Indirect RKKY interaction in doped armchair nanotube due to electron phonon interaction effects

We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in doped armchair nanotube in the presence of gap parameter. The effects of both next nearest neighbor hopping parameter and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments have been analyzed. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain the transverse static spin susceptibility of armchair graphene nanoribbon in the presence of electron-phonon coupling and gap parameter. The spin susceptibility components are calculated using Green’s function approach for Holstein model Hamiltonian. The effects of electron doping on dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of next nearest neighbor hopping parameter on the spatial behavior of RKKY interactions are different in the presence of electron phonon coupling.     

RKKY interaction in AB-stacked multilayer graphene

The RKKY interaction between two magnetic impurities absorbed on the surface layer of half-filled AB-stacked multilayer graphene (ABSMLG) is theoretically studied based on the lattice Green's function technique. In comparison with the case of monolayer graphene, the RKKY interaction in such multilayer graphene presents distinct properties in some aspects. Firstly, from the numerical results, we find that the thickness of the ABSMLG influences the RKKY interaction in a complicated manner, depending on the odd/even parity of the number of layers and the sublattice attribution of the positions of the two magnetic impurities. Then, we derive the asymptotic expressions of the RKKY interactions in ABSMLG in the long-distance limit. For even-layered ABSMLG, we find that the RKKY interactions of the 1A-1A, 1B-1A and 1B-1B couplings fall off as 1/R(2), 1/R(4) and 1/R(6) (1A and 1B stand for, respectively, the sublattice points in the surface layer, which are positioned directly on the plaquette and on a lattice point of the layer underneath). On the other hand, in odd-layered ABSMLG, the decays of these interactions follow the 1/R(2), 1/R(3) and 1/R(3) power laws respectively. In addition, we also find that these analytical expressions are quantitatively valid to describe the RKKY interaction in ABSMLG when the distance between the two magnetic impurities is larger than the lattice constant of graphene by one order of magnitude.     

Electronic transport through zigzag/armchair graphene nanoribbon heterojunctions

The electronic transport properties of a graphene nanoribbon (GNR) are known to be sensitive to its width, edges and defects. We investigate the electronic transport properties of a graphene nanoribbon heterojunction constructed by fusing a zigzag and an armchair graphene nanoribbon (zGNR/aGNR) side by side. First principles results reveal that the heterojunction can be either metallic or semiconducting, depending on the width of the nanoribbons. Intrinsic rectification behaviors have been observed, which are largely sensitive to the connection length between the zGNR and aGNR. The microscopic origins of the rectification behavior have been revealed. We find that the carrier type can alter from electrons to holes with the bias voltage changing from negative to positive; the asymmetrical transmission spectra of electrons and holes induced by the interface defects directly results in the rectification behavior. The results suggest that any methods which can enhance the asymmetry of the transmission spectra between holes and electrons could be used to improve the rectification behavior in the zGNR/aGNR heterojunction. Our findings could be useful for designing graphene based electronic devices.     

Spin-dependent transport properties of an armchair boron-phosphide nanoribbon embedded between two graphene nanoribbon electrodes

Using non-equilibrium Green׳s function and ab initio calculations we investigate structural, electronic, and transport properties of a junction consisting of armchair hexagonal boron phosphide nanoribbon (ABPNR) contacted by two semi-infinite electrodes composed of armchair graphene nanoribbons (AGNRs). We consider three different configurations including the pristine AGNR–BP–GNR and substitutions for Iron atoms, namely on phosphorus and boron atoms at one edge of the BP nanoribbon. The spin current polarization in all these cases is extracted for each structure and bias. Such hybrid system is found to exhibit not only significant spin-filter efficiency (SFE) but also tunable negative differential resistance (NDR).     

A graphene quantum dot realized by an armchair graphene nanoribbon with line defect

The electron transport in a semiconducting armchair graphene nanoribbon with line defect is theoretically investigated, by coupling it to two normal metallic leads. It is found that the line defect induces a new localized quantum state near the Dirac point, and that the coupling between this state and the leads provides a channel for the resonant tunneling. This means that such a finite‐size nanoribbon can be viewed as a quantum dot. When two line defects are present simultaneously, a coupled quantum dot forms, leading to the splitting of the conductance peaks. With these results, we propose such a structure to be a promising candidate of an electron transistor. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Charge susceptibilities of armchair graphene nanoribbon in the presence of magnetic field

We present the behaviors of both dynamical and static charge susceptibilities of undoped armchair graphene nanoribbon using the Green's function approach in the context of tight binding model Hamiltonian.Specifically,the effects of magnetic field on the the plasmon modes of armchair graphene nanoribbon are investigated via calculating the correlation function of charge density operators.Our results show that the increase of magnetic field makes the high-frequency plasmon mode for both metallic and insulating cases disappear.We also show that low-frequency plasmon mode for metallic nanoribbon appears due to increase of magnetic field.Furthermore,the number of collective excitation modes increases with ribbon width at zero magnetic field.Finally,the temperature dependence of the static charge structure factor of armchair graphene nanoribbon is studied.The effects of both magnetic field and ribbon width on the static charge structure factor are discussed in detail.     

Electronic transport across a junction between armchair graphene nanotube and zigzag nanoribbon

Based on the well known nearest-neighbor tight-binding approximation for graphene, an exact expression for the electronic conductance across a zigzag nanoribbon/armchair nanotube junction is presented for non-interacting electrons. The junction results from the removal of a half-row of zigzag dimers in armchair nanotube, or equivalently by partial rolling of zigzag nanoribbon and insertion of a half-row of zigzag dimers in between. From the former point of view, a discrete form of Dirichlet condition is imposed on a zigzag half-line of dimers assuming the vanishing of wave function outside the physical structure. A closed form expression is provided for the reflection and transmission moduli for the outgoing wave modes for each given electronic wave mode incident from either side of the junction. It is demonstrated that such a contact junction between the nanotube and nanoribbon exhibits negligible backscattering, and the transmission has been found to be nearly ballistic. In contrast to the previously reported studies for partially unzipped carbon nanotubes (CNTs), using the same tight binding model, it is found that due to the “defect” there is certain amount of mixing between the electronic wave modes with even and odd reflection symmetries. But the junction remains a perfect valley filter for CNTs at certain energy ranges. Applications aside from the electronic case, include wave propagation in quasi-one-dimensional honeycomb structures of graphene-like constitution. The paper includes several numerical calculations, analytical derivations, and graphical results, which complement the provision of succinct closed form expressions.     

Rashba spin-orbit interaction in graphene armchair nanoribbons

We study graphene nanoribbons (GNRs) with armchair edges in the presence of Rashba spin- orbit interactions (RSOI). We impose the boundary conditions on the tight binding Hamiltonians for bulk graphene with RSOI by means of a sine transform and study the influence of RSOI on the spectra and the spin polarization in detail. We derive the low energy approximation of the RSOI Hamiltonian for the zeroth and first order in momentum and test their ranges of validity. The choice of a basis appropriate for armchair boundaries is important in the case of mode-coupling effects and leads to results that are easy to work with.     

Impurity scattering,Friedel oscillations and RKKY interaction in graphene

We investigate Friedel Oscillations (FO) surrounding a point scatterer in graphene. We find that the long-distance decay of FO depends on the symmetry of the scatterer. In particular, the FO of the charge density around a Coulomb impurity show a faster, δρ∼1/ r³, decay than in conventional 2D electron systems. In contrast, the FO of the exchange field which surrounds atomically sharp defects breaking the hexagonal symmetry of the honeycomb lattice decay according to the 1/r² law. We discuss the consequences of these findings for the temperature dependence of the resistivity of the material and the RKKY interaction between magnetic impurities.     

Exciton effects in armchair graphene nanoribbons

We have studied the exciton effects in armchair graphene nanoribbons systematically, using the nonorthogonal tight-binding model supplement by the long-range Coulomb interactions. It is found from our calculations that the excitation energies, the exciton binding energies and the exciton wave function sizes of the E ₁₁ and E ₂₂ excitons all exhibit oscillation as a function of the ribbon width. And there is a phase shift of π between the oscillation of the E ₁₁ and E ₂₂ excitons.     

Dynamical spin polarization in single-layer graphene

In the present work the dynamical behavior of $\mathrm{\pi }\mathrm{-}\mathrm{electronic}$ spin in graphene is investigated. The $\mathrm{\pi }\mathrm{-}\mathrm{electron}$ is under the influence of a normal uniform magnetic field and the Rashba spin–orbit coupling. Introducing a Casimir operator, we show that the governing Hamiltonian and, consequently, the time-evolution matrix is block-diagonal. We then proceed to calculate the temporal behavior of different spin components, when it is initially in-plane polarized. Our calculations show that the spin is dynamically polarized in a plane normal to the graphene sheet and follows the patterns of collapse-revivals. The dependence of amplitudes as well as the collapse-revivals’ periods on the external field and the Rashba spin–orbit coupling is also reported.     

锯齿型石墨烯纳米窄带中量子霍尔体系的电场调控

应用含自洽格点在位库仑作用的Kane-Mele模型,研究锯齿型石墨烯纳米窄带平面内横向电场对边界带能带结构和量子自旋霍尔(QSH)体系的影响.研究结果显示,当电场强度较弱时,外加电场的方向可以调控自旋向下的两个边界带一起朝不同方向移动,导致波矢q=0.5处自旋向下的两个纯边界态的能量简并劈裂方向可由电场调控;当电场强度进一步增强到超过0.69 V/nm,自旋向下的两个边界带出现较大带隙,能带反转,而自旋向上的电子结构无能隙,系统呈现半金属性,同时QSH体系不再是B类.特别当电场强度为1.17 V/nm时,在自旋向下能带的能隙中,q=0.5处存在自旋向上的纯边界态,意味着在8格点边界处可以产生自旋向上的纯边界电流.当电场强度持续增加时,QSH系统从B类到C类经历3个阶段的变化.当电场强度超过1.42 V/nm后,自旋向上的两个边界带也出现能带反转,分别成为导带和价带,系统成为C类的普通量子霍尔体系.     

The modulation effects on Landau levels in graphene nanoribbon

Magnetic-modulation effects in one-dimensional graphene nanoribbon have been investigated by the Peierls tight-binding model. The energy dispersion exhibits unusual oscillatory behavior which is mainly dominated by the modulation strength, the period, and the ribbon width. The main features of energy band are directly reflected in density of states, such as the structure, the height, the position, and the number of prominent peaks.     

Thermally driven spin transport through a transverse-biased zigzag-edge graphene nanoribbon

In the framework of the Landauer-Büttiker formalism, we investigate coherent spin transport through a transverse-biased magnetic zigzag-edge graphene nanoribbon, with a temperature difference applied between the source and the drain. It is shown that a critical source temperature is needed to generate a spin-polarized current due to the presence of a forbidden transport gap. The magnitude of the obtained spin polarization exceeds 90% in a wide range of source temperatures, and its polarization direction could be changed by reversing the transverse electric field. We also find that, at fixed temperature difference, the spin-polarized current undergoes a transition from increasing to decreasing as the source temperature rises, which is attributed to the competition between the excited energy of electrons and the relative temperature difference. Moreover, by modulating the transverse electric field, the source temperature and the width of the ribbon, we can control the device to work well for generating a highly spin-polarized current.     

Screening, Kohn anomaly, Friedel oscillation, and RKKY interaction in bilayer graphene

We calculate the screening function in bilayer graphene (BLG) in both the intrinsic (undoped) and the extrinsic (doped) regimes within the random phase approximation, comparing our results with the corresponding single layer graphene and the regular two-dimensional electron gas. We find that the Kohn anomaly is strongly enhanced in BLG. We also discuss the Friedel oscillation and the RKKY interaction, which are associated with the nonanalytic behavior of the screening function at q=2k(F). We find that the Kohn anomaly, the Friedel oscillation, and the RKKY interaction are all qualitatively different in the BLG compared with the single layer graphene and the two-dimensional electron gas.     

Bandgap tuning in armchair MoS(2) nanoribbon

We report on the first-principles calculations of bandgap modulation in armchair MoS(2) nanoribbon (AMoS(2)NR) by transverse and perpendicular electric fields respectively. In the monolayer AMoS(2)NR case, it is shown that the bandgap can be significantly reduced and be closed by transverse field, whereas the bandgap modulation is absent under perpendicular field. The critical strength of transverse field for gap closure decreases as ribbon width increases. In the multilayer AMoS(2)NR case, in contrast, it is shown that the bandgap can be effectively reduced by both transverse and perpendicular fields. Nevertheless, it seems that the two fields exhibit different modulation effects on the gap. The critical strength of perpendicular field for gap closure decreases with increasing number of layers, while the critical strength of transverse field is almost independent of it.     

Multilayer transition in a spin 3/2 Blume-Capel model with RKKY interaction

Using Monte Carlo simulation and mean-field theory, we have studied the effect of RKKY interaction on the multi-layer transition and magnetic properties of a spin-3/2 Blume-Capel model of a system formed by two magnetic multi-layer materials, of different thicknesses, separated by a non-magnetic spacer of thickness M. It is found that the multi-layer magnetic order-disorder transition temperature depends strongly on the thicknesses of the magnetic layer and the non-magnetic layer. The transition temperature increases with increasing thickness of the magnetic multi-layers and decreases with increasing thickness of the non-magnetic one. Furthermore, there exists a critical thickness M_L of the non-magnetic spacer beyond which the effect of the RKKY interaction becomes negligible and separate transitions occur in the two magnetic layers. The critical thickness M_L decreases on increasing the magnetic crystal field and/or the Fermi level k_f. Moreover, the multi-layer transition temperature undergoes oscillations as a function of the Fermi level. The susceptibility critical exponents are computed within Monte Carlo simulations.     

Electronic transport for armchair graphene nanoribbons with a potential barrier

This paper studies the electronic transport property through a square potential barrier in armchair-edge graphene nanoribbon (AGNR). Using the Dirac equation with the continuity condition for wave functions at the interfaces between regions with and without a barrier, we calculate the mode-dependent transmission probability for both semiconducting and metallic AGNRs, respectively. It is shown that, by some numerical examples, the transmission probability is generally an oscillating function of the height and range of the barrier for both types of AGNRs. The main difference between the two types of systems is that the magnitude of oscillation for the semiconducting AGNR is larger than that for the metallic one. This fact implies that the electronic transport property for AGNRs depends sensitively on their widths and edge details due to the Dirac nature of fermions in the system.     

Electronic transport for armchair graphene nanoribbons with a potential barrier

We theoretically investigate the electronic transport properties through a rectangular potential barrier embedded in armchair-edge graphene nanoribbons (AGNRs) of various widths. Using the Landauer formula and Dirac equation with the continuity conditions for all segments of wave functions at the interfaces between regions inside and outside the barrier, we calculate analytically the conductance and Fano factor for the both metallic and semiconducting AGNRs, respectively. It is shown that, by some numerical examples, at Dirac point the both types of AGNRs own a minimum conductance associated with the maximum Fano factor. The results are discussed and compared with the previous relevant works.