We explore the possibility of coupling between planar strain and perpendicular magnetic field on electronic bandstructure of graphene. We study uni-axially, bi-axially and shear strained graphene under magnetic field. In line with Rammal’s formalism using nearest neighbor tight binding scheme we construct the Hamiltonian of the lattice. We examine the modification of electronic bandstructure under the coupled of strain and magnetic field with aid of Hofstadter-Rammal spectrums. It is found that a tiny strain in zigzag graphene under magnetic field can generate energy band gap. The band gap magnitude is found to increase with increase in strain. Also zero modes are found to exist only when certain cutoff of magnetic field is crossed for a given strain in zigzag graphene. The rationality of magnetic field is found to play crucial role in determining the existence of energygap or zero mode. We calculate the number of zero modes present over the complete range of rational flux i.e. 0 < φ/φo < 1. Energy gap shows non analytic behavior as a function of low magnetic flux φ for low strain values and when strain is sufficiently large the energy gap begins to behave in an exponential form as a function of weak magnetic flux φ. We further generalize the theory to study the special cases of bi-axially and shear strained graphene under magnetic field. Both the cases were found to be much different from uni-axial cases. New effective parameters were found and their rationality were demanded by the boundedness of the wavefunction. The parameters derived were not only found to depend upon the magnetic flux piercing through the deformed hexagonal lattice but also on the direction and magnitude of bi-axial/shear strain applied.
Chapter2 has been sent for publication and will be published by January 2011 in International Journal of Nanoscience (IJN).