Effects of the field modulation on the Hofstadter's spectrum

Abstract

We study the effect of spatially modulated magnetic fields on the energy spectrum of a two-dimensional (2D) Bloch electron. Taking into account four kinds of modulated fields and using the method of direct diagonalization of the Hamiltonian matrix, we calculate energy spectra with varying system parameters (i.e., the kind of the modulation, the relative strength of the modulated field to the uniform background field, and the period of the modulation) to elucidate that the energy band structure sensitively depends on such parameters: Inclusion of spatially modulated fields into a uniform field leads occurrence of gap opening, gap closing, band crossing, and band broadening, resulting distinctive energy band structure from the Hofstadter's spectrum. We also discuss the effect of the field modulation on the symmetries appeared in the Hofstadter's spectrum in detail.

7 pages (in two-column), 10 figures (including 2 tables)

References in corpus (2)

• Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
• Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field

Cited by in corpus (9)

• Birefringent break up of Dirac fermions in a square optical lattice
• From the Hofstadter to the Fibonacci butterfly
• Redistributing Chern numbers of Landau subbands: tight-binding electrons under staggered-modulated magnetic fields
• Ultracold bosons in a synthetic periodic magnetic field: Mott phases and re-entrant superfluid-insulator transitions
• Energy Spectrum of Bloch Electrons Under Checkerboard Field Modulations
• The effect of the Abrikosov vortex phase on spin and charge states in magnetic semiconductor-superconductor hybrids
• Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices
• A magnetic Hofstadter butterfly and its topologically quantized Hall conductance
• Peierls substitution in the energy dispersion of a hexagonal lattice