Effects of large disorder on the Hofstadter butterfly

Motivated by the recent experiments on periodically modulated, two dimensional electron systems placed in large transversal magnetic fields, we investigate the interplay between the effects of disorder and periodic potentials in the integer quantum Hall regime. In particular, we study the case where disorder is larger than the periodic modulation, but both are small enough that Landau level mixing is negligible. In this limit, the self-consistent Born approximation is inadequate. We carry extensive numerical calculations to understand the relevant physics in the lowest Landau level, such as the spectrum and nature (localized or extended) of the wave functions. Based on our results, we propose a qualitative explanation of the new features uncovered recently in transport measurements.Comment: 15 pages, 13 figures, several pictures have been shrunk to comply with the size requirement

Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases

We present an exact analytical solution of the fundamental system of quasi-one-dimensional spin-1 bosons with infinite delta-repulsion. The eigenfunctions are constructed from the wave functions of non-interacting spinless fermions, based on Girardeau's Fermi-Bose mapping, and from the wave functions of distinguishable spins. We show that the spinor bosons behave like a compound of non-interacting spinless fermions and non-interacting distinguishable spins. This duality is especially reflected in the spin densities and the energy spectrum. We find that the momentum distribution of the eigenstates depends on the symmetry of the spin function. Furthermore, we discuss the splitting of the ground state multiplet in the regime of large but finite repulsion.Comment: Revised to discuss large but finite interaction

Hofstadter-type energy spectra in lateral superlattices defined by periodic magnetic and electrostatic fields

We calculate the energy spectrum of an electron moving in a two-dimensional lattice which is defined by an electric potential and an applied perpendicular magnetic field modulated by a periodic surface magnetization. The spatial direction of this magnetization introduces complex phases into the Fourier coefficients of the magnetic field. We investigate the effect of the relative phases between electric and magnetic modulation on band width and internal structure of the Landau levels.Comment: 5 LaTeX pages with one gif figure to appear in Phys. Rev.

Effects of Electron Correlations on Hofstadter Spectrum

By allowing interactions between electrons, a new Harper's equation is derived to examine the effects of electron correlations on the Hofstadter energy spectra. It is shown that the structure of the Hofstadter butterfly ofr the system of correlated electrons is modified only in the band gaps and the band widths, but not in the characteristics of self-similarity and the Cantor set.Comment: 13 pages, 5 Postscript figure

Magnetization of noncircular quantum dots

We calculate the magnetization of quantum dots deviating from circular symmetry for noninteracting electrons or electrons interacting according to the Hartree approximation. For few electrons the magnetization is found to depend on their number, and the shape of the dot. The magnetization is an ideal probe into the many-electron state of a quantum dot.Comment: 11 RevTeX pages with 6 included Postscript figure

Manifestation of the Hofstadter butterfly in far-infrared absorption

The far-infrared absorption of a two-dimensional electron gas with a square-lattice modulation in a perpendicular constant magnetic field is calculated self-consistently within the Hartree approximation. For strong modulation and short period we obtain intra- and intersubband magnetoplasmon modes reflecting the subbands of the Hofstadter butterfly in two or more Landau bands. The character of the absorption and the correlation of the peaks to the number of flux quanta through each unit cell of the periodic potential depends strongly on the location of the chemical potential with respect to the subbands, or what is the same, on the density of electrons in the system.Comment: RevTeX file + 4 postscript figures, to be published Phys. Rev. B Rapid Com

Self-trapping of impurities in Bose-Einstein condensates: Strong attractive and repulsive coupling

We study the interaction-induced localization -- the so-called self-trapping -- of a neutral impurity atom immersed in a homogeneous Bose-Einstein condensate (BEC). Based on a Hartree description of the BEC we show that -- unlike repulsive impurities -- attractive impurities have a singular ground state in 3d and shrink to a point-like state in 2d as the coupling approaches a critical value. Moreover, we find that the density of the BEC increases markedly in the vicinity of attractive impurities in 1d and 2d, which strongly enhances inelastic collisions between atoms in the BEC. These collisions result in a loss of BEC atoms and possibly of the localized impurity itself.Comment: 7 pages, 5 figure

Cotunneling-mediated transport through excited states in the Coulomb blockade regime

We present finite bias transport measurements on a few-electron quantum dot. In the Coulomb blockade regime, strong signatures of inelastic cotunneling occur which can directly be assigned to excited states observed in the non-blockaded regime. In addition, we observe structures related to sequential tunneling through the dot, occuring after it has been excited by an inelastic cotunneling process. We explain our findings using transport calculations within the real-time Green's function approach, including diagrams up to fourth order in the tunneling matrix elements.Comment: 4 pages, 3 figure