Two-dimensional electrons in periodic magnetic fields: Finite-differences method study

Abstract

Using the finite-differences method, the electronic structures of two-dimensional electrons are investigated under a periodic magnetic field. To achieve accuracy, the exact profile of the magnetic field is employed in the numerical calculations. The results show that the system exhibits rich band structures, and the width of sub-bands becomes narrower as |ky| increases. In particular, many bound states are formed in the potential wells, and they are localized. Localization analysis confirms that extended, localized, and intermediate states coexist in the system, which is very different from the case without the modulated magnetic field. These results may help us to learn more about two-dimensional electrons in a periodic magnetic field.

Magnetic Properties of A Cavity‐Embedded Square Lattice of Quantum Dots or Antidots

“…The rich structure of the energy spectrum in such systems in a magnetic field is connected to the commensurability of the magnetic length and the lattice constant of the superlattice. [ 3–6 ] The fractal structure of the Landau band splitting have primarily been observed using the Peierls' substitution [ 2 ] in calculations of the energy dispersion for an electron in a superlattice (SL). Another method which has been used successfully is the direct diagonalization of the Hamiltonian with an appropriate choice of basis functions in which the magnetotranslation phases are included.…”

Interminiband absorption in a quantum ring superlattice in magnetic field with periodic vector potential

“…Since the appearance of the works of Azbel [25] and Hofstadter [26], the study of electronic spectra in a twodimensional lattice under the influence of a transverse (perpendicular to the lattice plane) magnetic field has become a field of continuous interest [14,[27][28][29][30][31][32][33][34]. Re- * Electronic address: vram@ysu.am cently the consideration of two-dimensional electrons in a spatially periodic transverse magnetic field or periodic magnetic potential is of special interest [28,32,[35][36][37]. In Ref.…”

“…In Ref. [32] the electronic band structure of GaAs/AlGaAs superlattice in a periodic magnetic field has been investigated. A general scheme for synthesizing a spatially periodic magnetic field, or a magnetic lattice is presented in Ref.…”