Sharif Digital Repository

Using tight binding theory the effect of topological ripples on the electronic band structure, density of states (DOS), and Fermi velocity of graphene are studied. The results show that by an increase in the ripple height the graphene Fermi velocity decreases and its DOS increases.- Moreover, we show that an increase in the ripple period causes the graphene band gap and DOS to decrease and its Fermi velocity to increase  

We construct the most generic Hamiltonian of the 8Pmmn structure of a borophene sheet in the presence of spin orbit, as well as background electric and magnetic fields. In addition to spin and valley Hall effects, this structure offers a framework to conveniently manipulate the resulting "tilt" of the Dirac equation by applying appropriate electric fields. Therefore, the tilt can be made space as well as time dependent. The border separating the low-field region with undertilted Dirac fermions from the high-field region with over-tilted Dirac fermions will correspond to a black-hole horizon. In this way, space-time-dependent electric fields can be used to design the metric of the resulting...