Session Q1: Ballistic Charge and Spin Transport in Graphene

Electronic spin transport and spin precession in single graphene layers at room temperature.

I will give a review of our experiments on spin injection, spin transport and spin precession in field effect transistors based on single graphene layers. We have employed a four terminal non-local measurement technique which allows us to fully separate the electronic charge and spin circuits. One pair of ferromagnetic electrodes is used as spin injectors, the other pair as spin detectors. By using different widths for the ferromagnetic electrodes we are able to control the coercive fields and prepare the magnetization direction of each with an applied magnetic field (in positive or negative x-direction). We observe clear signals due to spin diffusion from injector to detector electrodes. From the dependence of the spin signals on electrode spacing we obtain a spin relaxation length of 1.5 to 2 micrometer, and a corresponding spin relaxation time of about 100 ps [1]. These measurements are confirmed by Hanle-type spin precession measurements where the injected spins precess around a magnetic field applied perpendicular to the graphene plane. The spin signals only weakly depend on temperature (between 4.2 K and 300K), and also change little when the gate voltage is tuned from the metallic electron/hole regimes to the Dirac neutrality point. Recent experiments show that the spin relaxation times/lengths are similar for spin directions pointing in the graphene plane and perpendicular to the graphene plane [2]. Also the presence of an Al$_2$O$_3$ layer on top of the graphene does not significantly change the spin relaxation length and time. I will discuss these results in the light of existing theories for spin-orbit interaction in graphene. The implications for graphene spintronics and graphene qubits will be discussed. \newline \newline [1] N. Tombros, C. Jozsa, M. Popinciuc, H.T. Jonkman, and B.J. van Wees, Nature 448, 571 (2007) \newline [2] N. Tombros et al.,submitted to Phys. Rev. lett. \newline [3] M. Popinciuc et al., submitted to Phys. Rev. B. \newline [4] C. Jozs et al., submitted to Phys. Rev. Lett.   

Phase coherent transport in graphene

The investigation of transport phenomena originating from quantum interference of electronic waves has proven to be a very effective probe of the electronic properties of conducting materials. Recent work has shown that this is also the case for graphene, a novel material consisting of an individual layer of carbon atoms, in which the electron dynamics is governed by the Dirac equation. After introducing the peculiar aspect of the low-energy electronic properties of graphene that are important to understand quantum interference in this material, I will present our experimental work. I will first discuss our study of Aharonov-Bohm conductance oscillations in graphene ring-shaped devices -which demonstrates directly the phase coherent nature of transport in graphene-, and emphasize an unusual dependence of the oscillation amplitude on the device conductance. Next I will touch upon the anomalous behavior of weak-localization observed in the experiments and compare it with our observations of supercurrent and superconducting proximity effect in graphene Josephson junctions. I will conclude by discussing the relevance of the two valleys in graphene for the understanding of quantum interference in this material.   

Phase Coherent Charge Transport in Graphene Quantum Billiards

As an emergent model system for condensed matter physics and a promising electronic material, graphene's electrical transport properties has become a subject of intense focus. Via low temperature transport spectroscopy on single and bi-layer graphene devices, we show that the minimum conductivity value is geometry dependent and approaches the theoretical value of $4e^{2}/\pi h$ only for wide and short graphene strips. Moreover, we observe periodic conductance oscillations with bias and gate voltages, arising from quantum interference of multiply-reflected waves of charges in graphene. When graphene is coupled to superconducting electrodes, we observe gate tunable supercurrent and sub-gap structures, which originate from multiple Andreev reflection at the graphene-superconductor interfaces. Our results demonstrate that graphene can act as a quantum billiard with a long phase coherence length. \textit{This work was supported in part by DOD/DMEA-H94003-06-2-0608}.   

Ballistic Transport in Graphene.

Charge transport in ballistic graphene-based microstructures is described within the scattering formalism, which takes into account evanescent modes induced by metallic contacts. We discuss in detail new theoretical predictions for the charge transport and shot noise in the models which include local potential inhomogeneities, next to the nearest neighbor coupling, or ripples in the graphene plane.