5 research outputs found
A Green's function approach to transmission of massless Dirac fermions in graphene through an array of random scatterers
We consider the transmission of massless Dirac fermions through an array of
short range scatterers which are modeled as randomly positioned -
function like potentials along the x-axis. We particularly discuss the
interplay between disorder-induced localization that is the hallmark of a
non-relativistic system and two important properties of such massless Dirac
fermions, namely, complete transmission at normal incidence and periodic
dependence of transmission coefficient on the strength of the barrier that
leads to a periodic resonant transmission. This leads to two different types of
conductance behavior as a function of the system size at the resonant and the
off-resonance strengths of the delta function potential. We explain this
behavior of the conductance in terms of the transmission through a pair of such
barriers using a Green's function based approach. The method helps to
understand such disordered transport in terms of well known optical phenomena
such as Fabry Perot resonances.Comment: 22 double spaced single column pages. 15 .eps figure
Klein tunneling in graphene: optics with massless electrons
This article provides a pedagogical review on Klein tunneling in graphene,
i.e. the peculiar tunneling properties of two-dimensional massless Dirac
electrons. We consider two simple situations in detail: a massless Dirac
electron incident either on a potential step or on a potential barrier and use
elementary quantum wave mechanics to obtain the transmission probability. We
emphasize the connection to related phenomena in optics, such as the
Snell-Descartes law of refraction, total internal reflection, Fabry-P\'erot
resonances, negative refraction index materials (the so called meta-materials),
etc. We also stress that Klein tunneling is not a genuine quantum tunneling
effect as it does not necessarily involve passing through a classically
forbidden region via evanescent waves. A crucial role in Klein tunneling is
played by the conservation of (sublattice) pseudo-spin, which is discussed in
detail. A major consequence is the absence of backscattering at normal
incidence, of which we give a new shorten proof. The current experimental
status is also thoroughly reviewed. The appendix contains the discussion of a
one-dimensional toy model that clearly illustrates the difference in Klein
tunneling between mono- and bi-layer graphene.Comment: short review article, 18 pages, 14 figures; v3: references added,
several figures slightly modifie