Download or read book Electron Dynamics in Periodically Strained Graphene written by Md. Tareq Mahmud and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The search for new quantum mechanical phenomena by manipulating the electronic and transport properties of two-dimensional material have become an active research topic in the last decade. Among all the two dimensional materials, graphene got most of the attention due to its fascinating electronic and mechanical properties. Substrates are usually used to support graphene in experiments. The interactions between the substrate and graphene layer result into deformations in the system due to strain. Numerous techniques have already been developed to alter the local density of states and the band structure of graphene. Novel approaches implement engineered substrates to induce specifically targeted strain profiles. Inspired by this technique, we study the evolution of charge distribution with an increasing number of out-of-plane Gaussian deformations. This deformation profile serves as an introduction to model a finite size periodic substrate. We begin with a system of two overlapping deformations and determine the quantitative relations between its geometrical parameters and features in the local density of states. Extending the study to sets of three and four deformations in linear and two-dimensional arrays we observed the emergence of moire0 pattern in charge distributions. These moire0 patterns are more robust for an hexagonal cell composed of seven Gaussian bubbles. A comparison between the induced strain profiles and spatial maps of local density of states at different energies provides evidence of the existence of pseudo-magnetically confined states in the deformed regions. These confined states indicate the possibility of creating quantum dots in graphene via strain modulations. These states exhibit a linear dependence in the energy scaling in contrast to the scaling of pseudo-Landau levels. We further extend these studies to periodic deformation profiles with different periodicity other than the4 graphene lattice, creating a ’superlattice’. This superlattice structure folds the electronic bands and create mini Dirac cones. A pseudo-field configuration which breaks the global inversion symmetry open gaps at the symmetry points of the superlattice. By choosing the deformation parameters carefully one can not only create isolated flat-bands but also manipulate the gaps between them. We study the effects of deformation periodicity in the density of states and the local density of states with different choices of deformation parameters. The nature of the quantum states residing on the flat-bands lead us to identify states localized, from extended states. We find that bands contains this information in terms of a topological invariant known as a Chern number. Modifications on strain profiles may allow to produce phase transitions between trivial and Chern insulators.