Caio H. Lewenkopf

Conductance quantization and transport gaps in disordered graphene nanoribbons

We study numerically the effects of edge and bulk disorder on the conductance of graphene nanoribbons. We compute the conductance suppression due to Anderson localization induced by edge scattering and find that even for weak edge roughness, conductance steps are suppressed and transport gaps are induced. These gaps are approximately inversely proportional to the nanoribbon width. On/off conductance ratios grow exponentially with the nanoribbon length. Our results impose severe limitations to the use of graphene in ballistic nanowires.

The recursive Green's function method for graphene

We describe how to apply the recursive Green’s function method to the computation of electronic transport properties of graphene sheets and nanoribbons in the linear response regime. This method allows for an amenable inclusion of several disorder mechanisms at the microscopic level, as well as inhomogeneous gating, finite temperature, and, to some extend, dephasing. We present algorithms for computing the conductance, density of states, and current densities for armchair and zigzag atomic edge alignments. Several numerical results are presented to illustrate the usefulness of the method.

Numerical studies of conductivity and Fano factor in disordered graphene

Using the recursive Greens function method, we study the problem of electron transport in a disordered single-layer graphene sheet. The conductivity is of order

Quantum transport through ballistic cavities: soft vs. hard quantum chaos

{e}^{2}∕h

Measuring the Lyapunov exponent using quantum mechanics.

and its dependence on the carrier density has a scaling form that is controlled solely by the disorder strength and the ratio between the sample size and the correlation length of the disorder potential. The shot noise Fano factor is shown to be nearly density independent for sufficiently strong disorder, with a narrow structure appearing at the neutrality point only for weakly disordered samples. Our results are in good agreement with experiments and provide a way for extracting microscopic information about the magnitude of extrinsic disorder in graphene.

Universal transport properties of open microwave cavities with and without time-reversal symmetry

We study transport through a two-dimensional billiard attached to two infinite leads by numerically calculating the Landauer conductance and the Wigner time delay. In the generic case of a mixed phase space we find a power-law distribution of resonance widths and a power-law dependence of conductance increments apparently reflecting the classical dwell time exponent, in striking difference to the case of a fully chaotic phase space. Surprisingly, these power laws appear on energy scales below the mean level spacing, in contrast to semiclassical expectations.

A tight-binding model for MoS2 monolayers

We study the time evolution of two wave packets prepared at the same initial state, but evolving under slightly different Hamiltonians. For chaotic systems, we determine the circumstances that lead to an exponential decay with time of the wave packet overlap function. We show that for sufficiently weak perturbations, the exponential decay follows a Fermi golden rule, while by making the difference between the two Hamiltonians larger, the characteristic exponential decay time becomes the Lyapunov exponent of the classical system. We illustrate our theoretical findings by investigating numerically the overlap decay function of a two-dimensional dynamical system.

Semiclassical magnetotransport in graphene n-p junctions

We measure the transmission through asymmetric and reflection-symmetric chaotic microwave cavities in dependence on the number of attached waveguides. Ferrite cylinders are placed inside the cavities to break time-reversal symmetry. The phase-breaking properties of the ferrite and its range of applicability are discussed in detail. We use the random matrix theory accounting for absorption effects to calculate the universal distribution of transmission coefficients T and their energy derivatives dT/depsilon. Using the absorption strength as a fitting parameter, we find good agreement between universal transmission fluctuations predicted by the theory and the experimental data.

STATISTICAL DISTRIBUTIONS OF LEVEL WIDTHS AND CONDUCTANCE PEAKS IN IRREGULARLY SHAPED QUANTUM DOTS

We propose an accurate tight-binding parametrization for the band structure of MoS2 monolayers near the main energy gap. We introduce a generic and straightforward derivation for the band energies equations that could be employed for other monolayer dichalcogenides. A parametrization that includes spin-orbit coupling is also provided. The proposed set of model parameters reproduce both the correct orbital compositions and location of valence and conductance band in comparison with ab initio calculations. The model gives a suitable starting point for realistic large-scale atomistic electronic transport calculations.

Collective electronic excitations and their damping in small alkali clusters

We provide a semiclassical description of the electronic transport through graphene n-p junctions in the quantum Hall regime. This framework is known to experimentally exhibit conductance plateaus whose origin is still not fully understood. In the magnetic regime (E vF B), for a step-like electrostatic potential (abrupt on the scale of the magnetic length), we derive a semiclassical approximation for the conductance in terms of the various snake-like trajectories at the interface of the junction. For a symmetric configuration, the general result can be recovered using a simple scattering approach, providing a transparent analysis of the problem under study. We thoroughly discuss the semiclassical predicted behavior for the conductance and conclude that any approach using fully phase-coherent electrons will hardly account for the experimentally observed plateaus.