  We discuss the ground state properties of matter in outer and inner crusts of
neutron stars under the influence of strong magnetic fields. In particular, we
demonstrate the effects of Landau quantization of electrons on compositions of
neutron star crusts. First we revisit the sequence of nuclei and the equation
of state of the outer crust adopting the Baym, Pethick and Sutherland (BPS)
model in the presence of strong magnetic fields and most recent versions of the
theoretical and experimental nuclear mass tables. Next we deal with nuclei in
the inner crust. Nuclei which are arranged in a lattice, are immersed in a
nucleonic gas as well as a uniform background of electrons in the inner crust.
The Wigner-Seitz approximation is adopted in this calculation and each lattice
volume is replaced by a spherical cell. The coexistence of two phases of
nuclear matter - liquid and gas, is considered in this case. We obtain the
equilibrium nucleus corresponding to each baryon density by minimizing the free
energy of the cell. We perform this calculation using Skyrme nucleon-nucleon
interaction with different parameter sets. We find nuclei with larger mass and
charge numbers in the inner crust in the presence of strong magnetic fields
than those of the zero field case for all nucleon-nucleon interactions
considered here. However, SLy4 interaction has dramatic effects on the proton
fraction as well as masses and charges of nuclei. This may be attributed to the
behaviour of symmetry energy with density in the sub-saturation density regime.
Further we discuss the implications of our results to shear mode oscillations
of magnetars.
