Making devices with graphene necessarily involves making contacts with metals. We use density functional theory to study how graphene is doped by adsorption on metal substrates and find that weak bonding on Al, Ag, Cu, Au, and Pt, while preserving its unique electronic structure, can still shift the Fermi level with respect to the conical point by 0:5 eV. At equilibrium separations, the crossover from p-type to n-type doping occurs for a metal work function of 5:4 eV, a value much larger than the graphene work function of 4.5 eV. The numerical results for the Fermi level shift in graphene are described very well by a simple analytical model which characterizes the metal solely in terms of its work function, greatly extending their applicability. DOI: 10.1103/PhysRevLett.101.026803 PACS numbers: 73.63.ÿb, 73.20.Hb, 73.40.Ns, 81.05.Uw Recent progress in depositing a single graphene sheet on an insulating substrate by micromechanical cleavage enables electron transport experiments on this twodimensional system [1,2]. Such experiments demonstrate an exceptionally high electron mobility in graphene, quantization of the conductivity, and a zero-energy anomaly in the quantum Hall effect, in agreement with theoretical predictions [3][4][5][6][7]. The spectacular effects arise from graphene's unique electronic structure. Although it has a zero band gap and a vanishing density of states (DOS) at the Fermi energy, graphene exhibits metallic behavior due to topological singularities at the K points in the Brillouin zone [3,4] where the conduction and valence bands touch in conical (Dirac) points and the dispersion is essentially linear within 1 eV of the Fermi energy.In a freestanding graphene layer the Fermi energy coincides with the conical points but adsorption on metallic (or insulating) substrates can alter its electronic properties significantly [8][9][10][11][12][13][14][15]. Since electronic transport measurements through a graphene sheet require contacts to metal electrodes [2,12,16,17], it is essential to have a full understanding of the physics of metal-graphene interfaces. In this Letter we use first-principles calculations at the level of density functional theory (DFT) to study the adsorption of graphene on a series of metal substrates. The (111) surfaces of Al, Co, Ni, Cu, Pd, Ag, Pt, and Au, covering a wide range of work functions and chemical bonding, form a suitable system for a systematic study.Our results show that these substrates can be divided into two classes. The characteristic electronic structure of graphene is significantly altered by chemisorption on Co, Ni, and Pd but is preserved by weak adsorption on Al, Cu, Ag, Au, and Pt. Even when the bonding is weak, however, the metal substrates cause the Fermi level to move away from the conical points in graphene, resulting in doping with either electrons or holes. The sign and amount of doping can be deduced from the difference of the metal and graphene work functions only when they are so far apart that there is no wave function overlap. At the e...

Based upon the observations (i) that their in-plane lattice constants match almost perfectly and (ii) that their electronic structures overlap in reciprocal space for one spin direction only, we predict perfect spin filtering for interfaces between graphite and (111) fcc or (0001) The observation [1,2] of giant magnetoresistance in systems where the transmission through interfaces between normal and ferromagnetic metals (FM) is spin dependent has driven a major effort to study spin filtering effects in other systems and extend applications from field sensing to storage [3], reprogrammable logic [4], and quantum computing [5]. An ideal spin filter would allow all carriers with one spin through but none with the other spin. Interfaces with half-metallic ferromagnets (HMFs) [6] should have this property but progress in exploiting it has been slow because of the difficulty of making stoichiometric HMFs with the theoretically predicted bulk properties and then making devices maintaining these properties at interfaces [7].If the nonmagnetic metal is replaced by an insulator (I) or semiconductor (SC), spin filtering still occurs giving rise to tunneling magnetoresistance (TMR) in FMjIjFM magnetic tunnel junctions and spin-injection at FMjSC interfaces. If the spin polarization of the ferromagnet is not complete, then the conductivity mismatch between metals and semiconductors or insulators has been identified as a serious obstacle to efficient spin injection [8]. It can be overcome if there is a large spin-dependent interface resistance but this is very sensitive to the detailed atomic structure and chemical composition of the interface. Knowledge of the interface structure is a necessary preliminary to analyzing spin filtering theoretically and progress has been severely hampered by the difficulty of experimentally characterizing FMjI and FMjSC interfaces.The situation improved with the confirmation of large values of TMR in tunnel barriers based upon crystalline MgO [9,10] which had been predicted by detailed electronic structure calculations [11,12]. While the record values of TMR-in excess of 500% at low temperatures [13]-are undoubtedly correlated with the crystallinity of MgO, the nature of this relationship is not trivial [14]. The sensitivity of TMR (and spin injection) to details of the interface structure [15,16] make it difficult to close the quantitative gap between theory and experiment. In view of the reactivity of the open-shell transition metal (TM) ferromagnets Fe, Co, and Ni with typical semiconductors and insulators, preparing interfaces where disorder does not dominate the spin filtering properties remains a challenge. With this in mind, we wish to draw attention to a quite different material system which should be intrinsically ordered, for which an unambiguous theoretical prediction of perfect spin filtering can be made in the absence of disorder, and which is much less sensitive to interface roughness and alloy disorder than TMR or spin injection.

Landauer's formula relates the conductance of a quantum wire or interface to transmission probabilities. Total transmission probabilities are frequently calculated using Green function techniques and an expression first derived by Caroli. Alternatively, partial transmission probabilities can be calculated from the scattering wave functions that are obtained by matching the wave functions in the scattering region to the Bloch modes of ideal bulk leads. An elegant technique for doing this, formulated originally by Ando, is here generalized to any Hamiltonian that can be represented in tight-binding form. A more compact expression for the transmission matrix elements is derived and it is shown how all the Green function results can be derived from the mode matching technique. We illustrate this for a simple model which can be studied analytically, and for an Fe|vacuum|Fe tunnel junction which we study using first-principles calculations.

A systematic, quantitative study of the effect of interface roughness and disorder on the magnetoresistance of FeCo|vacuum|FeCo magnetic tunnel junctions is presented based upon parameter-free electronic structure calculations. Surface roughness is found to have a very strong effect on the spinpolarized transport while that of disorder in the leads (leads consisting of a substitutional alloy) is weaker but still sufficient to suppress the huge tunneling magneto-resistance (TMR) predicted for ideal systems.Tunneling magnetoresistance (TMR) refers to the dependence of the resistance of a FM 1 |I|FM 2 (ferromagnet|insulator|ferromagnet) magnetic tunnel junction (MTJ) on the relative orientation of the magnetization directions of the ferromagnetic electrodes when these are changed from being antiparallel (AP) to parallel (P):Since the discovery of large values of TMR in MTJs based upon ultrathin layers of amorphous Al 2 O 3 as insulator, 1 a considerable effort has been devoted to exploiting the effect in sensors and as the basis for non-volatile memory elements. Understanding TMR has been complicated by the difficulty of experimentally characterizing FM|I interfaces. The chemical composition of the interface has been shown 2 to have a strong influence on the magnitude and polarization of the TMR and knowledge of the interface structure is a necessary preliminary to analyzing MTJs theoretically. In the absence of detailed structural models of the junctions and the materials-specific electronic structures which could be calculated with such models, the effect was interpreted in terms of electrode conduction-electron spin polarizations P i , using a model suggested by Julliere 3 in which the TMR = 2P 1 P 2 /(1 − P 1 P 2 ). A great deal of discussion has focussed on the factors contributing to the quantity 4 P but the use of amorphous oxide as barrier material made impossible a detailed theoretical study with which to confront experiment. 6,7 The situation changed quite drastically with the recent observation of large values of TMR at room temperature in FeCo|MgO|FeCo MTJs in which the MgO tunnel barrier was mono-8,9 or poly-crystalline. 10 This work was motivated in part by the prediction 11,12 by materialsspecific transport calculations of huge TMR values for ideal Fe|MgO|Fe structures. This new development lends fresh urgency to the need to understand the factors governing the sign and magnitude of TMR because the largest observed value of 353% at low temperature, 9 is still well below the ab-initio predicted values of order 10,000% for the relevant thicknesses of MgO. 11 Some effort has been devoted to explaining the discrepancy in terms of interface relaxation 13 or the formation of a layer of FeO at the interface 14,15 but the role of interface disorder has only been speculated upon. 16

The in-plane lattice constants of close-packed planes of fcc and hcp Ni and Co match that of graphite almost perfectly so that they share a common two dimensional reciprocal space. Their electronic structures are such that they overlap in this reciprocal space for one spin direction only allowing us to predict perfect spin filtering for interfaces between graphite and (111) fcc or (0001) hcp Ni or Co. First-principles calculations of the scattering matrix show that the spin filtering is quite insensitive to amounts of interface roughness and disorder which drastically influence the spinfiltering properties of conventional magnetic tunnel junctions or interfaces between transition metals and semiconductors. When a single graphene sheet is adsorbed on these open d-shell transition metal surfaces, its characteristic electronic structure, with topological singularities at the K points in the two dimensional Brillouin zone, is destroyed by the chemical bonding. Because graphene bonds only weakly to Cu which has no states at the Fermi energy at the K point for either spin, the electronic structure of graphene can be restored by dusting Ni or Co with one or a few monolayers of Cu while still preserving the ideal spin injection property.