Alexander Struck

Wigner crystal versus Friedel oscillations in the one-dimensional Hubbard model

We analyze the fermion density of the one-dimensional Hubbard model using bosonization and numerical density matrix renormalization group calculations. For finite systems we find a relatively sharp crossover even for moderate short-range interactions into a region with 4kF density waves as a function of density. The results show that the unstable fixed point of a spin-incoherent state can dominate the physical behavior in a large region of parameter space in finite systems. The crossover may be observable in ultracold fermionic gases in optical lattices and in finite quantum wires.

Electron Correlations and Single-Particle Physics in the Integer Quantum Hall Effect

The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical results for the influences of interaction and disorder on the compressibility as a function of the particle density and the strength of the magnetic field are presented. Localization-delocalization transitions associated with a highly compressible region in the energy spectrum are found at half-integer filling factors. Coulomb blockade effects are found near integer fillings in the regions of low compressibility. Results are compared with recent experiments.

Lattice defects and boundaries in conducting carbon nanotubes

We consider the effect of various defects and boundary structures on the low energy electronic properties in conducting zigzag and armchair carbon nanotubes. The tight binding model of the conduction bands is mapped exactly onto simple lattice models consisting of two uncoupled parallel chains. Imperfections such as impurities, structural defects or caps can be easily included into the effective lattice models, allowing a detailed physical interpretation of their consequences. The method is quite general and can be used to study a wide range of possible imperfections in carbon nanotubes. We obtain the electron density patterns expected from a scanning tunneling microscopy experiment for half fullerene caps and two typical impurities in the bulk of a tube, namely the Stone-Wales defect and a single vacancy.

Unconventional conductance plateau transitions in quantum Hall wires with spatially correlated disorder

Quantum transport properties in quantum Hall wires in the presence of spatially correlated random potential are investigated numerically. It is found that the potential correlation reduces the localization length associated with the edge state, in contrast to the naive expectation that the potential correlation increases it. The effect appears as the sizable shift of quantized conductance plateaus in long wires, where the plateau transitions occur at energies much higher than the Landau band centers. The scale of the shift is of the order of the strength of the random potential and is insensitive to the strength of magnetic fields. Experimental implications are also discussed.

Local density of states for individual energy levels in finite quantum wires.

The local density of states in finite quantum wires is calculated as a function of discrete energies and position along the wire. By using a combination of numerical density matrix renormalization group calculations and analytical bosonization techniques, it is possible to obtain a good understanding of the local spectral weights along the wire in terms of the underlying many-body excitations.

Nonchiral Edge States at the Chiral Metal Insulator Transition in Disordered Quantum Hall Wires

The quantum phase diagram of disordered wires in a strong magnetic field is studied as a function of wire width and energy. The two-terminal conductance shows zero-temperature discontinuous transitions between exactly integer plateau values and zero. In the vicinity of this transition, the chiral metal-insulator transition (CMIT), states are identified that are superpositions of edge states with opposite chirality. The bulk contribution of such states is found to decrease with increasing wire width. Based on exact diagonalization results for the eigenstates and their participation ratios, we conclude that these states are characteristic for the CMIT, have the appearance of nonchiral edges states, and are thereby distinguishable from other states in the quantum Hall wire, namely, extended edge states, two-dimensionally (2D) localized, quasi-1D localized, and 2D critical states.

Conductance-plateau transitions in quantum Hall wires with spatially correlated random magnetic fields

Quantum transport properties in quantum Hall wires in the presence of spatially correlated disordered magnetic fields are investigated numerically. It is found that the correlation drastically changes the transport properties associated with the edge state, in contrast to the naive expectation that the correlation simply reduces the effect of disorder. In the presence of correlation, the separation between the successive conductance-plateau transitions becomes larger than the bulk Landau-level separation determined by the mean value of the disordered magnetic fields. The transition energies coincide with the Landau levels in an effective magnetic field stronger than the mean value of the disordered magnetic field. For a long wire, the strength of this effective magnetic field is of the order of the maximum value of the magnetic fields in the system. It is shown that the effective field is determined by a part where the stronger magnetic-field region connects both edges of the wire.