Session W5: Focus Session: Graphene: Transport and Optical Phenomena: Nanostructures

Large Scale Mesoscopic Transport in Nanostructured Graphene

We report the observation of strong 2D Anderson localization at the charge neutrality point (CNP) in nanostructured antidot graphene samples. A localization length of 2 micron is obtained through sample size scaling up to 10 micron. Localization length is seen to increase with applied magnetic field, in accurate agreement with the theoretical prediction of Ono [Prog. Theor. Phys. Suppl. 84, 138 (1985)]. Our observation is made possible by the very large dephasing length of 10 micon, owing to the opening of a Coulomb quasigap, observable below 25 K, that suppresses the inelastic electron-electron scatterings. Such a large dephasing length is further substantiated by the observation of a crossover from the mesoscopic transport (with exponential size scaling) to diffusive transport (with size independence) at 10 micron. Large scale mesoscopic transport may provide promising future to graphene nanoelectronic device applications.   

Ballistic transport in nanometer-scale suspended graphene

We study electron transport in suspended ultra-short graphene transistors. We fabricate narrow bowtie gold junctions on exfoliated graphene, and use oxygen plasma to etch away the graphene crystal except under the gold junctions. We then use a wet etch to remove the SiO$_{2}$ under the junctions and suspend the devices. Finally, we use a feedback-control electromigration procedure to break the gold junctions and expose sections of graphene which are $\sim$100 nm wide, and as short as $\sim$10 nm. Using low-temperature electron transport, we observe Fabry-Perot oscillations in the conductivity as a function of charge density, as expected for ballistic transport. The conductivity is asymmetric for electron and hole gate-doping, signaling charge doping from the gold contacts and the formation of p-n junctions. At temperatures below $\approx$ 1 Kelvin, a very strong hysteresis is observed in the gate-dependence of conductivity. We study these devices as a function of charge density, temperature, magnetic field and aspect ratio.   

The Effects of the Mean-Field Interaction on the Anderson Localization of Graphene Nanoribbons

A generalized tight-binding (TB) model,\footnote{Hancock {\em et al.} PRB {\textbf 81}, 245402 (2010).} which includes a mean-field Hubbard-{\em U} and up to 3rd nearest-neighbor hopping terms, is applied to edge-disordered zigzag graphene nanoribbons in order to study spin-transport within the Landauer-B\"utticker formalism. Edge-disorder is modeled by random perturbation of the on-site energy in the range $-E..E$ on all edge atoms, and the resulting Anderson localization lengths determined. We compared the Anderson localization lengths and spin-transport features obtained from the generalized model, an extended TB model (non-interacting) and the simplified TB model (1st nearest neighbor hopping only). Within the range $\pm E=$0.5~eV the Anderson localization length for a single spin was found to decrease by 86.4\% with the introduction of the Hubbard-$U$ in the generalized model compared to the non-interacting models, whereas the opposite spin remained unchanged across all model types. For the range $\pm E=$2.0~eV the Anderson localization length for both spin types decreased by 71.4\% and 76.2\% in the generalized model when compared to the extended TB model, and 76.5\% and 80.4\% when compared to the simplified TB model.   

Graphene-based spaser

We propose graphene-based surface plasmon amplification by stimulated emission of radiation (spaser) formed in the graphene nanoribbon located near a semiconductor quantum dot (QD). The population inversion of the two electron levels of the QD can be achieved by applying external electric current or laser pumping. If the frequency of the dipole plasmon resonance in a graphene nanoribbon comes in the resonance with the transition frequency for the QD, it is possible to excite plasmons and generate the coherent surface plasmon states in the graphene nanoribbon. Therefore, the oscillating dipole in the QD excites coherent surface plasmons in the graphene nanoribbon. By solving the system of equations for the number of coherent localized plasmons in a graphene-based spaser the optimal design, optimal width of graphene nanoribbon and optimal regime for the graphene-based spaser are found. The minimal size and minimal threshold pumping intensity for the graphene-based spaser are obtained. The advantage of using graphene for the spaser is discussed.   

Shearing graphene and its transmission properties

Graphene being the thinnest possible membrane is prone to deformations under slight external forcing or even under thermal fluctuations. Here, we take advantage of this proneness to deformations to manipulate transport properties of graphene ribbons. We do so by using the spontaneous pattern produced when a wide ribbon is subject to shear. The deformation of the ribbon produces pseudo-magnetic fields as well as scalar potentials, resulting in the modification of transmission properties without the need of an external gate potential. Our proposal is a concrete realization of a quantum device that takes full advantage of an elastic instability that spans from the nano to macro-scales.   

Optical Properties of Graphene Nanoribbons

The electrical transport properties of graphene nanoribbons have been extensively studied. However, the experimental investigation of the optical properties is still lacking. In this paper, we present the infrared (IR) absorption measurement of graphene nanoribbons with width down to 50 nm. The optical response is dominated by plasmonic resonances in the mid-IR when the incident light polarization is perpendicular to the ribbon axis. By varying the width of the ribbons, we were able to determine the plasmon dispersion in graphene. Meanwhile, we revealed the important role of surface polar phonons and graphene intrinsic optical phonons in the plasmon dispersion and damping. In conjunction with theoretical analysis, we found that graphene plasmons are severely damped through the emission of an optical phonon together with an intraband electron-hole pair. Our study paves the way for graphene applications in infrared photonics and opto-electronics.   

The role of the disorder range and electronic energy in the graphene nanoribbons perfect transmission

Numerical calculations based on the recursive Green's function method in the tight-binding approximation are performed to calculate the dimensionless conductance g in disordered graphene nanoribbons with Gaussian scatterers. The influence of the transition from short- to long-ranged disorder on g is studied as well as its effects on the formation of a perfectly conducting channel. We also investigate the dependence of electronic energy on the perfectly conducting channel. We propose and calculate a backscattering estimate in order to establish the connection between the perfectly conducting channel (with g = 1) and the amount of intervalley scattering.   

First-principles calculation of the heat transport properties of strained graphene nanoribbons

We use density-functional theory coupled with a nonequilibrium Green function's method to calculate the characteristics of ballistic thermal transport (P.S.E. Yeo, K.P. Loh, and C.K.Gan, Nanotechnology, 2012, accepted and to appear) of tensile-strained armchair (AGNR) and zigzag (ZGNR) edge graphene nanoribbons, with widths between $3$ and $50$~\AA. The optimized lateral lattice constants for AGNRs of different widths display a three-family behavior when the ribbons are arranged according to $N$ modulo 3, where $N$ represents the number of carbon atoms across the width of the ribbon. Two lowest-frequency out-of-plane acoustic modes play an important role in increasing the thermal conductance of AGNR-$N$ at low temperatures. At high temperatures the effect of tensile strain is to reduce the thermal conductance of AGNR-$N$ and ZGNR-$N$. These results could be explained by the changes in force constants in the in-plane and out-of-plane directions when strain is applied. This fundamental atomistic understanding of the heat transport in graphene nanoribbons suggests a route to controlling heat transport properties via strain at various temperatures.   

Optical selection rules in graphene quantum dots

We theoretically study the optical absorption of graphene quantum dots for different shapes, sizes and edge types. We calculate the single particle energy spectrum using the tight-binding Hamiltonian and the Dirac-Weyl equation and show that dots with zigzag edges exhibit a degenerate shell of zero energy states, in agreement with previous results. Using standard group theoretical tools, we obtain the optical selection rules for triangular and hexagonal quantum dots and discuss the role of light polarization on the absorption spectrum. Finally, we calculate the oscillator strengths and absorption spectra for different quantum dot sizes and identify the contribution of the zero energy states therein.   

Immense Weak Localization Effect in CVD Graphene

In this study, we report magnetoresistance (MR) measurements on graphene grown by chemical vapor deposition (CVD) on copper. CVD graphene is transferred onto SiO$_{2}$/Si substrate and Hall bar devices with Au/Ti contacts are fabricated by photo-lithography. Measurements show that the diagonal resistance R$_{xx}$ varies logarithmically vs. temperature and magnetic field, as expected for weak localization. The interesting aspect here in CVD graphene is that weak localization effect is immense compared to the typical observation in dirty metals. At zero magnetic field, R$_{xx}$ increased by about 7$\%$ with decreasing temperature from 110 K to 1.5 K. From the observed weak localization, we extract characteristics lifetimes and length scales, and compare the results with theoretical expections [1], and other weak localization work on CVD graphene [2,3].\\[4pt] [1] McCann, E. et al. Phys. Rev. Lett. 97, 2006, 146805.\\[0pt] [2] Miao, Z. et al. J. Phys.: Condens. Matter 24, 2012, 475304.\\[0pt] [3] Wang, W. et al. Carbon, 2012.   

Conductance Fluctuation and Superconducting-to-Normal State Switching Measurements of Superconducting Graphene Devices

We report on gate voltage dependent conductance fluctuations (CF) in superconducting graphene devices and compare measurements in the superconducting versus normal state at temperatures down to 20 mK. The CF arise from the averaged interference of charge carrier wave functions caused by scattering in the graphene. An enhancement in the magnitude of the average CF is expected when in the superconducting state due to Andreev reflections. We fabricate devices by contacting graphene with two parallel superconducting leads that are spaced a few hundred nanometers apart. The leads are a Pd/Al or Ti/Al bilayer with the thin Pd or Ti layer providing high transparency contact to graphene. Additionally, we report on our ongoing superconducting-to-normal state switching measurements in graphene Josephson junctions. The distribution of the stochastic switching current gives insight into the dynamics of the junction such as the phase particle escape mechanisms and dissipation processes. The use of graphene as the weak link allows novel control of the critical current, and thus the dynamics of the junction. By gathering switching data, we can study the modified Josephson washboard potential in these devices (J. G. Lambert, et al., IEEE Trans. in Appl. Supercond. 21, 734 (2011)).   

Conductance fluctuation and dimensional crossover in hydrogenated graphene systems

The conductance of mesoscopic disordered systems in the localized transport regime exhibits extremely large sample-to-sample fluctuations. Thus, their transport properties must be understood in terms of the conductance distribution function. Although the distribution functions show distinctive behavior depending on the dimension of system, previous studies have been mainly focused on one, two, and three dimensional systems individually. Here, we investigate the dimensional transition from two-dimensional (2D) graphene to quasi-one-dimensional (Q1D) graphene nanoribbons and discuss the effect of the dimensional crossover on the conductance fluctuation. As a model system, we consider hydrogenated graphene systems which have attracted much attention due to the observation of a metal-insulator transition. Adopting two different strategies to examine the crossover behavior of conductance between Q1D and 2D systems, we find that a transition from 2D to Q1D is attainable by reducing the sample width, while it is not possible by increasing the length of the 2D system. Our results provide fundamental insights into the dimensionality change not only in graphene, but also in general mesoscopic systems in the localized regime.   

Impurity state and variable range hopping conduction in graphene

The variable range hopping (VRH) theory is widely accepted as explaining the temperature dependence of the conductivity of doped semiconductors. However, as formulated for exponentially localized impurity states, it does not necessarily apply in the case of graphene with covalently attached impurities. We analyze the localization of impurity states in graphene using the nearest neighbor tight-binding model of an adatom-graphene system with Green's function perturbation methods. The impurity states in graphene are characterized as resonant states in the band continuum and both low energy approximations and numerical evaluation of the Green's functions indicate that the amplitude of the wave function decays as a power law with exponents depending on sublattice, direction, and the impurity species. We revisit the VRH theory in view of this result and find that considering only the overlap and energy difference of the impurity states, the conductivity obeys a power law of the temperature with an exponent related to the localization of the wave function. Other factors that were ignored in the original VRH are included due to the weaker temperature dependence, which contribute an additional exponent. We show that this relationship is in agreement with available experimental results.   

Gate-tuned two-channel Kondo screening in Graphene: Universal scaling of the nonlinear conductance

We study the nonlinear conductance through magnetic adatoms on Graphene. In particular, we address the finite-temperature crossover from a quantum critical to the two-channel Kondo regime expected to occur in doped Graphene. Based on the non-crossing approximation, We calculate both the linear and nonlinear conductance within the two-lead single-impurity Anderson model where the conduction electron density of states vanishes in a power-law fashion $ \propto |\omega-\mu_F|^r$ with $r=1$ near the Fermi energy, appropriately for Graphene. For given gate voltage, we study the universal crossover from a 2-channel Kondo (2CK) phase to a un-screened local momemt (LM) phase. We extract universal scaling functions governing charge transport through the adatom and discuss our results in the context of a recent scanning tunneling spectroscopy (STM) experiment on Co-doped Graphene.