Study On The Strain-dependent Electronic Properties And Transport Properties Of Graphene

Graphene is composed of carbon atoms arranged on a hexagonal honeycombstructure. In2004, individual graphene planes were first isolated. Graphene has longattracted attention because of appealing electronic properties. In this paper, based ontight-binding model and Dirac equation, the dependence of electronic properties andtransport properties of graphene sheets and graphene nanoribbons on uniformdeformation has been discussed. The main work and results involve:(1) The electronic properties of perfect graphene sheets zigzag and armchair graphenenanoribbons were discussed base on tight-binding model. Graphene can bedescribed at low energies by Dirac fermions following relativistic quantummechanics. The bonding and anti-bonding π bands cross the Fermi level at sixhighly-symmetric apices in the Brillouin zone of graphene where show a lineardispersion relation of spectrum. The quasi-one-dimensional graphene nanoribbonsshow different spectrum due to quantum confinement. The spectrum of nanoribbonsdepend very much on the nature of their edges-zigzag or armchair. For zigzagnanoribbons, the wave vectors vertical to the edges are associated with those parallelto the edges. A zigzag ribbon is metallic. It presents a band with a zero-energy modewhich is the surface state living near the edge of the graphene ribbon. The bottom ofthe bands of the confined modes is located near the Dirac points. The surface state isabsent in armchair nanoribbons. The two directional wave vectors mentioned aboveare irrelevant. Based on tight-binding theory, the armchair ribbons with atom linesN=3m1(m is an integer) are metallic and the other cases are insulators.(2) The Hamiltonian of π electrons of uniformly deformed graphene is given based ontight-binding model. The strained-dependent spectrum was obtained. The electronicproperties of graphene sheets and nanoribbons under uniaxial strains and shearstrains are discussed. The problems including the shift of Dirac points, the change ofspectrum, the critical condition of gap-opening and the dependence of energy gap onstrains are discussed in detail.(3) The change of transport properties of graphene under several strains has beeninvestigated based on Landau theory and classical Boltzmann equation. First, thechange of the quantum conductance of graphene nanoribbons under longitudinaltension and compression was calculated. The change results from several factors including the mean free path of electrons, electronic longitudinal and transversevelocities, and effective channels. According to the calculation, the difference ofquantum conductance under strains along armchair and zigzag direction is small insituation of small strain, whereas the difference is great when large strains areapplied. This is because the isotropy of spectrum in perfect structure is broken underthe uniaxial strains, and the difference shows out along zigzag and armchairdirection, which leads to the difference in band spectrum along the two directions.Second, the group velocity of Fermi electron show anisotropy under strains and theFermi surface is deformed. The effect of the two uniaxial strains along armchair andzigzag direction on the group velocity is different. This indicates the energy band ofgraphene is anisotropic. The uniaxial tension affects the velocity of electron in thesame direction the most, and makes it the minimum among all the directions, andmakes the velocity vertical to it the maximum. The anisotropy of the Fermi surfaceresults in the anisotropic transport. The conductance of direct current was evaluatedwith Boltzmann equation. The anisotropic ratio of conductance is2.91under12%tension along zigzag direction, and the ratio is2.33under12%tension alongarmchair direction. Third, the extraordinary transport properties appear inshear-strained graphene. It is founded the shear strain can cause the off-diagonalelement in band spectrum. Based on Boltzmann equation and relaxation timeapproximation, it is proved the off-diagonal element leads to the new transverseelectric field in uniaxially-conducting graphene ribbons, i.e. the shear strain acted asthe magnetic field in Hall Effect. In addition, deformation induces gage potentialand results in pseudo magnetic field. It is proved that only shear strains can yielduniform magnetic field.