The Charge And Magnetic Response In Bilayer Graphene

Graphene, a two-dimensional single layer of carbon atoms arranged on a honey-comb lattice, is a very hot research field of condensed matter physics in recent years.On its applied side, experimental physicists have found that the graphene system hasan extremely high mobility, which is even two orders higher than that of the semicon-ductor material silicon. Thus it is regarded as a new semiconductor material to replacesilicon. On its academic side, the charge carrier of graphene has a chiral mass-less lin-ear Dirac dispersion, which is rather peculiar in present physical systems. Due to thisdispersion, the graphene system has many unique properties and phenomena rather dif-ferent from the regular systems, and therefore attracts much attentions from theoreticalinvestigators. Bilayer graphene, which is formed by stacking two single layer graphenein Bernal stacking, is anther significant graphene-related system. In its low energy ef-fective theory, the charge carrier of bilayer graphene has a chiral mass-less parabolicdispersion. It is different from that of single layer graphene and 2 dimensional electrongas system, but in some parts it is similar to them. In some sense, bilayer graphene isconsidered as the intermediate between single layer graphene and 2 dimensional elec-tron gas system. Similar to the single layer graphene, bilayer graphene also has a veryhigh mobility. Because bilayer graphene is easy to open a gap and became a semicon-ductor by an external electric field, it is expected as a new ultra high speed material ofthe field effect transistor.As we know, investigating the responses to the external fields is a very importantmethod to understand the internal properties of the system: On one side, the responsescan be calculated theoretically by using the linear response theory, and on the other sidethey can determined directly from experiments. Therefore they can be considered asa bridge connecting the theories and experiments and used to check whether the theo-ries are correct by comparing with the experimental results. Through the experimentalinvestigation, the most common and important responses of a system are its charge re-sponse to the external electric field and magnetic response to the magnetic field, whichare actually the density-density response and current-current response of this system.For a certainty it is significant to investigate the charge and magnetic responses of asystem, and that is the issue we have done in this thesis for bilayer graphene.In the first chapter of this thesis, we simply review some basic concepts of graphene and bilayer graphene and the wondrous effects occurring in these systems, including theanumalous quantum Hall effect, Klein tunneling and the specular Andreev re?ection. Inthe second and third chapters, we represent our two works on the charge and magneticresponses of bilayer graphene.(1) In terms of the charge response, we calculate the temperature-dependent chargecarrier transport of bilayer graphene impacted by Coulomb impurity scattering withinthe random-phase approximation. In conditions of the present laboratory, many sam-ples of graphene and bilayer graphene are laid upon the substrates, where the screenedCoulomb impurities will have an unavoidable in?uence on the charge carrier trans-port of graphene and bilayer graphene. Therefore, it is significative to investigate theCoulomb screening and the screening-induced temperature-dependent behavior of con-ductivity in graphene-related systems. Before this work, the Coulomb screening of sin-gle layer graphene at zero and finite temperatures and bilayer graphene at zero temper-ature have been well investigated, however, the analytically investigation of Coulombscreening of bilayer graphene, which is the issue we will discuss in the second chapter,has not yet been provided.We analytically calculate the temperature-dependent behaviors of the polarizabil-ity of bilayer graphene in all wave vector regimes:We find the polarizability at zero mo-mentum transfer is equal to the density of states and enhanced by a factor log 4 at largemomentum transfer for arbitrary temperature while the around k_F it has nonmonotonictemperature-dependent behavior. The sharp cusp of static polarizability arising fromthe strong 2k_F backward scattering would been smoothed by the increasing tempera-tures. In all wave-vector regimes, the static polarizability shows a weak temperaturedependence, representing the distinctive electron property of bilayer graphene. We alsofirstly obtain the asymptotic behaviors of conductivity of bilayer graphene at low andhigh temperature at the high carrier density, and finds the behavior of bilayer grapheneturns from a two-dimensional electron gas like linear temperature metallic behaviorto a single-layer graphene and quadratic temperature insulating behavior as the tem-perature increases. We argue this shows a crossover behavior of bilayer graphene asintermediate between the single layer graphene and 2 dimensional electron gas.(2) In terms of the magnetic response, within the linear response theorem we inves-tigate the orbital diamagnetism of a weak-doped bilayer graphene in spatially smoothlyvarying magnetic field. As shown in the early investigations, compared with the Pauliparamagnetism, Landau diamagnetism (i.e., orbital diamagnetism) dominates the con-tribution to the whole magnetism of graphite. The same argument is fit for the case of graphene and bilayer graphene. Therefore, it is significant to investigate orbital dia-magnetism of graphene systems for understanding their magnetism. Before our work,the orbital susceptibility of single layer graphene at zero temperature with finite Fermienergy, zero and finite wave vector and bilayer graphene at zero temperature with finiteFermi energy, zero wave vector have been studies, but the analytically investigation oforbital susceptibility of bilayer graphene at zero temperature with finite Fermi energyand finite wave vector, which is the issue we will discuss in third chapter, has not yetbeen provided.In this part, we obtain the general analytic expression of the orbital susceptibilityof bilayer graphene, with finite wave vector and Fermi energy, at zero temperature.We find that the magnetic field screening factor of bilayer graphene is dependent withthe wave vector, which results in a more complicated screening behavior comparedwith that of single layer graphene. We also study the induced magnetization, electriccurrent in bilayer graphene under several types of nonuniform magnetic field, and findthey are qualitatively different from that in single layer graphene and 2 dimensionalelectron gas. However, we find that similar to the single layer graphene, the magneticobject placed above bilayer graphene is repelled by a diamagnetic force from bilayergraphene, approximately equivalent to a force produced by its mirror image on the otherside of bilayer graphene with a reduced amplitude dependent with the typical length ofthe systems.In the last chapter, we make a summary and scope of our works.