Superlattice potential modulation can produce flat minibands in Bernal-stacked bilayer graphene. In this work we study how band topology and interaction-induced symmetry-broken phases in this system are controlled by tuning the displacement field and the shape and strength of the superlattice potential. We use an analytic perturbative analysis to demonstrate that topological flat bands are favored by a honeycomb-lattice-shaped potential, and numerics to show that the robustness of topological bands depends on both the displacement field strength and the periodicity of the superlattice potential. At integer fillings of the topological flat bands, the strength of the displacement field and the superlattice potential tune phase transitions between quantum anomalous Hall insulator, trivial insulator, and metallic states. We present mean-field phase diagrams in a gate voltage parameter space at filling factor $ν=1$, and discuss the prospects of realizing quantum anomalous Hall insulators and fractional Chern insulators when the superlattice potential modulation is produced by dielectric patterning or adjacent moiré materials.
Employing graphene as a template, we fabricate moiré superlattices by stacking bilayer or folded bilayer-bilayer graphene (BLG or fBBLG) and hexagonal boron nitride (hBN), i.e., hBN/BLG/hBN or hBN/fBBLG/hBN stacks, with a small twist angle between the graphene and one of the two hBN layers. Because of the modulation due to the hBN, higher-generation Dirac points can emerge with a narrow bandwidth and van Hove singularities. In the moiré superlattice devices, we can therefore access the higher-generation Dirac points by in-situ gate tuning. This study is based on our previous paper (Appl. Phys.…
Energy band structure of the bilayer graphene superlattices with $δ$-function magnetic barriers and zero average magnetic flux is studied within the four-band continuum model, using the transfer matrix method. The periodic magnetic potential effects on the zero-energy Dirac point of pristine bilayer graphene are exactly analyzed. Magnetic potential is shown also to generate finite-energy Dirac points at the edges of Brillouin zone the positions of which and the related dispersions are determined in the case of symmetric potentials.
We report on transport properties in dual-gated hexagonal boron nitride (hBN)/bilayer-graphene (BLG) superlattices. Here, BLG is nontwisted, i.e., plain. This paper focuses on the charge neutrality point (CNP) for a plain BLG. Under a perpendicular magnetic field, transitions between two insulating phases at the CNP are detected by varying a displacement field with the study on the resistance-temperature characteristics and the magnetoresistance. This work opens avenues for exploring the global phase diagram of the hBN/BLG superlattices beyond the CNP.
A model of a superlattice consisting of alternating strips of single-layer and bilayer graphene is proposed, whose parameters of the energy spectrum can be controlled by changing the external electric field perpendicular to the surface of the sample. Using the Kronig-Penney model, the dispersion equation is obtained, based on the analysis of which the energy spectrum of a graphene superlattice is studied depending on the ratio of the strip widths of single-layer and bilayer graphene. The results of the analytical solution are compared with the results of modeling by methods of the theory of th…
Moiré superlattice created by twist stacking has multiple physical properties. These physical properties depend on the twist angle, hence investigation of the twist angle dependency is important for the deep understanding of physical phenomena in moiré superlattice. In this work, negative magnetoresistance owing to weak localization (WL) was investigated in twisted double bilayer graphene (TDBG) as a function of the twist angle. The ratio of the intervalley scattering time to the intravalley scattering time, estimated using the WL formula for bilayer graphene, tended to decrease as the twist a…
We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of 'topological' edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Br…
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 with Berry curvature accumulating at the charge neutral point (CNP), and it…
Motivated by recent experimental findings on the low-energy spectrum of Kekulé-patterned graphene, the optoelectronic signatures of graphene superlattices with a spatial modulation that triples the size of the unit cell and folds the valleys to the center of the Brillouin zone are studied. For superlattices like those visualized in recent experiments, the optoelectronic response reveals multiple species of carriers distinguished by their effective masses or Fermi velocities. Their signatures are similar to those of systems hosting multifold fermions in which different frequency intervals are d…
Common models describing magnetotransport properties of periodically modulated two--dimensional systems often either directly start from a semiclassical approach or give results well conceivable within the semiclassical framework. Recently, magnetoresistance oscillations have been found on samples with strong unilateral modulation and short period (d=15 nm) which cannot be explained on a semiclassical level (magnetic breakdown). We use a simple fully quantum mechanical model which gives us both magnetoresistance data nicely comparing to the experiments and a good intuitive insight into the eff…
Twisted bilayer graphene (TwBLG) is one of the simplest van der Waals heterostructures, yet it yields a complex electronic system with intricate interplay between moiré physics and interlayer hybridization effects. We report on electronic transport measurements of high mobility small angle TwBLG devices showing clear evidence for insulating states at the superlattice band edges, with thermal activation gaps several times larger than theoretically predicted. Moreover, Shubnikov-de Haas oscillations and tight binding calculations reveal that the band structure consists of two intersecting Fermi …
Graphene-based superlattice (SL) formed by a periodic gap modulation is studied theoretically using a Dirac-type Hamiltonian. Analyzing the dispersion relation we have found that new Dirac points arise in the electronic spectrum under certain conditions. As a result, the gap between conduction and valence minibands disappears. The expressions for the position of these Dirac points in ${\bf k}$-space and threshold value of the potential for their emergence were obtained. At some parameters of the system, we have revealed interface states which form the top of the valence miniband.
Energy band structure of the bilayer graphene superlattices with zero-averaged periodic $δ$-function potentials are studied within the four-band continuum model. Using the transfer matrix method, studies are mainly focused on examining the touching points between adjacent minibands. For the zero-energy touching points the dispersion relation derived shows the Dirac-like double-cone shape with the group velocity which is periodic in the potential strength $P$ with the period of $π$ and becomes anisotropic at relatively large $P$. From the finite-energy touching points we have identified those l…
We review recent work on superlattices in monolayer and bilayer graphene. We highlight the role of the quasiparticle chirality in generating new Dirac fermion modes with tunable anisotropic velocities in one dimensional (1D) superlattices in both monolayer and bilayer graphene. We discuss the structure of the Landau levels and magnetotransport in such superlattices over a wide range of perpendicular (orbital) magnetic fields. In monolayer graphene, we show that an orbital magnetic field can reverse the anisotropy of the transport imposed by the superlattice potential, suggesting possible switc…
Stack of correlated insulating states in bilayer graphene kagome superlattice
State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院量子功能材料国家重点实验室）；ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University（上海科技大学拓扑物理实验室）；Department of Physics and Astronomy, University of California, Riverside（加州大学河滨分校物理与天文学系）；Department of Physics, University of Oxford（牛津大学物理系）；School of Information Science and Technology, ShanghaiTech University（上海科技大学信息科学与技术学院）
Lattice reconstruction in twisted transition-metal dichalcogenide (TMD) bilayers gives rise to piezo- and ferroelectric moiré potentials for electrons and holes, as well as a modulation of the hybridisation across the bilayer. Here, we develop hybrid $\mathbf{k}\cdot \mathbf{p}$ tight-binding models to describe electrons and holes in the relevant valleys of twisted TMD homobilayers with parallel (P) and anti-parallel (AP) orientations of the monolayer unit cells. We apply these models to describe moiré superlattice effects in twisted WSe${}_2$ bilayers, in conjunction with microscopic \emph{ab…
Based on first-principles calculations we showed that superlattices of periodically repeated junctions of hydrogen saturated silicon nanowire segments having different lengths and diameters form multiple quantum well structures. The band gap of the superlattice is modulated in real space as its diameter does and results in a band gap in momentum space which is different from constituent nanowires. Specific electronic states can be confined in either narrow or wide regions of superlattice. The type of the band lineup and hence the offsets of valence and conduction bands depend on the orientatio…
Gapless bilayer graphene (GBG), like monolayer graphene, is a material system with unique properties, such as anti-Klein tunneling and intrinsic Fano resonances. These properties rely on the gapless parabolic dispersion relation and the chiral nature of bilayer graphene electrons. In addition, propagating and evanescent electron states coexist inherently in this material, giving rise to these exotic properties. In this sense, bilayer graphene is unique, since in most material systems in which Fano resonance phenomena are manifested an external source that provides extended states is required. …
Due to low dimensionality, the controlled stacking of the 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…
Twistronic van der Waals heterostrutures offer exciting opportunities for engineering optoelectronic properties of nanomaterials. Here, we use multiscale modeling to study trapping of charge carriers and excitons by ferroelectric polarisation and piezoelectric charges by domain structures in twistronic WX$_2$/MoX$_2$ bilayers (X=S,Se). For almost aligned 2H-type bilayers, we find that holes and electrons are trapped in the opposite -- WMo and XX (tungsten over molybdenum {\it versus} overlaying chalcogens) -- corners of the honeycomb domain wall network, swapping their position at a twist angl…
We consider the electronic structure of a slightly twisted graphene bilayer and show the coexistence of van Hove singularities (VHSs) and superlattice Dirac points in a continuum approximation. The graphene-on-graphene moiré pattern gives rise to a periodic electronic potential, which leads to the emergence of the superlattice Dirac points due to the chiral nature of the charge carriers. Owning to the distinguishing real and reciprocal structures, the sublattice exchange even and odd structures of the twisted graphene bilayer (the two types of commensurate structures) result in two different s…
We study the magneto-optical conductivity of a number of Van der Waals heterostructures, namely, twisted bilayer graphene, AB-AB and AB-BA stacked twisted double bilayer graphene and monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride. As magnetic field increases, the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum. Whilst twisted bilayer graphene displays only weak circular dichroism, monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride show specifically strong circular dichro…
We review the energy spectrum and transport properties of several types of one- dimensional superlattices (SLs) on single-layer and bilayer graphene. In single-layer graphene, for certain SL parameters an electron beam incident on a SL is highly collimated. On the other hand there are extra Dirac points generated for other SL parameters. Using rectangular barriers allows us to find analytic expressions for the location of new Dirac points in the spectrum and for the renormalization of the electron velocities. The influence of these extra Dirac points on the conductivity is investigated. In the…
We theoretically investigate the electronic structures of moiré superlattices arising in monolayer / bilayer graphene stacked on hexagonal boron nitride (hBN) in presence and absence of magnetic field. We develop an effective continuum model from a microscopic tight-binding lattice Hamiltonian, and calculate the electronic structures of graphene-hBN systems with different rotation angles. Using the effective model, we explain the characteristic band properties such as the gap opening at the corners of the superlattice Brillouin zone (mini-Dirac point). We also investigate the energy spectrum a…
The quantum Goos-Hänchen shifts of the transmitted electron beam through an AA-stacked bilayer graphene superlattices is investigated. We found that the band structures of graphene superlattices can have more than one Dirac point, their locations do not depend on the number of barriers. It was revealed that any $n$-barrier structure is perfectly transparent at normal incidence around the Dirac points created in the superlattices. We showed that the Goos-Hänchen shifts display sharp peaks inside the transmission gap around two Dirac points ($E= V_B + τ$, $E= V_W + τ$), which are equal to those …
In this review article we discuss the recent progress in studying ballistic transport for charge carriers in graphene through highly inhomogenous magnetic field known as magnetic barrier in combination with gate voltage induced electrostatic potential. Starting with cases for a single or double magnetic barrier we also review the progress in understanding electron transport through the superlattices created out of such electromagnetic potential barriers and discuss the possibility of experimental realization of such systems. The emphasis is particularly on the analogy of such transport with pr…
We investigate the electronic Bloch oscillation in bilayer graphene gradient superlattices using transfer matrix method. By introducing two kinds of gradient potentials of square barriers along electrons propagation direction, we find that Bloch oscillations up to terahertz can occur. Wannier-Stark ladders, as the counterpart of Bloch oscillation, are obtained as a series of equidistant transmission peaks, and the localization of the electronic wave function is also signature of Bloch oscillation. Forthermore, the period of Bloch oscillation decreases linearly with increasing gradient of barri…
Quantum tunneling and defect-induced transport modulation in twisted bilayer graphene superlattices
Multidisciplinary Research and Innovation Laboratory, EMAFI team, Polydisciplinary Faculty, Sultan Moulay Slimane University（苏丹穆莱·斯莱曼大学多学科创新研究实验室）；Advanced Laboratory in Industrial Engineering and Logistics (LARILE) National School of Electrical and Mechanical Engineering, Hassan II University（哈桑二世大学电气机械工程学院工业工程与物流高级实验室）
It is well known that stacking domains form in moiré superlattices due to the competition between the interlayer van der Waals forces and intralayer elastic forces, which can be recognized as polar domains due to the local spontaneous polarization in bilayers without centrosymmetry. We propose a theoretical model which captures the effect of an applied electric field on the domain structure. The coupling between the spontaneous polarization and field leads to uneven relaxation of the domains, and a net polarization in the superlattice at nonzero fields, which is sensitive to the moiré period. …
High mobility single and few-layer graphene sheets are in many ways attractive as nanoelectronic circuit hosts but lack energy gaps, which are essential to the operation of field-effect transistors. One of the methods used to create gaps in the spectrum of graphene systems is to form long period moire patterns by aligning the graphene and hexagonal boron nitride (h-BN) substrate lattices. Here, we use planar tunneling devices with thin h-BN barriers to obtain direct and accurate tunneling spectroscopy measurements of the energy gaps in single- and bi-layer graphene-h-BN superlattice structures…
The electronic properties of bilayer graphene strongly depend on relative orientation of the two atomic lattices. Whereas Bernal-stacked graphene is most commonly studied, a rotational mismatch between layers opens up a whole new field of rich physics, especially at small interlayer twist. Here we report on magnetotransport measurements on twisted graphene bilayers, prepared by folding of single layers. These reveal a strong dependence on the twist angle, which can be estimated by means of sample geometry. At small rotation, superlattices with a wavelength in the order of 10 nm arise and are o…
In stacks of two-dimensional crystals, mismatch of their lattice constants and misalignment of crystallographic axes lead to formation of moiré patterns. We show that moiré superlattice effects persist in twisted bilayer graphene (tBLG) with large twists and short moiré periods. Using angle-resolved photoemission, we observe dramatic changes in valence band topology across large regions of the Brillouin zone, including the vicinity of the saddle point at $M$ and across 3 eV from the Dirac points. In this energy range, we resolve several moiré minibands and detect signatures of secondary Dirac …
Recently the small-twist-angle (< 2°) bilayer graphene has received extraordinary attentions due to its exciting physical properties. Compared with monolayer graphene, the Brillouin zone folding in twisted bilayer graphene (TBG) leads to the formation of superlattice bandgap and significant modification of density of states. However, these emerging properties have rarely been leveraged for the realization of new optoelectronic devices. Here we demonstrate the strong, gate-tunable photoresponse in mid-infrared wavelength range of 5 to 12 um. A maximum extrinsic photoresponsivity of 26 mA/W has …
The recently observed unconventional ferroelectricity in AB bilayer graphene sandwiched by hexagonal Boron Nitride (hBN) presents a new platform to manipulate correlated phases in multilayered van der Waals heterostructures. We present a low-energy continuum model for AB bilayer graphene encapsulated by the top and bottom layers of either hBN or graphene, with two independent twist angles. For the graphene/hBN heterostructures, we show that twist angle asymmetry leads to a layer polarization of the valence and conduction bands. We also show that an out-of-plane displacement field not only tune…
We show that a sliding motion between the two layers of a \moire superlattice induces an electric current and realizes a two-dimensional version of the topological Thouless pump when the Fermi energy lies in one of the minigaps. Interestingly, a chiral charge pump, namely, a transverse current induced by the sliding motion, is possible in twisted homobilayers. This result is confirmed by a concrete calculation of the adiabatic current in twisted bilayer graphene. Our work reveals an interesting link between mechanical motion and electricity unique to \moire superlattices, and may find applicat…
We present a theoretical study of Weiss oscillations in magnetoconductivity of bilayer graphene. Bilayer graphene in the presence of a perpendicular magnetic field and a unidirectional weak electric modulation is considered.We determine the $σ_{yy}$ component of the magnetoconductivity tensor for this system which is shown to exhibit Weiss oscillations. We show that Weiss oscillations in the magnetoconductivity of bilayer graphene are enhanced and more robust with temperature compared to those in conventional two-dimensional electron gas systems whereas they are less robust with temperature co…
In two-dimensional (2D) twisted bilayers, the van der Waals (vdW) interlayer interaction introduces atomic-scale reconstruction at interface by locally rotating lattice to form strain-field vortex networks in their moiré superlattice. However, direct imaging the tiny local lattice rotation of the strain-field vortex requires extremely high spatial resolution and is an outstanding challenge in experiment. Here, a topmost small-period graphene moiré pattern is introduced to magnify sub-Angstrom distortions of the lattice and tiny local lattice rotation in underlying twisted bilayer graphene (TBG…
We study transport properties of graphene nanostructures consisted of alternating slabs of gapless and gapped graphene in the presence of piecewise constant external potential equal to zero in the gapless regions. The transmission through single-, double-barrier structures and superlattices has been studied. It was revealed that any n-barrier structure is perfectly transparent at certain conditions defining the positions of new Dirac points created in the superlattice. The conductance and the shot noise were as well computed and investigated for the considered graphene systems. In a general ca…
Twisted bilayer graphene (tBLG) provides us with a large rotational freedom to explore new physics and novel device applications, but many of its basic properties remain unresolved. Here we report the synthesis and systematic Raman study of tBLG. Chemical vapor deposition was used to synthesize hexagon- shaped tBLG with a rotation angle that can be conveniently determined by relative edge misalignment. Superlattice structures are revealed by the observation of two distinctive Raman features: folded optical phonons and enhanced intensity of the 2D-band. Both signatures are strongly correlated w…
Moiré structures in van der Waals heterostructures lead to emergent phenomena including superconductivity in twisted bilayer graphene and optically accessible strongly-correlated electron states in transition metal dichalcogenide heterobilayers. Dual periodicity moiré structures (DPMS) formed in layered structures with more than two layers have been shown to lead to ferromagnetism and multiple secondary Dirac points in TBG. Whilst in principle it is possible to obtain DPMS in bilayers there has not been clear experimental evidence of this yet. In this paper we present signatures of DPMS in a t…
We investigate theoretically the anisotropic electronic and optical behaviors of a monolayer black phosphorus (phosphorene) modulated by periodic potential superlattices in arbitrary directions. We demonstrate that different strength and orientation of the phosphorene potential superlattice can give rise to distinct energy spectra, i.e., tuning the intrinsic electronic anisotropy. Accordingly, the anisotropic effective mass, and optical absorption modulated by superlattice strength and orientation are addressed systematically. This feature enables tuning capability more than one order of magni…
The electronic structure of a graphene superlattice composed by two periodic regions with different Fermi velocity, energy gap and electrostatic potential is investigated by using an effective Dirac-like Hamiltonian. It must be expected that the change of the Fermi velocity in one region of the graphene superlattice is equivalent to changing the width of this region keeping the Fermi velocity unchanged, provided that the time taken to charge carriers cross the region is the same. However, it is shown here that these two systems are not equivalent. We found extra Dirac points induced by the per…
The formation of a superstructure - with a related Moiré pattern - plays a crucial role in the extraordinary optical and electronic properties of twisted bilayer graphene, including the recently observed unconventional superconductivity. Here we put forward a novel, interdisciplinary approach to determine the Moiré angle in twisted bilayer graphene based on the photonic spin Hall effect. We show that the photonic spin Hall effect exhibits clear fingerprints of the underlying Moiré pattern, and the associated light beam shifts are well beyond current experimental sensitivities in the near-infra…
