Splitting of the Zero-Energy Landau Level and Universal Dissipative Conductivity at Critical Points in Disordered Graphene

We report on robust features of the longitudinal conductivity ($\sigma_{xx}$) of the graphene zero-energy Landau level in presence of disorder and varying magnetic fields. By mixing an Anderson disorder potential with a low density of sublattice impurities, the transition from metallic to insulating states is theoretically explored as a function of Landau-level splitting, using highly efficient real-space methods to compute the Kubo conductivities (both $\sigma_{xx}$ and Hall $\sigma_{xy}$). As long as valley-degeneracy is maintained, the obtained critical conductivity $\sigma_{xx}\simeq 1.4 e^{2}/h$ is robust upon disorder increase (by almost one order of magnitude) and magnetic fields ranging from about 2 to 200 Tesla. When the sublattice symmetry is broken, $\sigma_{xx}$ eventually vanishes at the Dirac point owing to localization effects, whereas the critical conductivities of pseudospin-split states (dictating the width of a $\sigma_{xy}=0$ plateau) change to $\sigma_{xx}\simeq e^{2}/h$, regardless of the splitting strength, superimposed disorder, or magnetic strength. These findings point towards the non dissipative nature of the quantum Hall effect in disordered graphene in presence of Landau level splitting

Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity

We report an order-N approach to compute the Kubo Hall conductivity for disorderd two-dimensional systems reaching tens of millions of orbitals, and realistic values of the applied external magnetic fields (as low as a few Tesla). A time-evolution scheme is employed to evaluate the Hall conductivity $\sigma_{xy}$ using a wavepacket propagation method and a continued fraction expansion for the computation of diagonal and off-diagonal matrix elements of the Green functions. The validity of the method is demonstrated by comparison of results with brute-force diagonalization of the Kubo formula, using (disordered) graphene as system of study. This approach to mesoscopic system sizes is opening an unprecedented perspective for so-called reverse engineering in which the available experimental transport data are used to get a deeper understanding of the microscopic structure of the samples. Besides, this will not only allow addressing subtle issues in terms of resistance standardization of large scale materials (such as wafer scale polycrystalline graphene), but will also enable the discovery of new quantum transport phenomena in complex two-dimensional materials, out of reach with classical methods.Comment: submitted PRB pape

Unconventional Features in the Quantum Hall Regime of Disordered Graphene: Percolating Impurity States and Hall Conductance Quantization

We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy bandgap and Landau level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size and magnetic length, we elucidate the origin of anomalous quantum Hall features as magnetic-field dependent impurity states, which percolate at some critical energies. These findings shed light on unidentified states and quantum transport anomalies reported experimentally.Comment: 7 pages, 7 figures. Accepted in PR

Linear Scaling Approach for Optical Excitations Using Maximally Localized Wannier Functions

We present a theoretical method for calculating optical absorption spectra based on maximally localized Wannier functions, which is suitable for large periodic systems. For this purpose, we calculate the exciton Hamiltonian, which determines the Bethe-Salpeter equation for the macroscopic polarization function and optical absorption characteristics. The Wannier functions are specific to each material and provide a minimal and therefore computationally convenient basis. Furthermore, their strong localization greatly improves the computational performance in two ways: first, the resulting Hamiltonian becomes very sparse and, second, the electron-hole interaction terms can be evaluated efficiently in real space, where large electron-hole distances are handled by a multipole expansion. For the calculation of optical spectra we employ the sparse exciton Hamiltonian in a time-domain approach, which scales linearly with system size. We demonstrate the method for bulk silicon - one of the most frequently studied benchmark systems - and envision calculating optical properties of systems with much larger and more complex unit cells, which are presently computationally prohibitive.Comment: submitted to J. Phys. Mate

Polaron Transport in Organic Crystals: Temperature Tuning of Disorder Effects

We explore polaronic quantum transport in three-dimensional models of disordered organic crystals with strong coupling between electronic and vibrational degrees of freedom. By studying the polaron dynamics in a static disorder environment, temperature dependent mobilities are extracted and found to exhibit different fingerprints depending on the strength of the disorder potential. At low temperatures and for strong enough disorder, coherence effects induce weak localization of polarons. These effects are reduced with increasing temperature (thermal disorder) resulting in mobility increase. However at a transition temperature, phonon-assisted contributions driven by polaron-phonon scattering prevail, provoking a downturn of the mobility. The results provide an alternative scenario to discuss controversial experimental features in molecular crystals

Magnetoresistance in Disordered Graphene: The Role of Pseudospin and Dimensionality Effects Unraveled

We report a theoretical low-field magnetotransport study unveiling the effect of pseudospin in realistic models of weakly disordered graphene-based materials. Using an efficient Kubo computational method, and simulating the effect of charges trapped in the oxide, different magnetoconductance fingerprints are numerically obtained in system sizes as large as 0.3 micronmeter squared, containing tens of millions of carbon atoms. In two-dimensional graphene, a strong valley mixing is found to irreparably yield a positive magnetoconductance (weak localization), whereas crossovers from positive to a negative magnetoconductance (weak antilocalization) are obtained by reducing disorder strength down to the ballistic limit. In sharp contrast, graphene nanoribbons with lateral size as large as 10nm show no sign of weak antilocalization, even for very small disorder strength. Our results rationalize the emergence of a complex phase diagram of magnetoconductance fingerprints, shedding some new light on the microscopical origin of pseudospin effects.Comment: 8 pages, 5 figure

Charge Transport in Organic Crystals

The understanding of charge transport is one of the central goals in the research on semiconducting crystals. For organic crystals this is particularly complicated due to the strength of the electron-phonon interaction which requires the description of a seamless transition between the limiting cases of a coherent band-transport mechanism and incoherent hopping. In this thesis, charge transport phenomena in organic crystals are studied by theoretical means. A theory for charge transport in organic crystals is developed which covers the whole temperature range from low T, where it reproduces an expression from the Boltzmann equation for band transport, via elevated T, where it generalizes Holstein's small-polaron theory to finite bandwidths, up to high T, for which a temperature dependence equal to Marcus' electron-transfer theory is obtained. Thereby, coherent band transport and thermally induced hopping are treated on equal footing while simultaneously treating the electron-phonon interaction non-perturbatively. By avoiding the approximation of narrow polaron bands the theory allows for the description of large and small polarons and serves as a starting point for computational studies. The theoretical description is completed by using ab initio material parameters for the selected crystals under study. These material parameters are taken from density functional theory calculations for durene, naphthalene, and guanine crystals. Besides the analysis of the transport mechanism, special focus is put on the study of the relationship between mobility anisotropy and structure of the crystals. This study is supported by a 3D-visualization method for the transport channels in such crystals which has been derived in this thesis