Wurm, Jürgen and Richter, Klaus and Adagideli, Inanc (2011) Edge effects in graphene nanostructures: From multiple reflection expansion to density of states. Physical Review B (PRB) 84, 075468.
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We study the influence of different edge types on the electronic density of states of graphene nanostructures. To this end we develop an exact expansion for the single particle Green's function of ballistic graphene structures in terms of multiple reflections from the system boundary, that allows for a natural treatment of edge effects. We first apply this formalism to calculate the average density of states of graphene billiards. While the leading term in the corresponding Weyl expansion is proportional to the billiard area, we find that the contribution that usually scales with the total length of the system boundary differs significantly from what one finds in semiconductor-based, Schrodinger type billiards: The latter term vanishes for armchair and infinite mass edges and is proportional to the zigzag edge length, highlighting the prominent role of zigzag edges in graphene. We then compute analytical expressions for the density of states oscillations and energy levels within a trajectory based semiclassical approach. We derive a Dirac version of Gutzwiller's trace formula for classically chaotic graphene billiards and further obtain semiclassical trace formulae for the density of states oscillations in regular graphene cavities. We find that edge dependent interference of pseudospins in graphene crucially affects the quantum spectrum.
|Date:||12 August 2011|
|Institutions:||Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter|
|Projects:||GRK 1570, Elektronische Eigenschaften von Nanostrukturen auf Kohlenstoff-Basis|
|Research groups and research centres:||Not selected|
|Keywords:||graphene, semiclassical physics, density of states, Green function|
|Subjects:||500 Science > 530 Physics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Partially|
|Deposited On:||27 Apr 2011 07:15|
|Last Modified:||19 Jun 2012 15:21|