Electronic Transport in Graphene: Quantum Effects and Role of Local Defects

In this paper we present generic properties of quantum transport in mono-layer graphene. In the scheme of the Kubo-Geenwood formula, we compute the square spreading of wave packets of a given energy with is directly related to conductivity. As a first result, we compute analytically the time dependent diffusion for pure graphene. In addition to the semi-classical term a second term exists that is due to matrix elements of the velocity operator between electron and hole bands. This term is related to velocity fluctuations i.e. Zitterbewegung effect. Secondly, we study numerically the quantum diffusion in graphene with simple vacancies and pair of neighboring vacancies (divacancies), that simulate schematically oxidation, hydrogenation and other functionalisations of graphene. We analyze in particular the time dependence of the diffusion and its dependence on energy in relation with the electronic structure. We compute also the mean free path and the semi-classical value of the conductivity as a function of energy in the limit of small concentration of defects.Comment: 10 pages, 5 figure

Influence of static disorder and polaronic band formation on interfacial electron transfer in organic photovoltaic devices

Understanding the interfacial charge-separation mechanism in organic photovoltaics requires, due to its high level of complexity, bridging between chemistry and physics. To elucidate the charge separation mechanism, we present a fully quantum dynamical simulation of a generic one-dimensional Hamiltonian, which physical parameters model prototypical PCBM or $\text{C}_{60}$ acceptor systems. We then provide microscopic evidence of the influence random static and dynamic potentials have on the interfacial charge-injection rate. In particular, we unveil that dynamic potentials, due to strong electron-vibration interactions, can lead to the formation of polaronic bands. Such dynamical potentials, when compared to random static potentials, can provide the main detrimental influence on the efficiency of the process of interfacial charge-separation

Conductivity of graphene with resonant and non-resonant adsorbates

We propose a unified description of transport in graphene with adsorbates that fully takes into account localization effects and loss of electronic coherence due to inelastic processes. We focus in particular on the role of the scattering properties of the adsorbates and analyze in detail cases with resonant or non resonant scattering. For both models we identify several regimes of conduction depending on the value of the Fermi energy. Sufficiently far from the Dirac energy and at sufficiently small concentrations the semi-classical theory can be a good approximation. Near the Dirac energy we identify different quantum regimes, where the conductivity presents universal behaviors.Comment: 6 page

Conductivity of Graphene with Resonant Adsorbates: Beyond the Nearest Neighbor Hopping Model

Adsorbates on graphene can create resonances that lead to efficient electron scattering and strongly affect the electronic conductivity. Therefore a proper description of these resonances is important to get a good insight of their effect on conductivity. The characteristics of the resonance and in particular its T-matrix depend on the adsorbate itself but also on the electronic structure of graphene. Here we show that a proper tight-binding model of graphene which includes hopping beyond the nearest-neighbor lead to sizable modifications of the scattering properties with respect to the mostly used nearest neighbor hopping model. We compare results obtained with hopping beyond the nearest-neighbor to those of our recent work Phys. Rev. Lett. 113, 146601 (2013). We conclude that the universal properties discussed in our recent work are unchanged but that a detailed comparison with experiments require a sufficiently precise tight-binding model of the graphene layer.Comment: 8 pages, 5 figure

Anomalous electronic transport in Quasicrystals and related Complex Metallic Alloys

We analyze the transport properties in approximants of quasicrystals alpha-AlMnSi, 1/1-AlCuFe and for the complex metallic phase lambda-AlMn. These phases presents strong analogies in their local atomic structures and are related to existing quasicrystalline phases. Experimentally they present unusual transport properties with low conductivities and a mix of metallic-like and insulating-like characteristics. We compute the band structure and the quantum diffusion in the perfect structure without disorder and introduce simple approximations that allow to treat the effect of disorder. Our results demonstrate that the standard Bloch-Boltzmann theory is not applicable to these intermetallic phases. Indeed their dispersion relation are flat indicating small band velocities and corrections to quantum diffusion that are not taken into account in the semi-classical Bloch-Boltzmann scheme become dominant. We call this regime the small velocity regime. A simple Relaxation Time Approximation to treat the effect of disorder allows us to reproduce the main experimental facts on conductivity qualitatively and even quantitatively.Comment: 14 page

Phenomenological model for charge dynamics and optical response of disordered systems: application to organic semiconductors

We provide a phenomenological formula which describes the low-frequency optical absorption of charge carriers in disordered systems with localization. This allows to extract, from experimental data on the optical conductivity, the relevant microscopic parameters determining the transport properties, such as the carrier localization length and the elastic and inelastic scattering times. This general formula is tested and applied here to organic semiconductors, where dynamical molecular disorder is known to play a key role in the transport properties. The present treatment captures the basic ideas underlying the recently proposed transient localization scenario for charge transport, extending it from the d.c. mobility to the frequency domain. When applied to existing optical measurements in rubrene FETs, our analysis provides quantitative evidence for the transient localization phenomenon. Possible applications to other disordered electronic systems are briefly discussed.Comment: extended version with optical conductivity formulas for both non-degenerate and degenerate electron system

Quantum transport in quasicrystals and complex metallic alloys

The semi-classical Bloch-Boltzmann theory is at the heart of our understanding of conduction in solids, ranging from metals to semi-conductors. Physical systems that are beyond the range of applicability of this theory are thus of fundamental interest. This is the case of disordered systems which present quantum interferences in the diffusive regime, i.e. Anderson localization effects. It appears that in quasicrystals and related complex metallic alloys another type of breakdown of the semi-classical Bloch-Boltzmann theory operates. This type of quantum transport is related to the specific propagation mode of electrons in these systems. We develop a theory of quantum transport that applies to a normal ballistic law but also to these specific diffusion laws. As we show phenomenological models based on this theory describe correctly the experimental transport properties. Ab-initio calculations performed on approximants confirm also the validity of this anomalous quantum diffusion scheme. Although the present chapter focuses on electrons in quasicrystals and complex metallic alloys, the concept that are developed here can be useful for phonons in these systems. There is also a deep analogy between the type of quantum transport described here and the conduction properties of other systems where charge carriers are also slow, such as some heavy fermions or polaronic systems.Comment: review article. 65 page