Electron band structure in a two-dimensional periodic magnetic field

Magnon Landau Levels and Spin Responses in Antiferromagnets

We study gauge fields produced by gradients of the Dzyaloshinskii-Moriya interaction and propose a model of an AFM topological insulator of magnons. In the long wavelength limit, the Landau levels induced by the inhomogeneous Dzyaloshinskii-Moriya interaction exhibit relativistic physics described by the Klein-Gordon equation. The spin Nernst response due to the formation of magnonic Landau levels is compared to similar topological responses in skyrmion and vortex-antivortex crystal phases of AFM insulators. Our studies show that AFM insulators exhibit rich physics associated with topological magnon excitations.

The integer quantum Hall effect of a square lattice with an array of point defects

The electronic properties of a square lattice under an applied perpendicular magnetic field in the presence of impurities or vacancies are investigated by the tight-binding method including up to second nearest neighbor interactions. These imperfections result in new gaps and bands in the Hofstadter butterfly even when the second order interactions break the bipartite symmetry. In addition, the whole spectrum of the Hall conduction is obtained by the Kubo formula for the corresponding cases. The results are in accordance with the Thouless-Kohmoto-Nightingale-den Nijs integers when the Fermi energy lies in an energy gap. We find that the states due to the vacancies or impurities with small hopping constants are highly localized and do not contribute to the Hall conduction. However, the impurities with high hopping constants result in new Hall plateaus with constant conduction of σ(xy) =± e(2)/h, since high hopping constants increase the probability of an electron contributing to the conduction.

Electron dynamics in inhomogeneous magnetic fields

This review explores the dynamics of two-dimensional electrons in magnetic potentials that vary on scales smaller than the mean free path. The physics of microscopically inhomogeneous magnetic fields relates to important fundamental problems in the fractional quantum Hall effect, superconductivity, spintronics and graphene physics and spins out promising applications which will be described here. After introducing the initial work done on electron localization in random magnetic fields, the experimental methods for fabricating magnetic potentials are presented. Drift-diffusion phenomena are then described, which include commensurability oscillations, magnetic channelling, resistance resonance effects and magnetic dots. We then review quantum phenomena in magnetic potentials including magnetic quantum wires, magnetic minibands in superlattices, rectification by snake states, quantum tunnelling and Klein tunnelling. The third part is devoted to spintronics in inhomogeneous magnetic fields. This covers spin filtering by magnetic field gradients and circular magnetic fields, electrically induced spin resonance, spin resonance fluorescence and coherent spin manipulation.

Manipulating spin and charge in magnetic semiconductors using superconducting vortices

The continuous need for miniaturization and increase in device speed drives the electronics industry to explore new avenues of information processing. One possibility is to use electron spin to store, manipulate and carry information. All such 'spintronics' applications are faced with formidable challenges in finding fast and efficient ways to create, transport, detect, control and manipulate spin textures and currents. Here we show how most of these operations can be performed in a relatively simple manner in a hybrid system consisting of a superconducting film and a paramagnetic diluted magnetic semiconductor (DMS) quantum well. Our proposal is based on the observation that the inhomogeneous magnetic fields of the superconducting film create local spin and charge textures in the DMS quantum well, leading to a variety of effects such as Bloch oscillations and an unusual quantum Hall effect. We exploit recent progress in manipulating magnetic flux bundles (vortices) in superconductors and show how these can create, manipulate and control the spin textures in DMSs.