Role of the trigonal warping on the minimal conductivity of bilayer graphene

Using a reformulated Kubo formula we calculate the zero-energy minimal conductivity of bilayer graphene taking into account the small but finite trigonal warping. We find that the conductivity is independent of the strength of the trigonal warping and it is three times as large as that without trigonal warping, and six times larger than that in single layer graphene. Although the trigonal warping of the dispersion relation around the valleys in the Brillouin zone is effective only for low energy excitations, our result shows that its role cannot be neglected in the zero-energy minimal conductivity.Comment: 4 pages, 1 figur

Crossover from Regular to Chaotic Behavior in the Conductance of Periodic Quantum Chains

The conductance of a waveguide containing finite number of periodically placed identical point-like impurities is investigated. It has been calculated as a function of both the impurity strength and the number of impurities using the Landauer-B\"uttiker formula. In the case of few impurities the conductance is proportional to the number of the open channels $N$ of the empty waveguide and shows a regular staircase like behavior with step heights $\approx 2e^2/h$. For large number of impurities the influence of the band structure of the infinite periodic chain can be observed and the conductance is approximately the number of energy bands (smaller than $N$) times the universal constant $2e^2/h$. This lower value is reached exponentially with increasing number of impurities. As the strength of the impurity is increased the system passes from integrable to quantum-chaotic. The conductance, in units of $2e^2/h$, changes from $N$ corresponding to the empty waveguide to $\sim N/2$ corresponding to chaotic or disordered system. It turnes out, that the conductance can be expressed as $(1-c/2)N$ where the parameter $0<c<1$ measures the chaoticity of the system.Comment: 5 pages Revte

Minimal longitudinal dc conductivity of perfect bilayer graphene

We calculated the minimal longitudinal conductivity in prefect single-layer and bilayer graphene by extending the two methods developed for Dirac fermion gas by A. W. W. Ludwig in Phys. Rev. B 50, 7526 (1994). Using the Kubo formula which was originally applied for spintronic systems we obtain sigma(min)(xx)=(J pi/2)e(2)/h while from the other formula used in the above-mentioned work we find (sigma) over bar (min)(xx)=(4J/pi)e(2)/h, where J=1 for single-layer and J=2 for bilayer graphene. The two universal values are different although they are numerically close to each other. Our two results are in the same order of magnitude as that of experiments and for the single-layer case one of our results agrees with many earlier theoretical predictions. However, for bilayer graphene only two studies are known with predictions for the minimal conductivity different from our calculated values. Similarly to the single-layer case, the physical origin of the minimal conductivity in bilayer graphene is also rooted back to the intrinsic disorder induced by the Zitterbewegung which is related to the trembling motion of the electron

Spectral Determinant Method for Interacting N-body Systems Including Impurities

A general expression for the Green's function of a system of $N$ particles (bosons/fermions) interacting by contact potentials, including impurities with Dirac-delta type potentials is derived. In one dimension for $N>2$ bosons from our {\it spectral determinant method} the numerically calculated energy levels agree very well with those obtained from the exact Bethe ansatz solutions while they are an order of magnitude more accurate than those found by direct diagonalization. For N=2 bosons the agreement is shown analytically. In the case of N=2 interacting bosons and one impurity, the energy levels are calculated numerically from the spectral determinant of the system. The spectral determinant method is applied to an interacting fermion system including an impurity to calculate the persistent current at the presence of magnetic field.Comment: revtex, 19 pages, 4 figure

Chiral currents in gold nanotubes

Results are presented for the electron current in gold chiral nanotubes (AuNTs). Starting from the band structure of (4,3) and (5,3) AuNTs, we find that the magnitude of the chiral currents are greater than those found in carbon nanotubes. We also calculate the associated magnetic flux inside the tubes and find this to be higher than the case of carbon nanotubes. Although (4,3) and (5,3) AuNTs carry transverse momenta of similar magnitudes, the low-bias magnetic flux carried by the former is far greater than that carried by the latter. This arises because the low-bias longitudinal current carried by a (4,3) AuNT is significantly smaller than that of a (5,3) AuNT.Comment: 5 pages, 6 figure

Diffraction in the semiclassical description of mesoscopic devices

In pseudo integrable systems diffractive scattering caused by wedges and impurities can be described within the framework of Geometric Theory of Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory of Diffraction (POTD). We derive formulas expressing the reflection and transition matrix elements for one and many diffractive points and apply it for impurity and wedge diffraction. Diffraction can cause backscattering in situations, where usual semiclassical backscattering is absent causing an erodation of ideal conductance steps. The length of diffractive periodic orbits and diffractive loops can be detected in the power spectrum of the reflection matrix elements. The tail of the power spectrum shows $\sim 1/l^{1/2}$ decay due to impurity scattering and $\sim 1/l^{3/2}$ decay due to wedge scattering. We think this is a universal sign of the presence of diffractive scattering in pseudo integrable waveguides.Comment: 18 pages, Latex , ep

Oscillating chiral currents in nanotubes: a route to nanoscale magnetic test tubes

With a view to optimising the design of carbon-nanotube (CNT) windmills and to maximising the internal magnetic field generated by chiral currents, we present analytical results for the group velocity components of an electron flux through chiral carbon nanotubes. Chiral currents are shown to exhibit a rich behaviour and can even change sign and oscillate as the energy of the electrons is increased. We find that the transverse velocity and associated angular momentum of electrons is a maximum for non-metallic CNTs with a chiral angle of 18$^o$. Such CNTs are therefore the optimal choice for CNT windmills and also generate the largest internal magnetic field for a given longitudinal current. For a longitudinal current of order $10^{-4}$ amps, this field can be of order $10^{-1}$Teslas, which is sufficient to produce interesting spintronic effects and a significant contribution to the self inductance.Comment: 4 pages, 1 figur