The magnetoconductivity of a square lattice in a periodically modulated magnetic field

The static magnetoconductivity components σxx and σyy are calculated as a function of magnetic field for a square lattice with period a in a periodically modulated magnetic field (PMMF) with period b. We develop a magneto-transport theory for a periodic magnetic field B1 sin(2πx/b). Our model permits us to predict anomalies, such as the appearance of peaks, arising from the commensurability ratio β=a/b between the period a of the crystal lattice and the period b of the PMMF, which originate from contributions to the conductivity due to the eigenstates whose energies are in the vicinity of the Fermi energy. Numerical results are obtained for the energy eigenvalue spectra as a function of the magnetic field and the energy dispersion.