We study the effect of disordered ripples on the conductivity of monolayer graphene flakes. We calculate the relaxation times and the Boltzmann conductivities associated with two mechanisms. First, we study the conductivity correction due to an external in-plane magnetic field B . Due to the irregular local curvature found at graphene sheets deposited over a substrate, B can be mapped into an effective random magnetic field perpendicular to the graphene surface. Second, we study the electron momentum relaxation due to intrinsic pseudo magnetic fields originated from deformations and strain. We find that the competition between these mechanisms gives rise to a strong anisotropy in the conductivity tensor. This result provides a new strategy to quantitatively infer the strength of pseudo-magnetic fields in rippled graphene flakes.

We study the electronic structure and transport properties of zigzag and armchair monolayer molybdenum disulfide nanoribbons using an 11-band tight-binding model that accurately reproduces the material's bulk band structure near the band gap. We study the electronic properties of pristine zigzag and armchair nanoribbons, paying particular attention to the edges states that appear within the MoS2 bulk gap. By analyzing both their orbital composition and their local density of states, we find that in zigzag-terminated nanoribbons these states can be localized at a single edge for certain energies independent of the nanoribbon width. We also study the effects of disorder in these systems using the recursive Green's function technique. We show that for the zigzag nanoribbons, the conductance due to the edge states is strongly suppressed by short-range disorder such as vacancies. In contrast, the local density of states still shows edge localization. We also show that long-range disorder has a small effect on the transport properties of nanoribbons within the bulk gap energy window.

We present a multiprobe recursive Green's function method to compute the transport properties of mesoscopic systems using the Landauer-Büttiker approach. By introducing an adaptive partition scheme, we map the multiprobe problem into the standard two-probe recursive Green's function method. We apply the method to compute the longitudinal and Hall resistances of a disordered graphene sample, a system of current interest. We show that the performance and accuracy of our method compares very well with other state-of-the-art schemes.

Previous works on deformed graphene predict the existence of valley-polarized states, however, optimal conditions for their detection remain challenging. We show that in the quantum Hall regime, edge-like states in strained regions can be isolated in energy within Landau gaps. We identify precise conditions for new conducting edges-like states to be valley polarized, with the flexibility of positioning them at chosen locations in the system. A map of local density of states as a function of energy and position reveals a unique braid pattern that serves as a fingerprint to identify valley polarization.Strained graphene has emerged as an important tool to implement valleytronic based devices, and in particular, in protocols for quantum computation [1][2][3][4][5][6][7][8][9][10][11][12]. Recent experimental developments show that substrate engineering can be used to design deformation geometries with specific strain profiles [13][14][15][16][17][18][19][20][21][22][23]. Clear signatures of valley splitting in confined geometries represent an important step in this direction, as exemplified by STM studies on graphene quantum dots [24]. In more extended configurations, similar observations have been reported on multiple fold structures [18,19] with preliminary evidence of valley polarized states. These studies are supported by previous work on extended deformations predicting valley polarized edge-like states at the strain region, which acts as a waveguide focusing electron currents [1][2][3][4][5]. These are all promising structures for potential device applications. However, several drawbacks are still present because optimal conditions for creation and detection of valley split currents are not well-defined.To take advantage of the existence of valley polarized channels, usually embedded in graphene's conducting background, it is crucial to separate their contribution from other extended states. We show that this can be achieved by introducing an external magnetic field large enough to take the system into the Quantum Hall regime. Such a configuration conveniently allows the isolation of the valley polarized edge states in energy and in real space. As we show below, it is possible to design configurations within available experimental capabilities to produce valley polarized currents for a wide energy range within Landau gaps. Moreover, the flexibility to place the deformation at different parts of the sample provides a wider versatility of contact probes to identify and collect these currents.We present local density of states (LDOS) results for a model of graphene with a fold-like deformation that predict valley split peaks that could be measured in STM experiments. As the deformed region is traversed across, maximum LDOS intensities for each valley evolve in en-ergy, leading to a braid structure that serves as a unique fingerprint of valley polarized states. Under bias, these states generate new extra conducting channels that can be visualized as new edge states created along the deformation region.In order to ...