Bilayer Zigzag Graphene Nanoribbons Research Articles

Twisted bilayer zigzag-graphene nanoribbon junctions with tunable edge states

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 revealed by density functional theory (DFT) calculations. We construct and characterize twisted bilayer zigzag graphene nanoribbon (TBZGNR) systems on a Au(111) surface using scanning tunneling microscopy. A detailed analysis of three prototypical orthogonal TBZGNR junctions exhibiting different stacking offsets by means of scanning tunneling spectroscopy reveals emergent near-zero-energy states. From a comparison with DFT calculations, we conclude that the emergent edge states originate from the formation of flat bands whose energy and spin degeneracy are highly tunable with the stacking offset. Our work highlights fundamental differences between 2D and 1D twistronics and spurs further investigation of twisted one-dimensional systems.

Tunable Magnetic State in AA-Stacked Bilayer Zigzag Graphene Nanoribbon by Increasing Thickness

The density functional theory was utilized to investigate the likelihood of a tunable magnetic state in the AA-stacked bilayer zigzag graphene nanoribbon. The non-magnetic ground states at certain thicknesses were found, but then the magnetic ground states at the other thicknesses were observed. This happens by increasing the thickness so that the van der Waals force becomes weak. This creates spin polarization as the bonding between layers can be overcome. The phase transitions of magnetic ground states were also observed at a large thickness as applying the doping. This signified that the new magnetic ground state is still tunable by applying dope.

Tuning the magnetic states in AA-stacked bilayer zigzag graphene nanoribbons

Available reports mentioned that the magnetic ground state in the AA-stacked bilayer zigzag graphene nanoribbons is the non-magnetic state. As a consequence, it is impossible to exploit magnetism for future electronic devices. This paper aims to show how to generate magnetism in the AA-stacked bilayer zigzag graphene nanoribbons by employing ?rst-principles calculations. As we stacked different ribbon widths, the magnetic ground states appeared for all the thicknesses. In general, the G-type antiferromagnetic state, which is the antiferromagnetic alignment between both intraplane- and interplane-edge carbon atoms, is the ground state for all the thicknesses. We also found that the degenerate magnetic ground states and excited states may appear under certain thicknesses, thus yielding the richness of the magnetic state. As hole-electron doping was applied, a phase transition of magnetic ground state emerged for certain thicknesses, indicating that a new magnetic ground state in the AA-stacked bilayer zigzag graphene nanoribbons can be tuned by the doping.

Hybrid Films Based on Bilayer Graphene and Single-Walled Carbon Nanotubes: Simulation of Atomic Structure and Study of Electrically Conductive Properties.

One of the urgent problems of materials science is the search for the optimal combination of graphene modifications and carbon nanotubes (CNTs) for the formation of layered hybrid material with specified physical properties. High electrical conductivity and stability are one of the main optimality criteria for a graphene/CNT hybrid structure. This paper presents results of a theoretical and computational study of the peculiarities of the atomic structure and the regularities of current flow in hybrid films based on single-walled carbon nanotubes (SWCNTs) with a diameter of 1.2 nm and bilayer zigzag graphene nanoribbons, where the layers are shifted relative to the other. It is found that the maximum stresses on atoms of hybrid film do not exceed ~0.46 GPa for all considered topological models. It is shown that the electrical conductivity anisotropy takes place in graphene/SWCNT hybrid films at a graphene nanoribbon width of 4 hexagons. In the direction along the extended edge of the graphene nanoribbon, the electrical resistance of graphene/SWCNT hybrid film reaches ~125 kOhm; in the direction along the nanotube axis, the electrical resistance is about 16 kOhm. The prospects for the use of graphene/SWCNT hybrid films in electronics are predicted based on the obtained results.

Electric-field-induced lowest state in bilayer zigzag graphene nanoribbon

We investigated the lowest state in the bilayer zigzag graphene nanoribbon by taking the electric field into account. In this calculation, we considered five collinear configurations of magnetic moment of carbon atoms at the four edges. We found that the lowest state changes as the electric field is applied. We also showed that at the high electric field, those five configurations almost become degenerate. This suggests that the lowest state is not robust to the electric field so that the electric field can control the lowest state in the bilayer zigzag graphene nanoribbon.

Electric-field-induced spin spiral state in bilayer zigzag graphene nanoribbons

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 spin stiffness. In this case, the energy scale exhibits a subtle nature that can only be considered at the low temperature. For the last discussion, we also revealed that the spin spiral ground state appears more rapidly when the thickness increases. Therefore, we justify that the large ribbon width and large thickness can generate many spiral states induced by the electric field.

Spin stiffness of bilayer zigzag graphene nanoribbon for several configurations

Abstract The spin stiffness of the bilayer zigzag graphene nanoribbon for several configurations was obtained by means of the total energy difference of the flat spiral formations within the self-consistent calculation. To realize it, the penalty functional was employed to fix the direction of the magnetic moment of the carbon atom at the edges. Using the experimental lattice constant and the interlayer distance, the results showed that the total energy of each configuration is inversely proportional to the spin stiffness, which implies that the most stable configuration has the highest spin stiffness. For the final discussion, we also justified that the most stable configuration is not robust to the interlayer distance.

Edge-State-Induced Stacking of Zigzag Graphene Nanoribbons.

We have investigated the structural stabilities and electronic properties for AA and the Bernal-stacked AB bilayer zigzag graphene nanoribbons (ZZGNRs) using first-principles calculations within density functional theory. The AB-stacked ZZGNR exhibits the spin-polarized state, while the AA-stacked ZZGNR has the nonmagnetic ground state, being more energetically stable than the AB-stacked one. For the AA-stacked ZZGNR, the interaction between the so-called edge states rather than the van der Waals (vdW) interaction plays an important role: the occupied up-spin and the unoccupied down-spin states at one end of ZZGNR interact with each other, and vice versa at the other end, forming the non-spin-polarized bonding and antibonding states at the zigzag edge. Thus, the structural stability for the AA-stacked ZZGNR is dominated by the trade-off between the edge–edge interaction and the vdW interaction of the basal plane of GNRs.

Band gap control of bilayer zigzag graphene nanoribbon by direction of magnetic moment

We have demonstrated the first-principles calculation to tune the band gap of the bilayer zigzag graphene nanoribbon by arranging the direction of the magnetic moments of carbon atoms at the edges. These directions were specified by the polar angle, as defined in the spherical coordinates. From the ferromagnetic configuration to the antiferromagnetic configuration, as the polar angle increases, the band gap increases. We also showed that the ferromagnetic configuration leads to the metallic system while the others lead to the insulator, in a good agreement with the previous calculations. These results indicated that the bilayer zigzag graphene nanoribbon is potential for the spintronics devices.

AB-stacked bilayer graphene zigzag nanoribbons: sensors for interlayer single molecule detection

A device is proposed consisting of a bilayer zigzag graphene nanoribbon (ZGNR) in AB stacking and β edge alignment to detect the presence of simple molecules in its interlayer space. Interlayer molecule detection is accomplished through analysis of the I-V characteristics of the device. Ab initio simulation is performed by applying spin-unpolarized density functional theory (DFT) and non-equilibrium Green’s function methods (NEGF) to the proposed model system. For interlayer molecule detection with improved sensitivity, we propose as model system a couple of AB-stacked ZGNR nanoribbons which are known to present edge states and edge magnetism at zero bias. For interlayer single molecules, we try CO, CO2, and H2O. Interlayer molecules induce local deformations into the ZGNR structure specific to each species and get efficiently trapped in the interlayer space experiencing subtle structural distortions under applied bias. I-V characteristics are fingerprints of molecules in the interlayer space displayed through negative differential resistance (NDR) phenomena and asymmetric behavior with respect to the sign of applied bias. The appearance of NDR can be understood in terms of the Landauer-Buttiker formalism. NDR in our device may be characterized as a rather weak and sharp one with a moderate peak current density.

Spin-dependent transport properties of AA-stacked bilayer graphene nanoribbon

In this paper, the spin-dependent transport of a spin-valve, based on bilayer graphene in which the AA-stacked bilayer zigzag graphene nanoribbon (BLG) connected to two ferromagnetic (FM) semi-infinite single-layer zigzag graphene nanoribbons (FM/BLG/FM system), is numerically studied. Using the non-equilibrium Green's function method and tight-binding model in the framework of Landauer-Büttiker formalism, the spin-dependent transmission function, current and tunnel magnetoresistance of the system are calculated. Results show that the transmission function is always nonzero near the zero energy for the parallel alignment of electrode magnetizations, while it is zero for the antiparallel alignment due to the band-selective rule. Consequently, there is a region for the tunnel magnetoresistance with the value of 100%. The magnitude of this region depends on the strength of magnetization in ferromagnetic electrodes. Also, the effects of bilayer/single-layer coupling geometry,inter-layer coupling strength and width of BLG on the spin-dependent transport of the system are investigated. These results can be useful for designing graphene based spintronic devices.

Effects of vacancies on spin-dependent behavior of monolayer and bilayer graphene nanoribbons

In this work, the effect of vacancies on magnetic properties and spin-dependent behaviors of monolayer and bilayer armchair and zigzag graphene nanoribbons is investigated using first principles calculations based on density functional theory (DFT). The armchair and zigzag graphene nanoribbons are composed of 6 rows and 4 rows of carbon atoms with the edges closed by the hydrogen atoms, respectively. Our results show that vacancies affect the magnetic properties and spin polarization of the graphene nanoribbons. It is seen that the monolayer armchair graphene nanoribbon with one vacancy in its supercell (24 carbon sites+8 hydrogen sites) gives the magnetic moment of 0.79 μB, while magnetic moment in the monolayer zigzag graphene nanoribbon with one vacancy in its supercell (24 carbon sites+6 hydrogen sites) is 1.72 μB (for site α) and 1.84 μB (for site β). The highest and lowest values of magnetic moment in different configurations of the bilayer armchair (zigzag) graphene nanoribbons with one vacancy in each layer of the supercell give 1.54 μB and 1.29 μB (3.51 μB and 2.72 μB), respectively. Numerical values of the magnetic moment in different configurations depended on the distance of vacancies from each other and from nanoribbon’s edge as well as their orientations.

Modulation of bandgap in bilayer armchair graphene ribbons by tuning vertical and transverse electric fields

We investigate the effects of external electric fields on the electronic properties of bilayer armchair graphene nano-ribbons. Using atomistic simulations with Tight Binding calculations and the Non-equilibrium Green's function formalism, we demonstrate that (i) in semi-metallic structures, vertical fields impact more effectively than transverse fields in terms of opening larger bandgap, showing a contrary phenomenon compared to that demonstrated in previous studies in bilayer zigzag graphene nano-ribbons; (ii) in some semiconducting structures, if transverse fields just show usual effects as in single layer armchair graphene nano-ribbons where the bandgap is suppressed when varying the applied potential, vertical fields exhibit an anomalous phenomenon that the bandgap can be enlarged, i.e., for a structure of width of 16 dimer lines, the bandgap increases from 0.255 eV to the maximum value of 0.40 eV when a vertical bias equates 0.96 V applied. Although the combined effect of two fields does not enlarge the bandgap as found in bilayer zigzag graphene nano-ribbons, it shows that the mutual effect can be useful to reduce faster the bandgap in semiconducting bilayer armchair graphene nano-ribbons. These results are important to fully understand the effects of electric fields on bilayer graphene nano-ribbons (AB stacking) and also suggest appropriate uses of electric gates with different edge orientations.

Role of interlayer spacing in electrical transport of bilayer graphene nanoribbon: Perpendicular and armchair direction

The electrical conductance of bilayer zigzag graphene nanoribbon is numerically investigated taking advantage of Green's function. The calculations are performed within the tight binding model, which describes the interaction between carbon atoms within a layer via nearest neighbor and carbon atoms of different layers using continuum model. Our findings reveal sensitivity of the bilayer graphene conductance to changes in its relative displacement of two layers in perpendicular and armchair directions. We find that the conductance oscillates as a function of system width, and finally reduces rapidly as the relative distance of two layers becomes larger than half the system width. The results show that the conductance of the bilayer graphene could be tuned via displacement of two layers. Moreover, we obtain different results for conductance of narrow and wide bilayer nanoribbon.

Tunable thermal property in edge hydrogenated AA-stacked bilayer graphene nanoribbons

The effect of edge hydrogenation on the thermal conductivity of AA-stacked bilayer graphene nanoribbons (BGNs) is explored by using the reverse non-equilibrium molecular dynamics method (RNEMD). We study the thermal transport properties of AA-stacked zigzag BGNs (ZBGNs) with different edge hydrogenation degrees in the range of 200–600K. The calculated results show that the interlayer van der Waals interaction has a big significant influence on the thermal conductivity of AA-stacked BGNs compared with monolayer graphene nanoribbons (GNRs) in the same simulation conditions. For AA-stacked ZBGNs with different edge hydrogenation degrees, thermal conductivities firstly increase with the temperature increasing, and then start to decrease when reaching certain maximum always reach maximum values at the temperature of 300K. Furthermore, the thermal conductivities of the simulation models have certain variation when the heat flow direction changes. In the meantime, the thermal rectification phenomenon is most obvious when the length ratio of the edge hydrogenated GNRs versus pristine one is 1. It is interesting that the thermal rectification effect is apparently weaken at high temperatures owing to obvious reduction of phonon power spectrum overlap, which implies that edge hydrogenated AA-stacked BGNs have the potential in future BGNs-based thermal rectification device applications.

Modulation of the band structure in bilayer zigzag graphene nanoribbons on hexagonal boron nitride using the force and electric fields

Modulation of semiconductor–halfmetal–metal transition in the antiferromagnetic (AF) ordering of bilayer zigzag graphene nanoribbons (BZGNRs) on hexagonal boron nitride (h-BN) heterostructure using the external force field Fext and transverse electric fields Eext (in the presence of interaction with the substrate) was performed within the framework of the density functional theory (DFT). We established critical values of Eext and interlayer distance in the bilayer providing for semiconductor–halfmetal–metal transition in one of electron spin configurations. Our calculations also show that the energy gap Eg in the AF-BZGNR/h-BN(0001) heterostructure can be controlled in a wide range of the Fext and Eext. This makes the AF-8-ZGNR/h-BN(0001) heterostructure being potentially promising for application in spintronic devices.

Investigation on optical properties of bilayer graphene nanoribbons

Using density functional theory, we investigate optical properties of $$\upalpha $$ and $$\upbeta $$ configuration of zigzag and armchair bilayer graphene nanoribbons. We demonstrate that depending on the width and edge symmetries, bilayer graphene nanoribbons could show various optical absorption spectra. These absorption spectra obey different rules. We show that these rules are based on parities of origin and destination wave functions that contribute in the optical absorption. In longitudinal polarization, the inter sub-band transitions occur when the contributed wave functions have different parities. However, in transverse direction, transitions existing between the same parities. This rule is followed by zigzag bilayer graphene nanoribbons. We check these rules for spin interactions and similar characteristic was observed. On the other hand, armchair bilayer graphene nanoribbons, based on width symmetry show either similar characteristic to zigzag or possessing mono frequency spectrum. In addition, $$\upalpha $$ configuration has slightly wider absorption region than $$\upbeta $$ ones. However, both show almost similar behavior in 1–2.47 $$\upmu $$ m region. These characteristics could be used as a tool in experimental investigations to scrutinize edge properties of samples.

Investigation on thermal conductivity of bilayer graphene nanoribbons

We investigated the thermal conductivity of bilayer graphene nanoribbons (BGNs) using nonequilibrium molecular dynamics method (NEMD). The relationships among thermal conductivity, different ways of stacking, size, interfacial temperature and edge shape were studied. Two different stacking ways for BGNs are AA-stacked type and AB-stacked type. The results show that the thermal conductivities of AA-stacked BGNs are slightly higher than those of AB-stacked BGNs under the same simulation conditions because of different crystal structures. The thermal conductivity of zigzag BGNs (ZBGNs) first increases and then decreases with increasing width. However, the thermal conductivity of armchair BGNs (ABGNs) monotonously increases with increasing width. The thermal conductivity of BGNs increases with the length of the simulation system. In addition BGNs show temperature dependence and edge-shape dependence for thermal conductivity. We have explained the simulation results by the inter-layer phonon coupling and the phonon scattering, which have been shown to significantly affect the thermal conductivity of BGNs. The systematic analysis of thermal conductivity of BGNs did not only help to obtain conclusions regarding the achievable thermal performance, but also provided the possibility to design different dimensional BGNs for different BGNs-based thermal and microelectronic components.

Semiconductor–halfmetal–metal transition and magnetism of bilayer graphene nanoribbons/hexagonal boron nitride heterostructure

The paper presents the results of ab initio study of electronic structure modulation and edge magnetism in the antiferromagnetic (AF) bilayer zigzag graphene nanoribbons (AF-BZGNR)/hexagonal boron nitride (h-BN(0001)) semiconductor heterostructure induced with transverse external electric field (Eext) and nanomechanical compression (extension), performed within the framework of the density functional theory using Grimme׳s DFT(PBE)-D2 scheme. For the first time we established critical values of Eext and interlayer distance in the bilayer for the BZGNR/h-BN(0001) heterostructure providing for semiconductor–halfmetal–metal phase transition for one of the electron spin configurations. We discovered the effect of preserved local magnetic moment (0.3μB) of edge carbon atoms of the lower (buffer) graphene nanoribbon during nanomechanical uniaxial compression (or extension) of the BZGNR/h-BN(0001) semiconductor heterostructure. It has been demonstrated that magnetic properties of the AF-BZGNR/h-BN(0001) semiconductor heterostructure can be controlled using Eext. In particular, the local magnetic moment of edge carbon atoms decreases by 10% at a critical value of the positive potential. We have established that local magnetic moments and band gaps can be altered in a wide range using nanomechanical uniaxial compression and Eext, thus making the AF-BZGNR/h-BN(0001) semiconductor heterostructure potentially promising for nanosensors, spin filters, and spintronics applications.

Configuration-dependent geometric and electronic properties of bilayer graphene nanoribbons

Configuration-dependent geometric and electronic structures of bilayer zigzag graphene nanoribbons are investigated by first-principles calculations. These properties are dominated by the stacking configurations, interlayer edge–edge interactions, spin arrangements, and ribbon widths. The optimal configuration exists between the AA and ABα (AA′ and ABβ) stackings, mainly owing to the competition of the stacking and quantum confinement effects. The interlayer edge–edge interactions lead to the destruction or creation of magnetism and cause the AA-stacked system to exhibit a pair of metallic linear bands. However, other stacked nanoribbons are exclusively indirect- or direct-gap semiconductors. The splitting of spin-up and spin-down states could be induced by different magnetic environments. The band-edge states, with a high density of states, are sensitive to changes in the relative displacement.