Quantum transport in ferromagnetic graphene: Role of Berry curvature

Abstract

The magnetic effects in ferromagnetic graphene basically depend on the principle of exchange interaction when ferromagntism is induced by depositing an insulator layer on graphene. Here we deal with the consequences of non-uniformity in the exchange coupling strength of the ferromagnetic graphene. We discuss how the in-homogeneity in the coordinate and momentum of the exchange vector field can provide interesting results in the conductivity analysis of the ferromagnetic graphene. Our analysis is based on the Kubo formalism of quantum transport.Graphene [1] is a two dimensional material consisting of a single layer of carbon atoms arranged in a honeycomb or chicken wire structure. The familiar pencil-lead, which is known as graphite, consists of layers of carbon atoms tightly bonded in the plane. This graphite layers are graphene and it is the thinnest as well as strongest material known till now. Graphene can conduct electricity as efficiently as copper and outperforms all other materials as a conductor of heat. Graphene is almost completely transparent, yet so dense that even the smallest atom helium cannot pass through it. Unlike in ordinary semiconductors, the figure of the dispersion relation is cone like which meet at a point, the Dirac point. The energy-momentum plot of quasiparticles behaves as if they were massless electrons, so-called Dirac fermions, that travel at a constant speed with a small but noteworthy fraction of the speed of light. Undoped graphene has a Fermi energy coinciding with the energy of the conical points. This have completely filled valence band and empty conduction band and there exists no bandgap in between and as such graphene is an example of gapless semiconductor and the Hamiltonian near K and K points can be written as, where σ are Pauli matrices. This form of the Hamiltonian is a two dimensional analogue of the Dirac Hamiltonian of massless fermions but instead of c, we have Fermi velocity v F ( ≈ c/300). The ultra flat geometry, high electron mobility and excellent intrinsic transport properties make graphene a unique material in condensed matter physics. Besides, the long spin flip length of graphene makes it a promising candidate for spintronic applications.The importance of ferromagnetism in industry and modern technology is well known. The ferromagnetism is the basis for many electrical and electro-mechanical devices, like electromagnets, electric motors, generators, transformers and also the magnetic storag devices as tape recorders and hard disks. After the observation of graphene in isolation it was very natural for the scientists to search ferromagnetism in graphene. There are variety of ways for the experimental realization of magnetized graphene or more precisely graphene with spin imbalance. There may exists some intrinsic ferromagnetic correlations in graphene. Use of an insulating ferromagnetic substrate or adding a magnetic material or magnetic dopants or defect on top of the graphene sheet may be other options to achieve ferro-magnetism in graphene. In particul...