valleys explains experimental results and indicates narrow moiré band. Our Letter demonstrates a platform to study continuous evolution of the moiré pattern, and provides an unprecedented approach for tailoring Dirac fermions with tunable intervalley coupling.

Investigation in double layer graphene superlattice and its electronic properties

This paper mainly discussed the graphene and other 2D materials, as well as their electronic properties. The history and theory prediction of graphene, and production of graphene (mechanical exfoliation and CVD method) are discussed. Graphene hBN superlattice and bi-layer graphene superlattice are presented, with following discussion of the superconductivity of the magic angle. Finally, characterization methods such as AFM and SEM are presented.

Moiré flat bands in twisted 2D hexagonal vdW materials

Moiré superlattices (MSL) in twisted bilayer graphene (TBG) and its derived structures can host exotic correlated quantum phenomena because the narrow moiré flat minibands in those systems effectively enhance the electron-electron interaction. Correlated phenomena are also observed in 2H-transitional metal dichalcogenides MSL. However, the number of moiré systems that have been explored in experiments are still very limited. Here we theoretically investigate a series of two-dimensional (2D) twisted bilayer hexagonal materials beyond TBG at fixed angles of 7.34∘ and 67.34∘ with 22 2D van der Waals layered materials that are commonly studied in experiments. First-principles calculations are employed to systemically study the moiré minibands in these systems. We find that flat bands with narrow bandwidth generally exist in these systems. Some of the systems such as twisted bilayer In2Se3, InSe, GaSe, GaS and PtS2 even host ultra-flat bands with bandwidth less than 20 meV even for such large angles, which makes them especially appealing for further experimental investigations. We further analysis the characters of moiré flat bands and provide guidance for further exploration of 2D MSL that could host strong electron correlations.

Moiré circuits: Engineering magic-angle behavior

Moir\'e superlattices in the twisted bilayer graphene provide an unprecedented platform to investigate a wide range of exotic quantum phenomena. Recently, the twist degree of freedom has been introduced into various classical wave systems, giving rise to new ideas for the wave control. The question is whether twistronics and moir\'e physics can be extended to electronics with potential applications in the twist-enabled signal processing. Here, we demonstrate both in theory and experiment that lots of fascinating moir\'e physics can be engineered using electric circuits with extremely high degrees of freedom. By suitably designing the interlayer coupling and biasing of one sublattice for the twisted bilayer circuit, the low-energy flat bands with large bandgaps away from other states can be realized at various twist angles. Based on the moir\'e circuit with a fixed twist angle, we experimentally demonstrate the effect of band narrowing as well as the localization of electric energy when a magic value of the interlayer coupling is applied. Furthermore, the topological edge states, which originate from the moir\'e potential induced pseudomagnetic field, are also observed for the first time. Our findings suggest a flexible platform to study twistronics beyond natural materials and other classical wave systems, and may have potential applications in the field of intergraded circuit design.

Growing twisted bilayer graphene at small angles

Growing twisted bilayer graphene at small angles

Long-range nontopological edge currents in charge-neutral graphene.

Van der Waals heterostructures display numerous unique electronic properties. Nonlocal measurements, wherein a voltage is measured at contacts placed far away from the expected classical flow of charge carriers, have been widely used in the search for novel transport mechanisms, including dissipationless spin and valley transport1-9, topological charge-neutral currents10-12, hydrodynamic flows13 and helical edge modes14-16. Monolayer1-5,10,15-19, bilayer9,11,14,20 and few-layer21 graphene, transition-metal dichalcogenides6,7 and moiré superlattices8,10,12 have been found to display pronounced nonlocal effects. However, the origin of these effects is hotly debated3,11,17,22-24. Graphene, in particular, exhibits giant nonlocality at charge neutrality1,15-19, a striking behaviour that has attracted competing explanations. Using a superconducting quantum interference device on a tip (SQUID-on-tip) for nanoscale thermal and scanning gate imaging25, here we demonstrate that the commonly occurring charge accumulation at graphene edges23,26-31 leads to giant nonlocality, producing narrow conductive channels that support long-range currents. Unexpectedly, although the edge conductance has little effect on the current flow in zero magnetic field, it leads to field-induced decoupling between edge and bulk transport at moderate fields. The resulting giant nonlocality at charge neutrality and away from it produces exotic flow patterns that are sensitive to edge disorder, in which charges can flow against the global electric field. The observed one-dimensional edge transport is generic and nontopological and is expected to support nonlocal transport in many electronic systems, offering insight into the numerous controversies and linking them to long-range guided electronic states at system edges.

Quantifying the Charge Carrier Interaction in Metallic Twisted Bilayer Graphene Superlattices.

The mechanism of charge carrier interaction in twisted bilayer graphene (TBG) remains an unresolved problem, where some researchers proposed the dominance of the electron–phonon interaction, while the others showed evidence for electron–electron or electron–magnon interactions. Here we propose to resolve this problem by generalizing the Bloch–Grüneisen equation and using it for the analysis of the temperature dependent resistivity in TBG. It is a well-established theoretical result that the Bloch–Grüneisen equation power-law exponent, p, exhibits exact integer values for certain mechanisms. For instance, p = 5 implies the electron–phonon interaction, p = 3 is associated with the electron–magnon interaction and p = 2 applies to the electron–electron interaction. Here we interpret the linear temperature-dependent resistance, widely observed in TBG, as , which implies the quasielastic charge interaction with acoustic phonons. Thus, we fitted TBG resistance curves to the Bloch–Grüneisen equation, where we propose that p is a free-fitting parameter. We found that TBGs have a smoothly varied p-value (ranging from 1.4 to 4.4) depending on the Moiré superlattice constant, λ, or the charge carrier concentration, n. This implies that different mechanisms of the charge carrier interaction in TBG superlattices smoothly transition from one mechanism to another depending on, at least, λ and n. The proposed generalized Bloch–Grüneisen equation is applicable to a wide range of disciplines, including superconductivity and geology.

Evidence for Moiré Trions in Twisted MoSe2 Homobilayers.

Moiré superlattices of van der Waals structures offer a powerful platform for engineering band structure and quantum states. For instance, Moiré superlattices in magic-angle twisted bilayer graphene, ABC trilayer graphene have been shown to harbor correlated insulating and superconducting states, while in transition metal dichalcogenide (TMD) twisted bilayers, Moiré excitons have been identified. Here we show that the effects of a Moiré superlattice on the band structure are general: In TMD twisted bilayers, excitons and exciton complexes can be trapped in the superlattice in a manner analogous to ultracold bosonic or Fermionic atoms in optical lattices. Using twisted MoSe2 homobilayers as a model system, we present evidence for Moiré trions. Our results thus open possibilities for designer van der Waals structures hosting arrays of Fermionic or bosonic quasiparticles, which can be used to realize tunable many-body states crucial for quantum simulation and quantum information processing.

Optical absorption in bilayer graphene superlattices

A periodic statistical potential applied in each layer of bilayer graphene can change it to a superlattice, enabling its application as a flexible light absorber. In this work, the effect of structural parameters on the optical absorption and bandgap of such a bilayer graphene superlattice is studied theoretically in detail. The bilayer graphene superlattice consists of two single layers of graphene with different patterns of static periodic potential applied. The role of the unit cell length, different ratios between the width of each region, and the magnitude of the applied potential in the optical absorption is analyzed in detail. The results reveal that the optical absorption can be enhanced by increasing the magnitude of the square static periodic potential applied to each single layer of graphene. The effect of light polarization is also addressed. It is observed that different ratios of the widths of periodic regions do not change the absorption, while the configuration and value of the square static periodic potential applied plays a crucial role in the absorption spectrum.

Spin-Twisted Optical Lattices: Tunable Flat Bands and Larkin-Ovchinnikov Superfluids.

Moiré superlattices in twisted bilayer graphene and transition-metal dichalcogenides have emerged as a powerful tool for engineering novel band structures and quantum phases of two-dimensional quantum materials. Here we investigate Moiré physics emerging from twisting two independent hexagonal optical lattices of atomic (pseudo-)spin states (instead of bilayers) that exhibit remarkably different physics from twisted bilayer graphene. We employ a momentum-space tight-binding calculation that includes all range real-space tunnelings and show that all twist angles θ≲6° can become magic and support gapped flat bands. Because of the greatly enhanced density of states near the flat bands, the system can be driven to superfluidity by weak attractive interaction. Strikingly, the superfluid phase corresponds to a Larkin-Ovchinnikov state with finite momentum pairing that results from the interplay between flat bands and interspin interactions in the unique single-layer spin-twisted lattice. Our work may pave the way for exploring novel quantum phases and twistronics in cold atomic systems.

Topologically derived dislocation theory for twist and stretch moiré superlattices in bilayer graphene

We develop a continuum dislocation description of twist and stretch moire superlattices in 2D material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moire structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints, and which minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer, and a Peierls-Nabarro like interfacial contribution arising from stacking disregistry. The dislocation core emerges naturally within the formalism as a result of the competition between the two contributions. The approach presented here captures the structure and energetics of twist and stretch moire superlattices of dislocations with arbitrary direction and character, without assuming an analytical solution a priori, with no adjustable parameters, while accounting naturally for dislocation-dislocation image interactions. In comparisons to atomistic simulations using classical potentials, the maximum structure deviation is 6%, while the maximum line energy deviation is 0.019 eV/Angstrom. Several applications of our model are shown, including predicting the variation of structure with twist angle, and describing dislocation line tension and junction energies.

Heteromoiré Engineering on Magnetic Bloch Transport in Twisted Graphene Superlattices.

Localized electrons subject to applied magnetic fields can restart to propagate freely through the lattice in delocalized magnetic Bloch states (MBSs) when the lattice periodicity is commensurate with the magnetic length. Twisted graphene superlattices with moiré wavelength tunability enable experimental access to the unique delocalization in a controllable fashion. Here, we report the observation and characterization of high-temperature Brown-Zak (BZ) oscillations which come in two types, 1/B and B periodicity, originating from the generation of integer and fractional MBSs, in the twisted bilayer and trilayer graphene superlattices, respectively. Coexisting periodic-in-1/B oscillations assigned to different moiré wavelengths are dramatically observed in small-angle twisted bilayer graphene, which may arise from angle-disorder-induced in-plane heteromoiré superlattices. Moreover, the vertical stacking of heteromoiré supercells in double-twisted trilayer graphene results in a mega-sized superlattice. The exotic superlattice contributes to the periodic-in-B oscillation and dominates the magnetic Bloch transport.

Spin-dependent group delay time and Hartman effect in ferromagnetic bilayer graphene superlattice

We theoretically study the spin-dependent group delay time through ferromagnetic bilayer graphene superlattice in the absence and presence of the bandgap. It is found that the group delay time depends on the spin degree of freedom and exhibits an oscillatory behavior with respect to the Fermi energy and barrier width. Furthermore, in the absence of the bandgap, the superluminal or Hartman effect exists only for the normal angle of incidence. Moreover, when bandgap value is large enough [Formula: see text], the Hartman effect can be observed for all angles of incidence. These results are contrary to the observed behavior for monolayer graphene superlattice.

Structure-properties relations in graphene derivatives and metamaterials obtained by atomic-scale modeling

ABSTRACTRecent findings of atomic-scale modelling studies are reviewed on graphene derivatives and metamaterials fabricated through chemical functionalization and/or defect engineering of graphene sheets. Results of molecular-statics and molecular-dynamics simulations according to a reliable bond-order potential, as well as first-principles density functional theory calculations are reviewed that have established useful structure-properties relations in two-dimensional materials, such as graphene nanomeshes (GNMs), electron-irradiated graphene, and interlayer-bonded twisted bilayer graphene. Quantitative relationships are established for the elastic moduli, mechanical properties, and thermal conductivity of GNMs as a function of the nanomesh porosity and the mechanical response of GNMs to uniaxial tensile straining is explored over the range of nanomesh porosities. The dependence of structural, mechanical, and thermal transport properties of electron-irradiated graphene sheets on the density of irradiation-induced defects is reviewed, highlighting an amorphization transition accompanied by a brittle-to-ductile transition and a transition in thermal transport mechanism beyond a critical defect concentration. The tunability of the electronic band structure, mechanical properties, and structural response to mechanical loading of graphene-diamond nanocomposite superstructures consisting of nanodiamond superlattices in interlayer-bonded twisted bilayer graphene also is demonstrated by precise control of the density and distribution of covalent interlayer C–C bonds.

Topological valley currents in bilayer graphene/hexagonal boron nitride superlattices

Graphene superlattices have recently been attracting growing interest as an emergent class of quantum metamaterials. In this paper, we report the observation of nonlocal transport in bilayer graphene (BLG) superlattices encapsulated between two hexagonal boron nitride (hBN) layers, which formed hBN/BLG/hBN moiré superlattices. We then employed these superlattices to detect a long-range charge-neutral valley current using an all-electrical method. The moiré superlattice with broken inversion symmetry leads to a “hot spot” at the charge-neutral point (CNP), and it harbors satellites of the CNP. We observed nonlocal resistance on the order of 1 kΩ, which obeys a scaling relation. This nonlocal resistance evolves from an analog of the quantum Hall effect but without magnetic field/time-reversal symmetry breaking, which is associated with a hot-spot-induced topological valley current. This study should pave the way for developing a Berry-phase-sensitive probe to detect hot spots in gapped Dirac materials with inversion-symmetry breaking.

Strain impacts on commensurate bilayer graphene superlattices: Distorted trigonal warping, emergence of bandgap and direct-indirect bandgap transition

Due to low dimensionality, the controlled stacking of graphene films and their electronic properties are susceptible to environmental changes including strain. The strain-induced modification of the electronic properties such as the emergence and modulation of bandgaps crucially depends on the stacking of the graphene films. However, to date, only the impact of strain on electronic properties of Bernal and AA-stacked bilayer graphene has been extensively investigated in theoretical studies. Exploiting density functional theory and tight-binding calculation, we investigate the impacts of in-plane strain on two different classes of commensurate twisted bilayer graphene (TBG) which are even/odd under sublattice exchange (SE) parity. We find that the SE odd TBG remains gapless whereas the bandgap increases for the SE even TBG when applying equibiaxial tensile strain. Moreover, we observe that for extremely large mixed strains both investigated TBG superstructures demonstrate direct-indirect bandgap transition.

Pairing symmetry of interacting fermions on a twisted bilayer graphene superlattice

The pairing symmetry of an effective Hamiltonian for interacting fermions on a twisted bilayer graphene superlattice is studied with the determinant quantum Monte Carlo method. The model has the symmetry of a triangle lattice and a nearly-flat low energy band, features which underlie the magic-angle twisted bilayer graphene superlattice. We show that the low temperature phase is insulating at half-filling, even for relatively weak interactions. The natures of the spin and pairing correlations upon doping are determined, and exhibit an electron-hole asymmetry consistent with experiment. Among the pairing symmetries allowed, we demonstrate that the dominating channels are $d$-wave, opening the possibility of condensation into an unconventional $d_{x^2-y^2}+id_{xy}$ phase, which is characterized by an integer topological invariant and gapless edge states.

Electronic correlations in bilayer-graphene superlattices

Electronic correlations in bilayer-graphene superlattices

Fano resonances in bilayer graphene superlattices

In this work, we address the ubiquitous phenomenon of Fano resonances in bilayer graphene. We consider that this phenomenon is as exotic as other phenomena in graphene because it can arise without an external extended states source or elaborate nano designs. However, there are not theoretical and/or experimental studies that report the impact of Fano resonances on the transport properties. Here, we carry out a systematic assessment of the contribution of the Fano resonances on the transport properties of bilayer graphene superlattices. Specifically, we find that by changing the number of periods, adjusting the barriers height as well as modifying the barriers and wells width it is possible to identify the contribution of Fano resonances on the conductance. Particularly, the coupling of Fano resonances with the intrinsic minibands of the superlattice gives rise to specific and identifiable changes in the conductance. Moreover, by reducing the angular range for the computation of the transport properties it is possible to obtain conductance curves with line-shapes quite similar to the Fano profile and the coupling profile between Fano resonance and miniband states. In fact, these conductance features could serve as unequivocal characteristic of the existence of Fano resonances in bilayer graphene.