锯齿型石墨烯纳米带的能带研究

运用π电子紧束缚模型,具体研究了锯齿型石墨烯纳米带(ZGNRs)的边界结构对能带,特别是费米面附近的导带和价带电子的影响.计算了七种不同边界结构的ZGNRs的能带色散关系及费米面附近价带电子在原胞中各原子上的分布情况.计算结果表明:两边界都无悬挂原子的NN-ZGNRs,只有一边界有悬挂原子的DN-ZGNRs,两边界都有五边形环的SPP-ZGNRs和ASPP-ZGNRs为金属性.两边界都有悬挂原子的DD-ZGNRs,一边界为五边形环另一边界无悬挂原子的PN-ZGNRs和一边界为五边形环另一边界有悬挂原子的P 关键词： 锯齿型石墨烯纳米带 紧束缚模型 电子密度分布 缺陷结构     

Band structure effects on the nonlinear optical response of bilayer graphene

Recently, Rabi-like oscillations that occur far from resonance were predicted in monolayer graphene. In bilayer graphene, when the trigonal warping effect is taken into account, this new Rabi frequency shows a zero non-trivial minimum as a function of the strength of the applied electric field in addition to the trivial minimum at zero field. The zero non-trivial minimum occurs where the ‘leg pocket’ of the Fermi surface develops, described in the pioneering work of McCann et al. [Eur. Phys. J. Special Topics 148, 91 (2007)]. Thereafter, the anomalous Rabi frequency varies linearly with the square of the intensity of the applied field consistent with a bilayer system without trigonal warping. It is seen that this anomalous Rabi frequency is affected much more by trigonal warping than the conventional Rabi frequency. The induced current is also significantly affected by the trigonal warping. A fully numerical solution of the optical Bloch equations completely corroborates the analytical findings and provides a basis for the approximation schemes employed.     

Band topology and the quantum spin Hall effect in bilayer graphene

We consider bilayer graphene in the presence of spin-orbit coupling, in order to assess its behavior as a topological insulator. The first Chern number n for the energy bands of single-layer graphene and that for the energy bands of bilayer graphene are computed and compared. It is shown that for a given valley and spin, n for a Bernal-stacked bilayer is doubled with respect to that for the monolayer. This implies that this form of bilayer graphene will have twice as many edge states as single-layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bernal-stacked bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. In contrast, we show that AA-stacked bilayer graphene is not a topological insulator unless the spin-orbit coupling is bigger than the interlayer hopping. Finally, we consider an intermediate situation in which only one of the two layers has spin-orbit coupling, and find that although individual valleys have non-trivial Chern numbers for the case of Bernal stacking, the spectrum as a whole is not gapped, so the system is not a topological insulator.     

Band structures of Bernal graphene modulated by electric fields

The tight-binding model is utilized to investigate the influence of modulation electric fields on bilayer Bernal graphene (BBG). The electric potential changes the parabolic bands into oscillatory ones, and induces more band-edge states. As the strength of field is strengthened, it would enhance the oscillation of energy band, affect larger range of energy, induced more band-edge states, and cause more overlapping of valence and conduction band. While the period of field is enhanced, the number of sub-bands and band-edge states would increase. However the deformation of energy band is less violent. The essential features of electronic structure are directly reflected on the density of states (DOS). DOS displays many prominent peaks resulting from the induced band-edge states.     

Band structures of symmetrical graphene superlattice with cells of three regions

We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity and the energy bands contours near Dirac points. We also discuss the evolution of gap edges and cutoff region near the vertical Dirac points.     

Band structure of non-ideal semiconductor superlattices

An ideal superlattice is an array of two (or more) alternating layers of materials with a single period, fixed barrier height and infinitely abrupt interfaces. A real superlattice differs from an ideal one in many aspects and this affects the band structure. They include unsharp interfaces, interface disorder, small fluctuations in thicknesses of quantum wells (barriers) and in the potential barrier heights from layer to layer. The band structure of superlattices in these realistic cases have been investigated. The relevance of these non-ideal cases to the shifting of the ground-state energy of the electrons, holes, and the effective energy gap are also discussed.     

Charge-transfer-induced cesium superlattices on graphene

We investigate cesium (Cs) adsorption on graphene formed on a 6H-SiC(0001) substrate by a combined scanning tunneling microscopy and density functional theory study. Individual Cs atoms adsorb preferentially at the rim region of the well-defined 6×6 substrate superstructure and on multilayer graphene. By finely controlling the graphene thickness and Cs coverages (1/3 ML and 1?ML), we here demonstrate two intriguing and well-ordered Cs superlattices on bilayer and multilayer graphene (<6 layers). Statistical analysis of the Cs-Cs interatomic distance reveals a hitherto unobserved Cs-Cs long-range electrostatic potential caused by charge transfer from Cs to graphene, which couples with the inhomogeneous substrate potential to stabilize the observed Cs superlattices. The present study provides a new avenue to fabricate atomic and molecular superlattices for applications in high-density recording and data storage.     

Band mixing effect in semiconductor superlattices

The band mixing effect on the electronic and optical properties of semiconductor superlattices is studied within the framework of the empirical tight-binding model. It is found that the superlattice periodic potentials mix the bulk heavy hole, light hole and spin-orbit-split bands in the valence band states. As a consequence, the optical matrix elements associated with various valence-to-conduction subband transitions are very sensitive to the variation of the wavevector in directions parallel to the interface ( _t). We find that band mixing in conjunction with the exciton effect can account for the Δn≠0 forbidden transitions observed in several recent experiments.     

电场调控双层石墨烯纳米带的电子结构和光学性质

利用基于密度泛函理论的第一性原理方法,研究了外加电场作用下双层AA堆垛的Armchair边缘石墨烯纳米带(BAGNRs)的电子结构和光学性质. BAGNRs具有半导体特性,其带隙随带宽(宽度为4～12个碳原子)的增加而振荡性减小.当施加电场后,BAGNRs的带隙随着电场强度的增加而逐渐减小,带隙越大对电场值的变化越敏感.当电场值为0.5 V/?时,所有BAGNRs的带隙都为零. BAGNRs具有各向异性的光学性质,其介电函数在垂直极化方向为半导体特性,而在平行极化方向为金属特性.在外加电场的作用下,BAGNRs的介电函数、吸收系数、折射系数、反射系数、电子能量损失系数和光电导率,其峰值向低能量区域移动,即产生红移现象.电场增强了能带间的跃迁几率.纳米带宽度对这些光学性质参数具有不同程度的影响.研究结果解释了电场调控BAGNRs光学性质的规律和微观机理.     

Minimal conductivity in bilayer graphene

Using the Landauer formula approach, it is proven that minimal conductivity of order e²/h found experimentally in bilayer graphene is an intrinsic property. For the case of ideal crystals, the conductivity turns out to be equal to e²/2h per valley per spin. A zero-temperature shot noise in bilayer graphene is considered and the Fano factor is calculated. Its value 1–2/π is close to the value 1/3 found earlier for single-layer graphene.     

Topological confinement in bilayer graphene

We study a new type of one-dimensional chiral states that can be created in bilayer graphene (BLG) by electrostatic lateral confinement. These states appear on the domain walls separating insulating regions experiencing the opposite gating polarity. While the states are similar to conventional solitonic zero modes, their properties are defined by the unusual chiral BLG quasiparticles, from which they derive. The number of zero mode branches is fixed by the topological vacuum charge of the insulating BLG state. We discuss how these chiral states can manifest experimentally and emphasize their relevance for valleytronics.     

Gate-tunable bandgap in bilayer graphene

The tight-binding model of bilayer graphene is used to find the gap between the conduction and valence bands as a function of both the gate voltage and the doping level by donors or acceptors. The total Hartree energy is minimized and an equation for the gap is obtained. This equation for the ratio of the gap to the chemical potential is determined only by the screening constant. Therefore, the gap is strictly proportional to the gate voltage or the carrier concentration in the absence of donors or acceptors. But in the case where the donors or acceptors are present, the gap demonstrates an asymmetric behavior on the electron and hole sides of the gate bias. A comparison with experimental data obtained by Kuzmenko et al. demonstrates a good agreement.     

Cyclotron resonance in bilayer graphene

We present the first measurements of cyclotron resonance of electrons and holes in bilayer graphene. In magnetic fields up to B=18 T, we observe four distinct intraband transitions in both the conduction and valence bands. The transition energies are roughly linear in B between the lowest Landau levels, whereas they follow square root[B] for the higher transitions. This highly unusual behavior represents a change from a parabolic to a linear energy dispersion. The density of states derived from our data generally agrees with the existing lowest order tight binding calculation for bilayer graphene. However, in comparing data to theory, a single set of fitting parameters fails to describe the experimental results.     

Spin-polarized transport in graphene nanoribbon superlattices

By the Green’s function method,we investigate spin transport properties of a zigzag graphene nanoribbon superlattice(ZGNS) under a ferromagnetic insulator and edge effect.The exchange splitting induced by the ferromagnetic insulator eliminates the spin degeneracy,which leads to spin-polarized transport in structure.Spin-dependent minibands and minigaps are exhibited in the conductance profile near the Fermi energy.The location and width of the miniband are associated with the geometry of the ZGNS.In the optimal structure,the spin-up and spin-down minibands can be separated completely near the Fermi energy.Therefore,a wide,perfect spin polarization with clear stepwise pattern is observed,i.e.,the perfect spin-polarized transport can be tuned from spin up to spin down by varying the electron energy.     

Weak localization in bilayer graphene

We have performed the first experimental investigation of quantum interference corrections to the conductivity of a bilayer graphene structure. A negative magnetoresistance--a signature of weak localization--is observed at different carrier densities, including the electroneutrality region. It is very different, however, from the weak localization in conventional two-dimensional systems. We show that it is controlled not only by the dephasing time, but also by different elastic processes that break the effective time-reversal symmetry and provide intervalley scattering.     

Magneto-optics of monolayer and bilayer graphene

The optical conductivity of graphene and bilayer graphene in quantizing magnetic fields is studied. Both dynamical conductivities, longitudinal and Hall’s, are analytically evaluated. The conductivity peaks are explained in terms of electron transitions. Correspondences between the transition frequencies and the magneto-optical features are established using the theoretical results. The main optical transitions obey the selection rule Δn = 1 with the Landau number n. The Faraday rotation and light transmission in the quantizing magnetic fields are calculated. The effects of temperatures and magnetic fields on the chemical potential are considered.     

Electronic compressibility of a graphene bilayer

We calculate the electronic compressibility arising from electron-electron interactions for a graphene bilayer within the Hartree-Fock approximation. We show that, due to the chiral nature of the particles in this system, the compressibility is rather different from those of either the two-dimensional electron gas or ordinary semiconductors. We find that an inherent competition between the contributions coming from intraband exchange interactions (dominant at low densities) and interband interactions (dominant at moderate densities) leads to a nonmonotonic behavior of the compressibility as a function of carrier density.     

Edge states of graphene bilayer strip

The electronic structure of the zig-zag bilayer strip is analyzed. The electronic spectraof the bilayer strip is computed. The dependence of the edge state band flatness on thebilayer width is found. The density of states at the Fermi level is analytically computed.It is shown that it has the singularity which depends on the width of the bilayer strip.There is also asymmetry in the density of states below and above the Fermi energy.     

旋转双层石墨烯的电子结构

本文将第一性原理和紧束缚方法结合起来, 研究了层间不同旋转角度对双层石墨烯的电子能带结构和态密度的影响. 分析发现, 旋转双层石墨烯具有线性的电子能量色散关系, 但其费米速度随着旋转角度的减小而降低. 进一步研究其电子能带结构发现, 不同旋转角度的双层石墨烯在M点可能会出现大小不同的的带隙, 而这些能隙会增强双层石墨烯的拉曼模强度, 并由拉曼光谱实验所证实. 通过对比双层石墨烯的晶体结构和电子态密度, 发现M点处带隙来自于晶体结构中的“类AB堆垛区”. 关键词： 旋转双层石墨烯 第一性原理 紧束缚 电子结构