Quantum transport in disordered and strain-engineered graphene
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The first part of the present thesis investigates the electronic transport in strain-engineered graphene, which has been proposed as a way to circumvent the problem of an absent bandgap in this material. To that end, we calculate the conductivity, the shot noise and the density of states in the Dirac-Kronig-Penney model, which describes the phase-coherent transport in clean monolayer samples with a one-dimensional periodic modulation of the strain and the electrostatic potential. We find that periodic strains induce large pseudo-gaps and suppress charge transport in the direction of the strain modulation while the effect for periodic electrostatic potentials is weakened by Klein tunnelling. The second part then deals with the transport properties of graphene at charge neutrality when disordered by adatoms or scalar impurities. A scattering theory for the Dirac equation yields an analytic expression for the conductivity given a particular impurity configuration; an averaging over impurity configurations is performed numerically. For strong magnetic fields, the conductivity equals the ballistic value, while for weaker fields, a rich scaling flow is obtained which is governed by fixed points of different symmetry classes. In the absence of a magnetic field, a surprising rise of the conductivity is observed when increasing the density of adatoms that are randomly arranged on sites of the same Bloch-phase.