3,408 research outputs found
Minimal conductivity and signatures of quantum criticality in ballistic graphene bilayer
We study the ballistic conductivity of graphene bilayer in the presence of
next-nearest neighbor hoppings between the layers. An undoped and unbiased
system was found in Ref. [1] to show a nonuniversal (length-dependent)
conductivity , approaching the value of
for large . Here we demonstrate
one-parameter scaling and determine the scaling function
. The scaling flow has an attractive
fixed point [, ] reproducing
the scenario predicted for random impurity scattering of Dirac fermions with
Coulomb repulsion, albeit the system considered is perfectly ballistic and
interactions are not taken into account. The role of electrostatic bias between
the layers is also briefly discussed.Comment: RevTeX, 5 pages, 4 figure
Magnetoconductance of the Corbino disk in graphene: Chiral tunneling and quantum interference in the bilayer case
Quantum transport through an impurity-free Corbino disk in bilayer graphene
is investigated analytically, by the mode-matching method for effective Dirac
equation, in the presence of uniform magnetic fields. Similarly as in the
monolayer case (see Refs. [1,2]), conductance at the Dirac point shows
oscillations with the flux piercing the disk area characterized by the
period , where () is the outer (inner) disk radius. The oscillations magnitude depends
either on the radii ratio or on the physical disk size, with the condition for
maximal oscillations reading (for ),
where is the interlayer hopping integral, is the Fermi velocity
in graphene, and is an {\em even} integer. {\em Odd}-integer values of
correspond to vanishing oscillations for the normal Corbino setup, or to
oscillations frequency doubling for the Andreev-Corbino setup. At higher Landau
levels (LLs) magnetoconductance behaves almost identically in the monolayer and
bilayer cases. A brief comparison with the Corbino disk in 2DEG is also
provided in order to illustrate the role of chiral tunneling in graphene.Comment: Typos corrected; acknowledgment added. RevTeX, 13 pages, 7 figure
Pseudodiffusive conductance, quantum-limited shot noise, and Landau-level hierarchy in biased graphene bilayer
We discuss, by means of mode-matching analysis for the Dirac equation, how
splittings of the Landau-level (LL) degeneracies associated with spin, valley,
and layer degrees of freedom affect the ballistic conductance of graphene
bilayer. The results show that for wide samples () the
Landauer-B\"{u}ttiker conductance reaches the maximum
at the resonance via each LL, with the
prefactor varying from if all three degeneracies are preserved, to
if all the degeneracies are split. In the absence of bias between the layers,
the degeneracies associated with spin and layer degrees of freedom may be split
by manipulating the doping and magnetic field; the conductance at the zeroth LL
is twice as large, while the conductance at any other LL equals to the
corresponding conductance of graphene monolayer. The presence of bias potential
allows one also to split the valley degeneracy. Our results show that the
charge transfer at each LL has pseudodiffusive character, with the second and
third cumulant quantified by and (respectively).
In case the electrochemical potential is allowed to slowly fluctuate in a
finite vicinity of LL, the resulting charge-transfer characteristics are still
quantum-limited, with and in the
limit of large fluctuations. The above values of and are
also predicted to be approached in the limit of high source-drain voltage
difference applied. The possible effects of indirect interlayer hopping
integrals are also briefly discussed.Comment: Minor revisions, refs. added; new Section V describing the possible
effects of indirect hoppings between the layers. Figure files optimized for
the faster download. RevTeX, 13 pages, 10 figure
Quantum-limited shot noise and quantum interference in graphene based Corbino disk
This is a theoretical study of finite voltage effects on the conductance, the
shot noise power, and the third charge-transfer cumulant for graphene-based
Corbino disk in the presence of external magnetic fields. Periodic
magnetoconductance oscillations, predicted in Refs. [1,2], become invisible for
relatively small source-drain voltages, as the current decays rapidly with
magnetic field. Quantum interference still governs the behavior of higher
charge-transfer cumulants.Comment: Minor revisions, PACS Nos. added. RevTeX, 5 pages, 3 figure
Conditions for Conductance Quantization in Mesoscopic Dirac Systems on the Examples of Graphene Nanoconstrictions
Ballistic transport through an impurity-free section of the Corbino disk in
graphene is investigated by means of the Landauer-B\"{u}ttiker formalism in the
mesoscopic limit. In the linear-responce regime the conductance is quantized in
steps close to integer multiples of , yet Fabry-Perot oscillations
are strongly suppressed. The quantization arises for small opening angles
and large radii ratios . We find that
the condition for emergence of the -th conductance step can be written as
. A brief comparison with the conductance spectra of
graphene nanoribbons with parallel edges is also provided.Comment: Typos corrected. RevTeX, 5 pages, 4 figures. Presented on "XVI
National Conference of Superconductivity", October 7-12, 2013, Zakopane,
Polan
Thermoelectric properties of gapped bilayer graphene
Unlike in conventional semiconductors, both the chemical potential and the
band gap in bilayer graphene (BLG) can be tuned via application of external
electric field. Among numerous device implications, this property also
designates BLG as a candidate for high-performance thermoelectric material. In
this theoretical study we have calculated the Seebeck coefficients for abrupt
interface separating weakly- and heavily-doped areas in BLG, and for a more
realistic rectangular sample of mesoscopic size, contacted by two electrodes.
For a given band gap () and temperature () the maximal Seebeck
coefficient is close to the Goldsmid-Sharp value , the deviations can be approximated by the asymptotic
expression , with the electron charge , the Boltzmann constant
, and . Surprisingly, the effects of trigonal
warping term in the BLG low-energy Hamiltonian are clearly visible at
few-Kelvin temperatures, for all accessible values of
meV. We also show that thermoelectric figure of merit
is noticeably enhanced () when a rigid substrate suppresses out-of-plane
vibrations, reducing the contribution from phonons to the thermal
conductivity.Comment: Minor revisions; notation clarified, a comment effective doping
added. RevTeX; 9 pages; 5 figure
Lifshitz transition and thermoelectric properties of bilayer graphene
This is a numerical study of thermoelectric properties of ballistic bilayer
graphene in the presence of trigonal warping term in the effective Hamiltonian.
We find, in the mesoscopic samples of the length m at sub-Kelvin
temperatures, that both the Seebeck coefficient and the Lorentz number show
anomalies (the additional maximum and minimum, respectively) when the
electrochemical potential is close to the Lifshitz energy, which can be
attributed to the presence of the van Hove singularity in a bulk density of
states. At higher temperatures the anomalies vanish, but measurable quantities
characterizing remaining maximum of the Seebeck coefficient still unveil the
presence of massless Dirac fermions and make it possible to determine the
trigonal warping strength. Behavior of the thermoelectric figure of merit
() is also discussed.Comment: Typos corrected. RevTeX, 11 pages, 8 figure
- …