Electron Band Structure in a Two Dimensional Periodic Magnetic Field

In this paper we study the energy spectrum of a two dimensional electron gas (2DEG) in a two dimensional periodic magnetic field. Both a square magnetic lattice and a triangular one are considered. We consider the general case where the magnetic field in a cell can be of any shape. A general feature of the band structure is bandwidth oscillation as a function of the Landau index. A triangular magnetic lattice on a 2DEG can be realized by the vortex lattice of a superconductor film coated on top of a heterojunction. Our calculation indicates a way of relating the energy spectrum of the 2DEG to the vortex structure. We have also derived conditions under which the effects of a weak magnetic modulation, periodic or not, may be reproduced by an electric potential modulation, and vice versa.Comment: 16 pages in TeX and 5 uuencoded figure

Bose-Einstein Condensation with Entangled Order Parameter

We propose a practically accessible non-mean-field ground state of Bose-Einstein condensation (BEC), which occurs in an interspecies two-particle entangled state, and is thus described by an entangled order parameter. A suitably defined entanglement entropy is used as the characterization of the non-mean-field nature, and is found to persist in a wide parameter regime. The interspecies entanglement leads to novel interference terms in the dynamical equations governing the single particle orbital wavefunctions. Experimental feasibility and several methods of probe are discussed. We urge the study of multi-channel scattering between different species of atoms.Comment: V1: 5 pages, 4 figures. Accepted by Phys. Rev. Lett.; V2: A couple of very minor typos corrected, publishe

Berry Phase Effects on Electronic Properties

Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.Comment: 48 pages, 16 figures, submitted to RM

Chiral anomaly and anomalous finite-size conductivity in graphene

Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two pairs of massless two-dimensional Dirac fermions in the absence of or with negligible spin-orbit coupling. It is known that the existence of non-zero electric polarization in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of zigzag nanoribbon. The Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges at different valleys can be realized in a confined ribbon of finite width. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and goes inversely with the square of the lateral dimension W, which is different from the finite-size correction inversely with W from boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and is measurable experimentally.Comment: 5 pages, 2 figure

Multi-Modal Multi-Scale Deep Learning for Large-Scale Image Annotation

Image annotation aims to annotate a given image with a variable number of class labels corresponding to diverse visual concepts. In this paper, we address two main issues in large-scale image annotation: 1) how to learn a rich feature representation suitable for predicting a diverse set of visual concepts ranging from object, scene to abstract concept; 2) how to annotate an image with the optimal number of class labels. To address the first issue, we propose a novel multi-scale deep model for extracting rich and discriminative features capable of representing a wide range of visual concepts. Specifically, a novel two-branch deep neural network architecture is proposed which comprises a very deep main network branch and a companion feature fusion network branch designed for fusing the multi-scale features computed from the main branch. The deep model is also made multi-modal by taking noisy user-provided tags as model input to complement the image input. For tackling the second issue, we introduce a label quantity prediction auxiliary task to the main label prediction task to explicitly estimate the optimal label number for a given image. Extensive experiments are carried out on two large-scale image annotation benchmark datasets and the results show that our method significantly outperforms the state-of-the-art.Comment: Submited to IEEE TI