One-dimensional electron systems on graphene edges

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Title: One-dimensional electron systems on graphene edges
Author: Hill, Jason Edward, 1978-
Abstract: In this dissertation several aspects on one -dimensional edge states in grapheme are studied . First , a background in the history and development of graphitic forms is presented . Then some novel features found in two -dimensional bulk graphene are presented . Here , some focus is given to the chiral nature of the Dirac equation and the symmetries found in the grahene . Magnetism and interactions in graphene is also briefly discussed . Finally , the graphene nanoribbon with its two typical edges : armchair and zigzag is introduced . Gaps due to finite -size effects are studied . Next , the problem of determining the zigzag ground state is presented . Later , we develop this in an attempt to add the Coulomb interaction to the zigzag flat -band states . These nanoribbons can be stimulated with a tight -binding code on a lattice model in which many different effects can be added , including an A /B sublattice asymmetry , spin -orbit coupling and external fields . The lowest Landau level solutions in the different ribbon orientations is of particular current interest . This is done in the context of understanding new physics and developing novel applications of graphene nanoribbon devices . Adding spin -orbit to a graphene ribbon Hamiltonian leads to current carrying electronic states localized on the sample edges . These states can appear on both zigzag and armchair edges in the semi -finite limit and differ qualitatively in dispersion and spin -polarization from the well known zigzag edge states that occur in models that do not include spin -orbit coupling . We investigate the properties of these states both analytically and numerically using lattice and continuum models with intrinsic and Rashba spin -orbit coupling and spin -independent gap producing terms . A brief discussion of the Berry curvature and topological numbers of graphene with spin -orbit coupling also follows .
URI: http : / /hdl .handle .net /2152 /3797
Date: 2008-08-29


One-dimensional electron systems on graphene edges. Doctoral dissertation, The University of Texas at Austin. Available electronically from http : / /hdl .handle .net /2152 /3797 .

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