We report the existence of confined massless fermion states in a graphene quantum well (QW) by means of analytical and numerical calculations. These states show an unusual quasi-linear dependence on the momentum parallel to the QW: their number depends on the wavevector and is constrained by electron-hole conversion in the barrier regions. An essential difference with nonrelativistic electron states is a mixing between free and confined states at the edges of the free-particle continua, demonstrated by the direction-dependent resonant transmission across a potential well.
We demonstrate theoretically that quantum dots in bilayers of graphene can be realized. A position-dependent doping breaks the equivalence between the upper and lower layer and lifts the degeneracy of the positive and negative momentum states of the dot. Numerical results show the simultaneous presence of electron and hole confined states for certain doping profiles and a remarkable angular momentum dependence of the quantum dot spectrum which is in sharp contrast with that for conventional semiconductor quantum dots. We predict that the optical spectrum will consist of a series of non-equidistant peaks.PACS numbers: 71.10. Pm, 81.05.Uw Two-dimensional (2D) carbon crystals, such as singlelayer and bilayer graphene, have been the subject of increasing interest due to the unusual mechanical and electronic properties, which may lead to their use in novel nanoelectronic devices. The relativistic-like properties of carriers in single-layer graphene 1,2,3,4,5 result from the gapless and approximately linear electron spectrum near the Fermi energy at two inequivalent points of the Brillouin zone. The charge carriers in these structures are described as massless relativistic fermions and are governed by the Dirac equation. In contrast, for a symmetric graphene bilayer the spectrum is parabolic at the vicinity of the K points.Among the unusual properties of single-layer graphene is the perfect forward transmission across potential barriers, known as Klein tunneling 6,7 , which is related to the absence of a gap in the carrier spectrum. This effect prevents the electrostatic confinement of charged particles and thus the realization of quantum dots. Recently, alternative strategies have been proposed to confine charged particles by using thin single-layer graphene strips 8,9 or non-uniform magnetic fields 10 . Here we propose a novel approach by considering a bilayer graphene, in which a charge imbalance between the layers gives rise to a gap in the spectrum, that can be used to create potential barriers 11,12 . Such bilayers of graphene can be obtained, e.g., from a graphite crystal by micromechanical cleavage 13 . A recent report described the synthesis of bilayer graphene sheets by graphitization of silicon carbide (SiC) surfaces in which the equivalence of the two graphene layers is broken by their interaction with the SiC substrate as well as by doping one of them with potassium atoms 14 . These recent experimental progresses raise the possibility of introducing a position-dependent modification of the spectrum at the Dirac point by changing the potassium density at different regions of the bilayer graphene sheet or by using microstructured gates. In this letter we propose a position-dependent potassium doping to manipulate the band structure of bilayer graphene in order to create nanometer-scale quantum structures such as quantum dots. Semiconductor quantum dots have been intensively investigated both theoretically and experimentally. Up to now, only quantum dots on graphite 15 have been obtained, with sample thic...
We evaluate the dispersion relation for massless fermions, described by the Dirac equation, and for zero-spin bosons, described by the Klein-Gordon equation, moving in two dimensions and in the presence of a one-dimensional periodic potential. For massless fermions the dispersion relation shows a zero gap for carriers with zero momentum in the direction parallel to the barriers in agreement with the well-known "Klein paradox". Numerical results for the energy spectrum and the density of states are presented. Those for fermions are appropriate to graphene in which carriers behave relativistically with the "light speed" replaced by the Fermi velocity. In addition, we evaluate the transmission through a finite number of barriers for fermions and zero-spin bosons and relate it with that through a superlattice.
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