Self-similar occurrence of massless Dirac particles in graphene under magnetic field

Intricate interplay between the periodicity of the lattice structure and that of the cyclotron motion gives rise to a well-known self-similar fractal structure of the energy eigenvalue, known as the Hofstadter butterfly, for an electron moving in lattice under magnetic field. Evolving from the $n=0$ Landau level, the central band of the Hofstadter butterfly is especially interesting since it may hold a key to the mysteries of the fractional quantum Hall effect observed in graphene. While the entire Hofstadter butterfly can be in principle obtained by solving Harper's equations numerically, the weak-field limit, most relevant for experiment, is intractable due to the fact that the size of the Hamiltonian matrix, that needs to be diagonalized, diverges. In this paper, we develop an effective Hamiltonian method that can be used to provide an accurate analytic description of the central Hofstadter band in the weak-field regime. One of the most important discoveries obtained in this work is that massless Dirac particles always exist inside the central Hofstadter band no matter how small the magnetic flux may become. In other words, with its bandwidth broadened by the lattice effect, the $n=0$ Landau level contains massless Dirac particles within itself. In fact, by carefully analyzing the self-similar recursive pattern of the central Hofstadter band, we conclude that massless Dirac particles should occur under arbitrary magnetic field. As a corollary, the central Hofstadter band also contains a self-similar structure of recursive Landau levels associated with such massless Dirac particles. To assess the experimental feasibility of observing massless Dirac particles inside the central Hofstadter band, we compute the width of the central Hofstadter band as a function of magnetic field in the weak-field regime.Comment: 17 pages, 9 figure

Emergent p-wave Kondo Coupling in Multi-Orbital Bands with Mirror Symmetry Breaking

We examine Kondo effect in the periodic Anderson model for which the conduction band is of multi-orbital character and subject to mirror symmetry breaking field imposed externally. Taking p-orbital-based toy model for analysis, we find the Kondo pairing symmetry of p-wave character emerges self-consistently over some regions of parameter space and filling factor even though only the on-site Kondo hybridization is assumed in the microscopic Hamiltonian. The band structure in the Kondo-hybridized phase becomes nematic, with only two-fold symmetry, due to the p-wave Kondo coupling. The reduced symmetry should be readily observable in spectroscopic or transport measurements for heavy fermion system in a multilayer environment such as successfully grown recently.Comment: 5 pages, 4 figure

Landau Level Quantization and Almost Flat Modes in Three-dimensional Semi-metals with Nodal Ring Spectra

We investigate novel Landau level structures of semi-metals with nodal ring dispersions. When the magnetic field is applied parallel to the plane in which the ring lies, there exist almost non-dispersive Landau levels at the Fermi level (E_F = 0) as a function of the momentum along the field direction inside the ring. We show that the Landau levels at each momentum along the field direction can be described by the Hamiltonian for the graphene bilayer with fictitious inter-layer couplings under a tilted magnetic field. Near the center of the ring where the inter-layer coupling is negligible, we have Dirac Landau levels which explain the appearance of the zero modes. Although the inter-layer hopping amplitudes become finite at higher momenta, the splitting of zero modes is exponentially small and they remain almost flat due to the finite artificial in-plane component of the magnetic field. The emergence of the density of states peak at the Fermi level would be a hallmark of the ring dispersion.Comment: 5 pages, 2 figure

Selective growth of perovskite oxides on SrTiO3 (001) by control of surface reconstructions

We report surface reconstruction (RC)-dependent growths of SrTiO3 and SrVO3 on a SrTiO3 (001) surface with two different coexisting surface RCs, namely (2x1) and c(6x2). Up to the coverage of several layers, epitaxial growth was forbidden on the c(6x2) RC under the growth conditions that permitted layer-by-layer epitaxial growth on the (2x1) RC. Scanning tunneling microscopy examination of the lattice structure of the c(6x2) RC revealed that this RC-selective growth mainly originated from the significant structural/stoichiometric dissimilarity between the c(6x2) RC and the cubic perovskite films. As a result, the formation of SrTiO3 islands was forbidden from the nucleation stage

Classification of flat bands according to the band-crossing singularity of Bloch wave functions

We show that flat bands can be categorized into two distinct classes, that is, singular and nonsingular flat bands, by exploiting the singular behavior of their Bloch wave functions in momentum space. In the case of a singular flat band, its Bloch wave function possesses immovable discontinuities generated by the band-crossing with other bands, and thus the vector bundle associated with the flat band cannot be defined. This singularity precludes the compact localized states from forming a complete set spanning the flat band. Once the degeneracy at the band crossing point is lifted, the singular flat band becomes dispersive and can acquire a finite Chern number in general, suggesting a new route for obtaining a nearly flat Chern band. On the other hand, the Bloch wave function of a nonsingular flat band has no singularity, and thus forms a vector bundle. A nonsingular flat band can be completely isolated from other bands while preserving the perfect flatness. All one-dimensional flat bands belong to the nonsingular class. We show that a singular flat band displays a novel bulk-boundary correspondence such that the presence of the robust boundary mode is guaranteed by the singularity of the Bloch wave function. Moreover, we develop a general scheme to construct a flat band model Hamiltonian in which one can freely design its singular or nonsingular nature. Finally, we propose a general formula for the compact localized state spanning the flat band, which can be easily implemented in numerics and offer a basis set useful in analyzing correlation effects in flat bands.Comment: 23 pages, 13 figure