Bernal bilayer graphene exhibits a band gap that is tunable through the infrared with an electric field. We show that sublattice odd commensurate twisted bilayer graphene (C-TBG) exhibits a band gap that is tunable through the terahertz with an electric field. We show that from the perspective of terahertz optics the sublattice odd and even forms of C-TBG are "inflated" versions of Bernal and AA stacked bilayer graphene respectively with energy scales reduced by a factor of 110 for the 21.79 degree commensurate unit cell. This lower energy scale is accompanied by a correspondingly smaller gate voltage, which means that the strong-field regime is more easily accessible than in the Bernal case. Finally, we show that the interlayer coherence energy is a directly accessible experimental quantity through the position of a power-law divergence in the optical conductivity.
Misoriented bilayer graphene with commensurate angles shows unique magneto-optical properties. The optical absorption spectra of such a system strongly depend on the angle of rotation. For a general commensurate twist angle the absorption spectra has a simple single-peak structure. However, our studies indicate that there are special angles at which the absorption spectra of the rotated bilayer exhibit well developed multi-peak structures. These angles correspond to even symmetry of the rotated graphene with respect to the sublattice exchange. Magneto-spectroscopy can therefore be a potentiall…
A commensurate-incommensurate phase transition in bilayer graphene is investigated in the framework of the Frenkel-Kontorova model extended to the case of two interacting chains of particles. Analytic expressions are derived to estimate the critical unit elongation of one of the graphene layers at which the transition to the incommensurate phase takes place, the length and formation energy of incommensurability defects (IDs) and the threshold force required to start relative motion of the layers on the basis of dispersion-corrected density functional theory calculations of the interlayer inter…
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…
Dislocations corresponding to a change of stacking in two-dimensional hexagonal bilayers, graphene and boron nitride, and associated with boundaries between commensurate domains are investigated using the two-chain Frenkel-Kontorova model on top of ab initio calculations. Structural transformations of bilayers in which the bottom layer is stretched and the upper one is left to relax freely are considered for gradually increased elongation of the bottom layer. Formation energies of dislocations, dislocation width and orientation of the boundary between commensurate domains are analyzed dependin…
The two-chain Frenkel-Kontorova model is applied for an analytical description of the energy and structure of the network of domain walls in bilayer graphene. Using this approach, the commensurate-incommensurate phase transition upon biaxial stretching of one of the graphene layers is considered. We demonstrate that formation of the equilateral triangular network of domain walls becomes energetically favourable above the critical relative biaxial elongation of the bottom layer of $3.0\cdot 10^{-3}$. It is shown that the optimal period of the triangular network of domain walls is inversely prop…
Spontaneous orbital magnetism observed in twisted bilayer graphene (tBG) on nearly aligned hexagonal boron nitride (BN) substrate builds on top of the electronic structure resulting from combined G/G and G/BN double moire interfaces. Here we show that tBG/BN commensurate double moire patterns can be classified into two types, each favoring the narrowing of either the conduction or valence bands on average, and obtain the evolution of the bands as a function of the interlayer sliding vectors and electric fields. Finite valley Chern numbers $\pm 1$ are found in a wide range of parameter space wh…
We study the commensurately-tilted bilayer graphene in the tight-binding model with changing the interlayer distance, which can be tuned by pressure. We find that at the commensurately-tilted bilayer graphene with moderate rotating angles, when the energy gap at K point is not negligible, the other Dirac points within the upper two bands move along the $Γ$-K-M line in the bilayer Brillouzone, when the interlayer distance is changed. The velocity at K point becomes zero due to the merging of the four Dirac points within upper two bands. This mechanism of zero velocity at K point is expected to …
We investigate theoretically the interplay between the effects of a perpendicular electric field and incommensurability at the interface on the electronic properties of a heterostructure of bilayer graphene and a semiconducting substrate with a unit cell almost three times larger then that of graphene. It is known that the former introduces an asymmetry in the distribution of the electronic wave function between the layers and opens a band gap in the electronic spectrum. The latter generates a long wavelength periodic moiré perturbation of graphene electrons which couples states in inequivalen…
The interlayer couplings in commensurate and incommensurate bilayer structures of transition metal dichalcogenides are investigated with perturbative treatment. The interlayer coupling in \pm K valleys can be decomposed into a series of hopping terms with distinct phase factors. In H-type and R-type commensurate bilayers, the interference between the three main terms leads to a sensitive dependence of the interlayer coupling strength on the translation. The magnitudes of the main hopping terms are found to some dozen of meV by fitting to the ab initio results. The interlayer couplings in Γvall…
Incommensurately twisted graphene bilayers are described by long-wavelength theories, but to date such theories exist only at small angles of interlayer rotation. We construct a long wavelength theory without such a restriction, instead requiring nearness to commensuration. The theory inherits its energy scale from the exactly commensurate bilayer that it is close to. It is a spatial interpolation between the low-energy theories of commensurate structures with the two possible sublattice exchange (SE) symmetries: SE even and SE odd. In addition to generalizing existing theories, our theory bri…
We have measured the Hall-plateau width and the activation energy of the bilayer quantum Hall (BLQH) states at the Landau-level filling factor $ν=1$ and 2 by tilting the sample and simultaneously changing the electron density in each quantum well. The phase transition between the commensurate and incommensurate states are confirmed at $ν=1$ and discovered at $ν=2$. In particular, three different $ν=2$ BLQH states are identified; the compound state, the coherent commensurate state, and the coherent incommensurate state.
A major theoretical challenge of studying twisted transition metal dichalcogenide (TMD) bilayers is that the unit cell of such structures is very large and therefore difficult to address using first-principles methods. However, twisted TMD bilayers form moiré patterns, which consist of regions of commensurate stacking, either smoothly interpolated into one another or separated by sharp domain walls. In this paper, we study twisted TMD bilayers by studying the properties of the constituent commensurate structures. Using density functional theory (DFT), we compute band structures for commensurat…
We extend the Composite Boson theory to study slightly im-balanced bi-layer Quantum Hall systems. In the global $ U(1) $ symmetry breaking excitonic superfluid side, as the imbalance increases, the system supports continuously changing fractional charges. In the translational symmetry breaking pseudo-spin density wave (PSDW) side, there are two quantum phase transitions from the commensurate PSDW to an in-commensurate PSDW and then to the excitonic superfluid state. We compare our theory with experimental data and also the previous microscopic calculations.
The Bistritzer-MacDonald continuum model (BM model) describes the low-energy moiré bands for twisted bilayer graphene (TBG) at small twist angles. We derive a generalized continuum model for TBG near any commensurate twist angle, which is characterized by complex interlayer hoppings at commensurate $AA$ stackings (rather than the real hoppings in the BM model), a real interlayer hopping at commensurate $AB/BA$ stackings, and a global energy shift. The complex phases of the $AA$ stacking hoppings and the twist angle together define a single angle parameter $ϕ_0$. We compute the model parameters…
We explore the device potential of tunable-gap bilayer graphene FET exploiting the possibility of opening a bandgap in bilayer graphene by applying a vertical electric field via independent gate operation. We evaluate device behavior using atomistic simulations based on the self-consistent solution of the Poisson and Schroedinger equations within the NEGF formalism. We show that the concept works, but bandgap opening is not strong enough to suppress band-to-band tunneling in order to obtain a sufficiently large Ion/Ioff ratio for CMOS device operation.
The line shape of the double-resonant $2D$ Raman mode in bilayer graphene is often considered to be characteristic for a certain laser excitation energy. Here, in a joint experimental and theoretical study, we analyze the dependence of the double-resonant Raman scattering processes in bilayer graphene on the electronic broadening parameter $γ$. We demonstrate that the ratio between symmetric and anti-symmetric scattering processes sensitively depends on the lifetime of the electronic states, explaining the experimentally observed variation of the complex $2D$-mode line shape.
We investigate the transport properties of double-gated bilayer graphene nanoribbons at room temperature. The devices were fabricated using conventional CMOS-compatible processes. By analyzing the dependence of the resistance at the charge neutrality point as a function of the electric field applied perpendicular to the graphene surface, we show that a band gap in the density of states opens, reaching an effective value of ~sim50 meV. This demonstrates the potential of bilayer graphene as FET channel material in a conventional CMOS environment.
We study the electronic properties of commensurate faulted bilayer graphene by diagonalizing the one-particle Hamiltonian of the bilayer system in a complete basis of Bloch states of the individual graphene layers. Our novel approach is very general and can be easily extended to any commensurate graphene-based heterostructure. Here, we consider three cases: i) twisted bilayer graphene, ii) bilayer graphene where triaxial stress is applied to one layer, and iii) bilayer graphene where uniaxial stress is applied to one layer. We show that the resulting superstructures can be divided into distinc…
Electric transport of double gated bilayer graphene devices is studied as a function of charge density and bandgap. A top gate electrode can be used to control locally the Fermi level to create a pn junction between the double-gated and single-gated region. These bilayer graphene pn diodes are characterized by non-linear currents and directional current rectification, and we show the rectified direction of the source-drain voltage can be controlled by using gate voltages. A systematic study of the pn junction characteristics allows to extract a gate-dependent bandgap value which ranges from 0 …
Despite the now vast body of two-dimensional materials under study, bilayer graphene remains unique in two ways: it hosts a simultaneously tunable band gap and electron density; and stems from simple fabrication methods. These two advantages underscore why bilayer graphene is critical as a material for optoelectronic applications. In the work that follows, we calculate the one- and two-photon absorption coefficients for degenerate interband absorption in a graphene bilayer hosting an asymmetry gap and adjustable chemical potential--all at finite temperature. Our analysis is comprehensive, char…
We demonstrate theoretically that quantum dots in bilayers of graphene can be realized. A position-dependent doping breaks the equivalence between the upper and lower layer and lifts the degeneracy of the positive and negative momentum states of the dot. Numerical results show the simultaneous presence of electron and hole confined states for certain doping profiles and a remarkable angular momentum dependence of the quantum dot spectrum which is in sharp contrast with that for conventional semiconductor quantum dots. We predict that the optical spectrum will consist of a series of non-equidis…
A graphene bilayer is known to perfectly reflect normally incident electrons due to their chirality. This is similar to Klein tunneling, which, in a monolayer, is instead responsible for perfect transmission at normal incidence. Stacking defaults turn each parabolic band crossing of a bilayer into pairs of Dirac cones. Here we show that, surprisingly, a stacking default (or shift) in a bilayer can result in perfect {\it transmission} at normal incidence as a result of Fabry-Pérot type resonances {\it at zero-energy}. These constructive interferences only happen for a specific orientation of th…
Recent experiments have measured local uniaxial strain fields in twisted bilayer graphene (TBG). Our calculations found that the finite Berry curvature generated by breaking the sublattice symmetry and the band proximity between narrow bands in these TBG induces a giant Berry dipole of order 10\,nm or larger. The large Berry dipole leads to transverse topological non-linear charge currents which dominates over the linear bulk valley current at experimentally accessible crossover in-plane electric field of $\sim 0.1 {\rm mV} / μ\rm{m}$. This anomalous Hall effect, due to Berry dipole, is strong…
We present a highly controllable double quantum dot device based on bilayer graphene. Using a device architecture of interdigitated gate fingers, we can control the interdot tunnel coupling between 1 to 4 GHz and the mutual capacitive coupling between 0.2 and 0.6 meV, independently of the charge occupation of the quantum dots. The charging energy and hence the dot size remains nearly unchanged. The tuning range of the tunnel coupling covers the operating regime of typical silicon and GaAs spin qubit devices.
We develop a general theory of the layer circular photogalvanic effect (LCPGE) in quasi two-dimensional chiral bilayers, which refers to the appearance of a polarization-dependent, out-of-plane dipole moment induced by circularly polarized light. We elucidate the geometric origin of the LCPGE as two types of interlayer coordinate shift weighted by the quantum metric tensor and the Berry curvature, respectively. As a concrete example, we calculate the LCPGE in twisted bilayer graphene, and find that it exhibits a resonance peak whose frequency can be tuned from visible to infrared as the twisti…
Employing density functional theory-based methods, we investigate monolayer and bilayer structures of hexagonal SnS$_{2}$, which is recently synthesized monolayer metal dichalcogenide. Comparison of 1H and 1T phases of monolayer SnS$_{2}$ confirms the ground state to be the 1T phase. In its bilayer structure we examine different stacking configurations of the two layers. It is found that the interlayer coupling in bilayer SnS$_{2}$ is weaker than that of typical transition-metal dichalcogenides (TMDs) so that alternative stacking orders have similar structural parameters and they are separated…
Bilayer graphene is a highly tunable material: not only can one tune the Fermi energy using standard gates, as in single-layer graphene, but the band structure can also be modified by external perturbations such as transverse electric fields or strain. We review the theoretical basics of the band structure of bilayer graphene and study the evolution of the band structure under the influence of these two external parameters. We highlight their key role concerning the ease to experimentally probe the presence of a Lifshitz transition, which consists in a change of Fermi contour topology as a fun…
We report on a double quantum dot which is formed in a width-modulated etched bilayer graphene nanoribbon. A number of lateral graphene gates enable us to tune the quantum dot energy levels and the tunneling barriers of the device over a wide energy range. Charge stability diagrams and in particular individual triple point pairs allow to study the tunable capacitive inter-dot coupling energy as well as the spectrum of the electronic excited states on a number of individual triple points. We extract a mutual capacitive inter-dot coupling in the range of 2 - 6 meV and an inter-dot tunnel couplin…
We present the ballistic quantum transport of a p-n-p bilayer silicene junction in the presence of spin-orbit coupling and electric field using a four-band model in combination with the transfer-matrix approach. A Mexican-hat shape of the low-energy spectrum is observed similarly to bilayer graphene under an interlayer bias. We show that while bilayer silicene shares some physics with bilayer graphene, it has many intriguing phenomena that have not been reported for the latter. First, the confined state producing a significantly non-zero transmission in Mexican hat. Second, the cloaking of the…
The chirality of electronic Bloch bands is responsible for many intriguing properties of layered two-dimensional materials. We show that in bilayers of transition metal dichalcogenides (TMDCs), unlike in few-layer graphene and monolayer TMDCs, both intra-layer and inter-layer couplings give important contributions to the Berry-curvature in the $K$ and $-K$ valleys of the Brillouin zone. The inter-layer contribution leads to the stacking dependence of the Berry curvature and we point out the differences between the commonly available 3R type and 2H type bilayers. Due to the inter-layer contribu…
Symmetry breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field electron interactions can cause spontaneous symmetry breaking within the spin and valley degrees of freedom, resulting in quantum Hall states (QHS) with complex order. Here we report fractional quantum Hall states (FQHS) in bilayer graphene which show phase transitions that can be tuned by a transverse el…
Adatom-decorated graphene offers a promising new path towards spintronics in the ultrathin limit. We combine experiment and theory to investigate the electronic properties of dilutely fluorinated bilayer graphene, where the fluorine adatoms covalently bond to the top graphene layer. We show that fluorine adatoms give rise to resonant impurity states near the charge neutrality point of the bilayer, leading to strong scattering of charge carriers and hopping conduction inside a field-induced band gap. Remarkably, the application of an electric field across the layers is shown to tune the resonan…
Interference between different possible paths lies at the heart of quantum physics. Such interference between coupled discrete and continuum states of a system can profoundly change its interaction with light as seen in Fano resonance. Here we present a unique many-body Fano system composed of a discrete phonon vibration and continuous electron-hole pair transitions in bilayer graphene. Mediated by the electron-phonon interactions, the excited state is described by new quanta of elementary excitations of hybrid phonon-exciton nature. Infrared absorption of the hybrid states exhibit characteris…
A remarkable feature of the band structure of bilayer graphene at small twist angle is the appearance of isolated bands near neutrality, whose bandwidth can be reduced at certain magic angles (eg. $θ\sim 1.05^\circ$). In this regime, correlated insulating states and superconductivity have been experimentally observed. A microscopic description of these phenomena requires an understanding of universal aspects of the band structure, which we discuss here. First, we point out the importance of emergent symmetries, such as valley conservation, which are excellent symmetries in the limit of small t…
The quantum anomalous Hall (QAH) effect - a macroscopic manifestation of chiral band topology at zero magnetic field - has only been experimentally realized by magnetic doping of topological insulators (1 - 3) and delicate design of Moire heterostructures (4 - 8). However, the seemingly simple bilayer graphene without magnetic doping or Moire engineering has long been predicted to host competing ordered states with QAH effects (9 - 11). Here, we explore states in bilayer graphene with conductance of 2 e2/h that not only survive down to anomalously small magnetic fields and up to temperatures o…
We investigate the electronic band structure and the proximity exchange effect in bilayer graphene on a family of ferromagnetic multilayers Cr$_2$X$_2$Te$_6$, X=Ge, Si, and Sn, with first principles methods. In each case the intrinsic electric field of the heterostructure induces an orbital gap on the order of 10 meV in the graphene bilayer. The proximity exchange is strongly band dependent. For example, in the case of Cr$_2$Ge$_2$Te$_6$, the low-energy valence band of bilayer graphene has exchange splitting of 8 meV, while the low energy conduction band's splitting is 30 times less (0.3 meV).…
We compare the main feature of the measured Raman scattering spectra from single layer graphene with a bilayer in which the two layers are arbitrarily misoriented. The profiles of the 2D bands are very similar having only one component, contrary to the four found for commensurate Bernal bilayers. These results agree with recent theoretical calculations and point to the similarity of the electronic structures of single layer graphene and misoriented bilayer graphene. Another new aspect is that the dependance of the 2D frequency on the laser excitation energy is different in these two latter sys…
We investigate the band structure of twisted monolayer-bilayer graphene (tMBG), or twisted graphene on bilayer graphene (tGBG), as a function of twist angles and perpendicular electric fields in search of optimum conditions for achieving isolated nearly flat bands. Narrow bandwidths comparable or smaller than the effective Coulomb energies satisfying $U_{\textrm{eff}} /W \gtrsim 1$ are expected for twist angles in the range of $0.3^{\circ} \sim 1.5^{\circ}$, more specifically in islands around $θ\sim 0.5^{\circ}, \, 0.85^{\circ}, \,1.3^{\circ}$ for appropriate perpendicular electric field magn…
We report the direct observation of intervalley exciton between the Q conduction valley and $Γ$ valence valley in bilayer WSe$_2$ by photoluminescence. The Q$Γ$ exciton lies at ~18 meV below the QK exciton and dominates the luminescence of bilayer WSe$_2$. By measuring the exciton spectra at gate-tunable electric field, we reveal different interlayer electric dipole moments and Stark shifts between Q$Γ$ and QK excitons. Notably, we can use the electric field to switch the energy order and dominant luminescence between Q$Γ$ and QK excitons. Both Q$Γ$ and QK excitons exhibit pronounced phonon re…
We theoretically investigate topological spin transport of the magnon-polarons in bilayer magnet with two-dimensional square lattices. Our theory is motivated by recent reports on the van der Waals magnets which show the reversible electrical switching of the interlayer magnetic order between antiferromagnetic and ferromagnetic orders. The magnetoelastic interaction opens band gaps and allows the interband transition between different excitation states. In the layered antiferromagnet, due to the interband transition between the magnon-polaron states, the spin Berry curvature which allows the t…
The low energy electronic spectra of rotationally faulted graphene bilayers are studied using a long wavelength theory applicable to general commensurate fault angles. Lattice commensuration requires low energy electronic coherence across a fault and preempts massless Dirac behavior near the neutrality point. Sublattice exchange symmetry distinguishes two families of commensurate faults that have distinct low energy spectra which can be interpreted as energy-renormalized forms of the spectra for the limiting Bernal and AA stacked structures. Sublattice-symmetric faults are generically fully ga…
We present atomistic calculations on structural and electronic properties of twisted double bilayer graphene (TDBG) consisting of two sets of rotationally misaligned Bernal-stacked bilayer graphene. Obtained equilibrium atomic structures exhibit in-plane strains and the modulation of the interlayer distances at the rotationally mismatched interface layers. We find that the electronic structure of TDBG can have an intrinsic band gap at the charge neutral point for a large range of the twist angle theta. Near theta = 1.25 degree, the intrinsic band gap disappears and TDBG hosts flat bands at the…
Moire superlattices in twisted transition metal dichalcogenide bilayers have emerged as a rich platform for exploring strong correlations using optical spectroscopy. Despite observation of rich Mott-Wigner physics stemming from an interplay between the periodic potential and Coulomb interactions, the absence of tunnel coupling induced hybridization of electronic states ensured a classical layer degree of freedom in these experiments. Here, we investigate a MoSe$_2$ homobilayer structure where inter-layer coherent tunnelling and layer-selective optical transitions allow for electric field contr…
Twisted bilayer graphene has recently attracted a lot of attention for its rich electronic properties and tunability. Here we show that for very small twist angles, $α\ll 1^\circ$, the application of a perpendicular electric field is mathematically equivalent to a new kind of artificial gauge field. This identification opens the door for the generation and detection of pseudo-Landau levels in graphene platforms within robust setups which do not depend on strain engineering and therefore can be realistically harvested for technological applications. Furthermore, this new artificial gauge field …
Twisted bilayer graphene (tBLG) forms a quasicrystal whose structural and electronic properties depend on the angle of rotation between its layers. Here we present a scanning tunneling microscopy study of gate-tunable tBLG devices supported by atomically-smooth and chemically inert hexagonal boron nitride (BN). The high quality of these tBLG devices allows identification of coexisting moiré patterns and moiré super-superlattices produced by graphene-graphene and graphene-BN interlayer interactions. Furthermore, we examine additional tBLG spectroscopic features in the local density of states be…
Berry curvature is analogous to magnetic field but in momentum space and is commonly present in materials with non-trivial quantum geometry. It endows Bloch electrons with transverse anomalous velocities to produce Hall-like currents even in the absence of a magnetic field. We report the direct observation of in situ tunable valley-selective Hall effect (VSHE), where inversion symmetry, and thus the geometric phase of electrons, is controllable by an out-of-plane electric field. We use high-quality bilayer graphene with an intrinsic and tunable bandgap, illuminated by circularly polarized mid-…
Second order optical nonlinear processes involve the coherent mixing of two electromagnetic waves to generate a new optical frequency, which plays a central role in a variety of applications, such as ultrafast laser systems, rectifiers, modulators, and optical imaging. However, progress is limited in the mid-infrared (MIR) region due to the lack of suitable nonlinear materials. It is desirable to develop a robust system with a strong, electrically tunable second order optical nonlinearity. Here we demonstrate theoretically that AB-stacked bilayer graphene (BLG) can exhibit a giant and tunable …
