We theoretically show that an interlayer bias voltage in the AB-stacked bilayer graphene nanoribbons with armchair edges induces an electric polarization along the ribbon. Both tight-binding and ab initio calculations consistently indicate that when the bias voltage is weak, the polarization shows opposite signs depending on the ribbon width modulo three. This nontrivial dependence is explained using a two-band effective model. A strong limit of the bias voltage in the tight-binding model shows either one-third or zero polarization, which agrees with topological argument.
We investigate electronic transport property of a graphene monolayer covered by a graphene nanoribbon. We demonstrate that electronic transmission of a monolayer can be reduced when covered by a nanoribbon. The transmission reduction occurs at different energies determined by the width of nanoribbon. We explain the transmission reduction by using interference between wavefunctions in the monolayer and the nanoribbon. Furthermore, we show the transmission reduction of a monolayer is combinable when covered by more than one nanoribbon and propose a concept of "combination of control" for nano-ap…
We study analytically, based on the tight-binding model, the electronic band structure of armchair AA-stacked bilayer graphene nanoribbons (BLGNRs) in several regimes. We apply hard-wall boundary conditions to determine the discretion dominating on the Bloch wavefunctions in the confined direction. First we consider an ideal case, perfect nanoribbons without any edge deformation, and show that their electronic properties are strongly size-dependent. We find that the narrow armchair AA-stacked BLGNRs (similar to single-layer graphene nanoribbons) may be metallic or semiconducting depending on t…
We study in this paper the edge polarizations and their consequences for a biased Bernal stacked bilayer graphene nanoribbon with zigzag termination. The magnetic states are classified according to the interlayer and intralayer couplings between the edge polarizations, and the magnetic phase diagram of doping versus bias voltage is given. Coplanar magnetic phase is found and the variation of its magnetic structure with the bias voltage is investigated. For all the magnetic states, we also discuss the possibility of the half-metallicity, and for a ribbon with perfect zigzag edges we predict sev…
Electronic properties of bilayer graphene are distinct from both the conventional two dimensional electron gas and monolayer graphene due to its particular chiral properties and excitation charge carrier dispersions. We study the effect of strain on the electronic structure, the edge-states and charge transport of bilayer graphene nanoribbon at zero-temperature. We demonstrate a valley polarized quantum Hall effect in biased bilayer graphene when the system is subjected to a perpendicular magnetic field. In this system a topological phase transition from a quantum valley Hall to a valley polar…
The interlayer magnetic interaction in bilayer CrI$_3$ plays a crucial role for its device applications. In this work, we studied the interlayer magnetic interaction in $π/3$-twisted bilayer CrI$_3$ using first-principles calculations. Our calculations show that the interlayer coupling can be ferromagnetic or antiferromagnetic depending crucially on lateral shift. The strongest antiferromagnetic interlayer interaction appears in the $\bar{A}A$-stacking. The magnetic force theory calculations demonstrate that such an antiferromagnetic interaction is dominanted by the $e_g$-$e_g$ channel. Partic…
Interlayer valley excitons in bilayer MoS2 feature concurrently large oscillator strength and long lifetime, and hence represent an advantageous scenario for valleytronic applications. However, control of valley pseudospin of interlayer excitons in pristine bilayer MoS2, which lies at the heart of valleytronics, has remained elusive. Here we report the observation of highly circularly polarized photoluminescence from interlayer excitons of bilayer MoS2 with both optical and magnetic addressability. Under excitation of circularly polarized light near exciton resonance, interlayer excitons of bi…
Zigzag nanoribbons of monolayer graphene-like two-dimensional materials host spontaneous edge magnetism at the zigzag terminations, whose configuration controls the band gap. In this article, the edge magnetism of zigzag nanoribbons of bilayer hexagonal crystals are studied. The specific models of bilayer graphene and bilayer silicene are both studied. As the gated voltage increases, the total energy level, magnetic structure and band structures of the ground state and the first quasi-stable excited state are tuned. For certain region of the gated voltage, the band gaps of spin up and down are…
We reveal that there exists a class of graphene structures (a sub-class of bilayer graphene nanoribbons) which has unusually strong optical response in the terahertz (THz) and far infrared (FIR) regime. The peak conductance of terahertz/FIR active bilayer ribbons is around two orders of magnitude higher than the universal conductance of $e^2/4\hbar$ observed in graphene sheets. The criterion for the terahertz/FIR active sub-class is a bilayer graphene nanoribbon with one-dimensional massless Dirac Fermion energy dispersion near the $Γ$ point. Our results overcome a significant obstacle that hi…
We study the transport properties of a twisted bilayer graphene flake contacted by two monolayer nanoribbons which act as leads. We analyze the conductance in terms of the spectra of the bilayer nanoribbon and the monolayer contacts. The low-energy transport properties are governed by the edge states with AB stacking. Remarkably, the electronic conductance in this energy region does not depend much on the relative position of the leads, in contrast with that of bilayer flakes with more symmetric stackings. We attribute this feature to the localization of these low-energy states in the AB edge …
We investigated the emergence of spin spiral ground state induced by the electric field in the bilayer zigzag graphene nanoribbons for the ferromagnetic edge states. To do that, we employed the generalized Bloch theorem to create flat spiral alignments for all the magnetic moments of carbon atoms at the edges within a constraint scheme approach. While the small ribbon width can preserve the ferromagnetic ground state, the large one shows the spiral ground state starting from a certain value of the electric field. We also pointed out that the spiral ground state is caused by the reduction of sp…
We study the interaction energy between two graphene nanoribbons by first principles calculations, including van der Waals interactions and spin polarization. For ultranarrow zigzag nanoribbons, the direct stacking is even more stable than Bernal, competing in energy for wider ribbons. This behavior is due to the magnetic interaction between edge states. We relate the reduction of the magnetization in zigzag nanoribbons with increasing ribbon width to the structural changes produced by the magnetic interaction, and show that when deposited on a substrate, zigzag bilayer ribbons remain magnetic…
The interlayer coupling of twisted bilayer graphene could markedly affect its electronic band structure. A current challenge required to overcome in experiment is how to precisely control the coupling and therefore tune the electronic properties of the bilayer graphene. Here, we describe a facile method to modulate the local interlayer coupling by adsorption of single molecule magnets onto the twisted bilayer graphene and report the characterization of its electronic band structure using scanning tunneling microscopy and spectroscopy. The low-energy Van Hove singularities (VHSs) and superlatti…
We present an analytical description of pi electrons of a finite size bilayer graphene within a framework of the tight-binding model. The bilayered structures considered here are characterized by a rectangular geometry and have a finite size in one or both directions with armchair- and zigzag-shaped edges. We provide an exact analytical description of the spectrum of pi electrons in the zigzag and armchair bilayer graphene nanoribbons and nanotubes. We analyze the dispersion relations, the density of states, and the conductance quantization.
In this work the tight binding model calculations are carried out for AA-Bilayer Graphene nanoribbons as an example of bilayer systems. The effects of edges, NNN hopping, and impurities of a single layer are introduced numerically as a change in the elements of the relevant block diagonal matrix appearing in the direct diagonalization method. The direct interlayer hopping between the top and the bottom single layers is constructed in the generalized direct diagonalization method by the off-diagonal block matrices in which the strength of the interlayer hopping is included.
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…
We theoretically investigate the thermoelectric properties of zigzag bilayer phosphorene nanoribbons (ZBPNR). We first, draw an analogy between the extended Su-Schrieffer-Heeger (SSH) ladder and ZBPNR edge states and obtain their corresponding band structure and wave functions analytically. Then, by applying the energy filtering method, we show that the electric power and thermoelectric efficiency of the ZBPNRs can be improved remarkably in the presence of mid-gap edge states. We also argue how to engineer the edge modes to further optimize thermoelectric power and efficiency of the system by …
Stacking two-dimensional layered materials such as graphene and transitional metal dichalcogenides with nonzero interlayer twist angles has recently become attractive because of the emergence of novel physical properties. Stacking of one-dimensional nanomaterials offers the lateral stacking offset as an additional parameter for modulating the resulting material properties. Here, we report that the edge states of twisted bilayer zigzag graphene nanoribbons (TBZGNRs) can be tuned with both the twist angle and the stacking offset. Strong edge state variations in the stacking region are first reve…
Coherent motion of the electrons in the Bloch states is one of the fundamental concepts of the charge conduction in solid state physics. In layered materials, however, such a condition often breaks down for the interlayer conduction, when the interlayer coupling is significantly reduced by e.g. large interlayer separation. We report that complete suppression of coherent conduction is realized even in an atomic length scale of layer separation in twisted bilayer graphene. The interlayer resistivity of twisted bilayer graphene is much higher than the c-axis resistivity of Bernal-stacked graphite…
The magnetoelectronic properties of quasi-one-dimensional zigzag graphene nanoribbons are investigated by using the Peierls tight-binding model. Quasi-Landau levels (QLLs), dispersionless Landau subbands within a certain region of k-space, are resulted from the competition between magnetic and quantum confinement effects. In bilayer system, the interlayer interactions lead to two groups of QLLs, one occurring at the Fermi level and the other one occurring at higher energies. Transverse electric fields are able to distort energy spectrum, tilt two groups of QLLs and cause semiconductor-metal tr…
A topological insulator is a novel quantum state, characterized by symmetry-protected non-trivial edge/surface states. Our first-principle simulations show the significant effects of the chemical decoration on edge states of topological Bi(111) bilayer nanoribbon, which remove the trivial edge state and recover the Dirac linear dispersion of topological edge state. By comparing the edge states with and without chemical decoration, the Bi(111) bilayer nanoribbon offers a simple system for assessing conductance fluctuation of edge states. The chemical decoration can also modify the penetration d…
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.
Diverse interlayer tunability of physical properties of two-dimensional layers mostly lies in the covalent-like quasi-bonding that is significant in electronic structures but rather weak for energetics. Such characteristics result in various stacking orders that are energetically comparable but may significantly differ in terms of electronic structures, e.g. magnetism. Inspired by several recent experiments showing interlayer anti-ferromagnetically coupled CrI3 bilayers, we carried out first-principles calculations for CrI3 bilayers. We found that the anti-ferromagnetic coupling results from a…
On the basis of tight-binding lattice model, the edge states of monolayer and bilayer graphene nanoribbons (GNRs) with different edge terminations are studied. The effects of edge-hopping modulation, spin-orbital coupling (SOC), and bias voltage on bilayer GNRs are discussed. We observe the following: (i) Some new extra edge states can be created by edge-hopping modulation for monolayer GNRs. (ii) Intralayer Rashba SOC plays a role in depressing the band energy gap $E_g$ opened by intrinsic SOC for both monolayer and bilayer GNRs. An almost linear dependent relation, i.e., $E_g\sim λ_R$, is fo…
The effects of Coulomb interactions on the electronic properties of bilayer graphene nanoribbons (BGNs) covered by a gate electrode are studied theoretically. The electron density distribution and the potential profile are calculated self-consistently within the Hartree approximation. A comparison to their single-particle counterparts reveals the effects of interactions and screening. Due to the finite width of the nanoribbon in combination with electronic repulsion, the gate-induced electrons tend to accumulate along the BGN edges where the potential assumes a sharp triangular shape. This has…
An interlayer distance modulation in twisted bilayer graphene is reported. This is achieved by an in-situ annealing technique. The transformation of systematic vacuum and hydrogen annealing effects in twisted bilayer CVD graphene on SiO2 surface is reported based on experimental results. Incoherent interlayer conduction is observed in the twisted bilayer device. In-situ annealing efficiently removes the residues in the graphene-to-graphene interface and enhances the interlayer conduction. We demonstrate graphene-to-graphene interlayer resistance modulated by an order of magnetite at 5 K. We al…
We investigate the electron transport and thermoelectric property of twisted bilayer graphene nanoribbon junction (TBGNRJ) in $0^o$, $21.8^o$, $38.2^o$ and $60^o$ rotation angles by first principles calculation with Landauer-Buttiker and Boltzmann theories. It is found that TBGNRJs exhibit negative differential resistance (NDR) in $21.8^o$ and $38.2^o$ rotation angles under $\pm$ 0.2 V bias voltage. More importantly, three peak ZT values of 2.0, 2.7 and 6.1 can be achieved in the $21.8^o$ rotation angle at 300K. The outstanding ZT values of TBGNRJs are interpreted as the combination of the red…
We develop a consistent theory of the interlayer exciton-polaron formed in atomically-thin bilayers. Coulomb attraction between an electron and a hole situated in the different layers results in their flexural deformation and provides an efficient mechanism of the exciton coupling with flexural phonons. We study the effect of layers tension on the polaron binding energy and effective mass leading to suppression of polaron formation by the tension both in the weak and strong coupling regimes. We also consider the role of the nonlinearity related to the interaction between the out- and in-plane …
We demonstrate gate-tunable resonant tunneling and negative differential resistance between two rotationally aligned bilayer graphene sheets separated by bilayer WSe2. We observe large interlayer current densities of 2 uA/um2 and 2.5 uA/um2, and peak-to-valley ratios approaching 4 and 6 at room temperature and 1.5 K, respectively, values that are comparable to epitaxially grown resonant tunneling heterostructures. An excellent agreement between theoretical calculations using a Lorentzian spectral function for the two-dimensional (2D) quasiparticle states, and the experimental data indicates th…
Coulomb bound electron-hole pairs, excitons, govern the optical properties of semi-conducting transition metal dichalcogenides like MoS$_2$ and WSe$_2$. We study optical transitions at the K-point for 2H homobilayer MoS$_2$ in Density Functional Theory (DFT) including excitonic effects and compare with reflectivity measurements in high quality samples encapsulated in hexagonal BN. In both calculated and measured spectra we find a strong interlayer exciton transition in energy between A and B intralayer excitons, observable for T$=4 -300$ K, whereas no such transition is observed for the monola…
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…
A twisted graphene bilayer exhibits a triangular Moiré pattern in the local stacking, that smoothly alternates between the three basic types AA', AB' and BA'. Under an interlayer bias U, the latter two types develop a spectral gap, characterised by opposite valley Chern numbers. We show that for large enough Moiré periods and bias, these regions become depleted electronically, and topologically protected helical modes appear at their boundaries. This gives rise to a delocalised topological network of the Chalker-Coddington type, composed of valley current vortices. This network can be tailored…
Coherent spin-dependent transport through a junction containing of Normal/Ferromagnetic/Normal bilayer graphene nanoribbon with zigzag edges is investigated by using Landauer formalism. In a more realistic set-up, the exchange field is induced by two ferromagnetic insulator strips deposited on the ribbon edges while a perpendicular electric field is applied by the top gated electrodes. Our results show that, for antiparallel configuration, a band gap is opened giving rise a semiconducting behavior, while for parallel configuration, the band structure has no band gap. As a result, a giant magne…
Van der Waals (vdW) coupling is emerging as a powerful method to engineer and tailor physical properties of atomically thin two-dimensional (2D) materials. In graphene/graphene and graphene/boron-nitride structures it leads to interesting physical phenomena ranging from new van Hove singularities1-4 and Fermi velocity renormalization5, 6 to unconventional quantum Hall effects7 and Hofstadter's butterfly pattern8-12. 2D transition metal dichalcogenides (TMDCs), another system of predominantly vdW-coupled atomically thin layers13, 14, can also exhibit interesting but different coupling phenomena…
We investigate the electronic transport properties of a bilayer graphene flake contacted by two monolayer nanoribbons. Such a finite-size bilayer flake can be built by overlapping two semiinfinite ribbons or by depositing a monolayer flake onto an infinite nanoribbon. These two structures have a complementary behavior, that we study and analyze by means of a tight-binding method and a continuum Dirac model. We have found that for certain energy ranges and geometries, the conductance of these systems oscillates markedly between zero and the maximum value of the conductance, allowing for the des…
Thin adhesive films can be removed from substrates, torn, and folded in distinct geometries under external driving forces. In two-dimensional materials, however, these processes can be self-driven as shown in previous studies on folded twisted bilayer graphene nanoribbons produced by spontaneous tearing and peeling from a substrate. Here, we use atomic force microscopy techniques to generate and characterize the geometrical structure of naturally self-grown folded nanoribbon structures. Measurements of nanoribbon width and interlayer separation reveal similar twist-angle dependences possibly c…
By using the first-principles method based on density of functional theory, we study the electronic properties of twisted bilayer graphene with some specific twist angles and interlayer spacings. With the decrease of the twist angle(the unit cell becomes larger), the energy band becomes narrower and Coulomb repulsion increases, leading to the enhancement of electronic correlation; On the other hand, as the interlayer spacing decreases and the interlayer coupling becomes stronger, the correlation becomes stronger. By tuning the interlayer coupling, we can realize the strongly correlated state w…
In this paper, we employ a fully microscopic approach to the study of interlayer excitons in hetero-bilayers. We use Fowler's and Karplus' method to access the dynamical polarizability of non--interacting interlayer excitons in a $\mathrm{WSe}_{2}/\mathrm{WS}_{2}$--based van der Waals heterostructure. Following from the calculation of the linear polarizability, we consider Svendsen's variational method to the calculation of the dynamic third--order polarizability. With this variational method, we study both two--photon absorption and third--harmonic generation processes for interlayer excitons…
We investigate the thermoelectric performance of armchair graphene nanoribbon (AGNR), bilayer GNRs junction (BGNRJ) and BGNRJ with holes (BGNRJ-H) by the first principles calculation with non-equilibrium Green function. It is found that the BGNRJ-H exhibits high ZT values of 9.65 and 5.55 at 300K. The reason of these significantly larger ZT values than previously observed has been calculated due to reduced thermal conductivity and enhanced electrical conductivity. The low thermal conductance comes from the van der waals (vdW) interaction between two graphene layers. The increased electrical co…
The incommensurate 30$^{\circ}$ twisted bilayer graphene (BG) possesses both relativistic Dirac fermions and quasiperiodicity with 12-fold rotational symmetry arising from the interlayer interaction [\href{https://science.sciencemag.org/content/361/6404/782}{Ahn et al., Science \textbf{361}, 782 (2018)} and \href{https://www.pnas.org/content/115/27/6928}{Yao et al., Proc. Natl. Acad. Sci. \textbf{115}, 6928 (2018)}]. Understanding how the interlayer states interact with each other is of vital importance for identifying and subsequently engineering the quasicrystalline order in the layered stru…
We study theoretically how energy and heat are transferred between the two-dimensional layers of bilayer carrier systems due to near-field interlayer carrier interaction. We derive general expressions for the interlayer heat transfer and thermal conductance. Approximation formulas and detailed calculations for semiconductor and graphene based bilayers are presented. Our calculations for GaAs, Si and graphene bilayers show that the interlayer heat transfer can exceed the electron-phonon heat transfer below (system dependent) finite crossover temperature. We show that disorder strongly enhances …
Tunneling and Coulomb drag are sensitive probes of spontaneous interlayer phase coherence in bilayer two-dimensional electron systems at total Landau level filling factor $ν_T = 1$. We find that the phase boundary between the interlayer phase coherent state and the weakly-coupled compressible phase moves to larger layer separations as the electron density distribution in the bilayer is imbalanced. The critical layer separation increases quadratically with layer density difference.
We study the effects of disorder on the interlayer transport properties of disordered semiconductor bilayers outside of the quantum Hall regime by performing self-consistent quantum transport calculations. We find that the addition of material disorder to the system affects interlayer interactions leading to significant deviations in the interlayer transfer characteristics. In particular, we find that disorder decreases and broadens the tunneling peak, effectively reducing the interacting system to the non-interacting system, when the mean-free path for the electrons becomes shorter than the s…
Two-dimensional layered materials offer the possibility to create artificial vertically stacked structures possessing an additional degree of freedom - $the$ $interlayer$ $twist$. We present a comprehensive optical study of artificially stacked bilayers (BLs) MoS$_2$ encapsulated in hexagonal BN with interlayer twist angle ranging from 0 to 60 degrees using Raman scattering and photoluminescence spectroscopies. It is found that the strength of the interlayer coupling in the studied BLs can be estimated using the energy dependence of indirect emission versus the A$_\textrm{1g}$-E$_\textrm{2g}^1…
The atomic structure, stacking sequences and electronic structure of folded graphene nanoribbons (FGNRs) are investigated by first-principles calculations. It reveals that the common configurations of all FGNRs are racket-like structures including a nanotube-like edge and two flat nanoribbons. Interestingly, the two flat nanoribbons can form new stacking styles instead of the most stable AB-stacking sequences for bilayer nanoribbons. The stability of the FGNRs are associated with several factors of initial structures, such as interlayer distance of two nanoribbons, stacking sequences, edge sty…
Electric-field-driven magnetic switching and tightly bound interlayer excitons in bilayer CrSBr
Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院）；School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）；National Institute for Material Science（日本国立材料研究所）
We show that gated bilayer graphene zigzag ribbons possess a fast and a slow edge, characterized by edge state velocities that differ due to non-negligible next-nearest-neighbor hopping elements. By applying bosonization and renormalization group methods, we find that the slow edge can acquire a sizable interaction-induced gap, which is tunable via an external gate voltage V_{g}. In contrast to the gate-induced gap in the bulk, the interaction-induced gap depends non-monotonously on the on-site potential V.
We have studied boron nitride monolayer and bilayer band structures. For bilayers, the ground state energies of the different five stackings are computed using DFT in order to determine the most stable configuration. Also, the interlayer distance for the five different types of stacking in which boron-nitride bilayers can be found is determined. Using a minimal tight binding model for the band structures of boron nitride bilayers, the hopping parameters and the onsite energies have been extracted by fitting a tight binding empirical model to the DFT results.
We study the superlattice minibands produced by the interplay between moiré pattern induced by hexagonal BN substrate on graphene layer and the interlayer coupling in bilayer graphene with Bernal stacking (BLG). We compare moiré miniband features in BLG, where they are affected by the interlayer asymmetry of BLG-hBN heterostructure and trigonal warping characteristic for electrons in Bernal-stacked bilayers with those found in monolayer graphene.
Raman measurements on monolayer graphene folded back upon itself as an ordered but skew-stacked bilayer (i.e. with interlayer rotation) presents new mechanism for Raman scattering in sp2 carbons that arises in systems that lack coherent AB interlayer stacking. Although the parent monolayer does not exhibit a D-band, the interior of the skewed bilayer produces a strong two-peak Raman feature near 1350 cm-1; one of these peaks is non-dispersive, unlike all previously observed D-band features in sp2 carbons. Within a double-resonant model of Raman scattering, these unusual features are consistent…
Graphene features topological edge bands that connect the pair of Dirac points through either sectors of the 1D Brillouin zone depending on edge configurations (zigzag or bearded). Because of their flat dispersion, spontaneous edge magnetisation can arise from Coulomb interaction in graphene nanoribbons, which has caught remarkable interest. We find an anomalous Bloch oscillation in such edge bands, in which the flat dispersion freezes electron motion along the field direction, while the topological connection of the bands through the bulk leads to electron oscillation in the transverse direct…
