As a strictly two-dimensional, two-atom thick crystalline material (the two carbon atoms located at two in-equivalent sites A and B), mono-layer graphene has attracted attention in the scientific and technical community mainly due to its unique electronic properties that result from its crystal structure. The low-energy electronic states that are dispersed linearly near two equivalent high-symmetry points in the Brillouin zone or k-space, K and K' (related by time-reversal symmetry) are gap-less and are chiral meaning left moving electrons and right moving electrons are not the same (this translates to pseudo-spin degrees of freedom has definite projection on the direction of the electron momentum i.e., it matters which sub-lattice A or B the electron resides at a given time). These contribute to interesting physical effects such as observation of room temperature ballistic transport which is independent of carrier concentrations, impurities, weak temperature dependence and half-integer quantum-Hall effect. The bi-layer graphene, in which two layers of graphene are stacked such that only half-of the atoms in the top layer are directly below the atoms of the bottom layer or vice-versa, electronic states are dispersed quadratically (1,2,3,4) (or parabolic shaped ) near  K and K¢ and are again gap-less.

Our research at SWAN is focused on testing the possible use of graphene (both mono- and bi-layers) as a channel material in “beyond CMOS” device by exploiting their unique electronic properties. The theoretical efforts are directed at understanding the structure-property relationship by using density functional theory and tight-binding methods. We observed that weak intrinsic spin-orbit coupling (due to relativistic nature of charge carriers) in mono-layer graphene opens up an insignificant gap (that can be probed only in dilute refrigeration temperature well below 1 K) and this gap is closed by an application of external electric field (due to Rashba spin-orbit coupling competing with intrinsic spin-orbit coupling)[1].

However, the finite size ribbons (which are cut in an armchair and zigzag fashion and are confined along the width direction) do exhibit a finite gap at K. Our unpublished (1,2) work shows that the gaps in both zigzag and arm-chair ribbons vary as a inverse width and a recent report by other authors show effect of ribbons’ length on the gaps as well. Moreover, in zig-zag ribbons, the lone p_z orbitals of the edge carbon atoms give rise to a magnetic order-ferromagnetic along the edges but anti-ferromagnetic across its width (that is not yet experimentally verified).

We observed a gap opening in a bulk bilayer graphene as a function of perpendicular external electric field [2]. We argued, based on, density functional theory and tight-binding Hartree method, that on-site potential difference between the two different sub-lattices (which are not directly above each other), the self-consistent charge screening and charge transfer across the layers are responsible for lifting the degeneracy of the carbon p_z orbitals (coming from A sub-lattice of the bottom layer and B sub-lattice of the top layer at K). We observe a gap of 0.2 eV with the applied bias of 0.4 volts and this gap saturates to 0.3 eV at a bias of 1 V. We proposed a device model (double-gated) with graphene bi-layer as a channel material and suggested that with independent control of the Fermi level by one gate and the charge carrier density by another, one can see the changes in I-V curve as a result of gap opening and closing.  This novel effect was recently verified in a carefully designed experiment [cond-mat/arXiv:0707.2487] by other authors (1,2,3,4)  The biased graphene bi-layers, with front and back gate, would then serve as a “beyond C-MOS” transistor in which the current in the channel is controlled by a gate through gap opening and closing. Much more needed to be done in this direction before bi-layer graphene can be utilized as a channel material.

We are currently investigating the effect of the finite size (width as well as length in both arm-chair and zigzag ribbons) and electric fields on the gap [3]. Our hope is such zero-dimensional ribbons will eventually be used as a channel material in graphene based devices. Many-body corrections to graphene electronic states and therefore correction to the optical gaps are being studied using GW approximation, a many-body perturabation theory, to the electron self-energy [4].

We also investigated [5] the role of substrates on the electronic properties of both mono- and bi-layer graphene. Our work on graphene layers on 4H SiC(0001) (1,2) surface [the surface re-construction was taken to be (√3*√3)R30º instead of  ( 6√3*6√3)R30º) showed that the layer next to the reconstructed surface of SiC is electronically dead meaning it is distorted too much. The layer projected bands shows a gap with no signature of mono-layer graphene electronic structure. The mono- and bi-layer features appear starting with two (1,2) and three layers. Whether SiC remain an academic curiosity or a suitable substrate for graphene electronics is unclear at present. Therefore, we are investigating graphene mono and bi-layers on other substrates such as Si (111) or Ge (111).

All-graphene building blocks (such as a p-n junction, three-terminal device, quantum point contact, quantum dot or Aharanov - Bohm   device structures) are interesting topics of future investigations and work has already begun in this direction.