Hofstadter butterfly and integer quantum Hall effect in three dimensions

For a three-dimensional lattice in magnetic fields we have shown that the hopping along the third direction, which normally tends to smear out the Landau quantization gaps, can rather give rise to a fractal energy spectram akin to Hofstadter's butterfly when a criterion, found here by mapping the problem to two dimensions, is fulfilled by anisotropic (quasi-one-dimensional) systems. In 3D the angle of the magnetic field plays the role of the field intensity in 2D, so that the butterfly can occur in much smaller fields. The mapping also enables us to calculate the Hall conductivity, in terms of the topological invariant in the Kohmoto-Halperin-Wu's formula, where each of $\sigma_{xy}, \sigma_{zx}$ is found to be quantized.Comment: 4 pages, 6 figures, RevTeX, uses epsf.sty,multicol.st

Gate-induced magneto-oscillation phase anomalies in graphene bilayers

The magneto-oscillations in graphene bilayers are studied in the vicinity of the K and K' points of the Brillouin zone within the four-band continuum model ased on the simplest tight-binding approximation involving only the nearest neighbor interactions. The model is employed to construct Landau plots for a variety of carrier concentrations and bias strengths between the graphene planes. The quantum-mechanical and quasiclassical approaches are compared. We found that the quantum magneto-oscillations are only asymptotically periodic and reach the frequencies predicted quasiclassically for high indices of Landau levels. In unbiased bilayers the phase of oscillations is equal to the phase of massive fermions. Anomalous behavior of oscillation phases was found in biased bilayers with broken inversion symmetry. The oscillation frequencies again tend to quasiclassically predicted ones, which are the same for $K$ and $K'$, but the quantum approach yields the gate-tunable corrections to oscillation phases, which differ in sign for K and K'. These valley-dependent phase corrections give rise, instead of a single quasiclassical series of oscillations, to two series with the same frequency but shifted in phase.Comment: 8 pages, 8 figure

The electronic properties of bilayer graphene

We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energy. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.Comment: review, 31 pages, 15 figure

Quantum electrodynamics with anisotropic scaling: Heisenberg-Euler action and Schwinger pair production in the bilayer graphene

We discuss quantum electrodynamics emerging in the vacua with anisotropic scaling. Systems with anisotropic scaling were suggested by Horava in relation to the quantum theory of gravity. In such vacua the space and time are not equivalent, and moreover they obey different scaling laws, called the anisotropic scaling. Such anisotropic scaling takes place for fermions in bilayer graphene, where if one neglects the trigonal warping effects the massless Dirac fermions have quadratic dispersion. This results in the anisotropic quantum electrodynamics, in which electric and magnetic fields obey different scaling laws. Here we discuss the Heisenberg-Euler action and Schwinger pair production in such anisotropic QEDComment: 5 pages, no figures, JETP Letters style, version accepted in JETP Letter

Probing the quantum vacuum with an artificial atom in front of a mirror

Quantum fluctuations of the vacuum are both a surprising and fundamental phenomenon of nature. Understood as virtual photons flitting in and out of existence, they still have a very real impact, \emph{e.g.}, in the Casimir effects and the lifetimes of atoms. Engineering vacuum fluctuations is therefore becoming increasingly important to emerging technologies. Here, we shape vacuum fluctuations using a "mirror", creating regions in space where they are suppressed. As we then effectively move an artificial atom in and out of these regions, measuring the atomic lifetime tells us the strength of the fluctuations. The weakest fluctuation strength we observe is 0.02 quanta, a factor of 50 below what would be expected without the mirror, demonstrating that we can hide the atom from the vacuum

Band-width control in a perovskite-type 3d^1 correlated metal Ca_{1-x}Sr_xVO_3. I. Evolution of the electronic properties and effective mass

Single crystals of the perovskite-type $3d^{1}$ metallic alloy system Ca$_{1-x}$Sr$_x$VO$_3$ were synthesized in order to investigate metallic properties near the Mott transition. The substitution of a Ca$^{2+}$ ion for a Sr$^{2+}$ ion reduces the band width $W$ due to a buckling of the V-O-V bond angle from $\sim180^\circ$ for SrVO$_3$ to $\sim160^\circ$ for CaVO$_3$. Thus, the value of $W$ can be systematically controlled without changing the number of electrons making Ca$_{1-x}$Sr$_x$VO$_3$: one of the most ideal systems for studying band-width effects. The Sommerfeld-Wilson's ratio ($\simeq2$), the Kadowaki-Woods ratio (in the same region as heavy Fermion systems), and a large $T^{2}$ term in the electric resistivity, even at 300 K, substantiate a large electron correlation in this system, though the effective mass, obtained by thermodynamic and magnetic measurements, shows only a systematic but moderate increase in going from SrVO$_3$ to CaVO$_3$, in contrast to the critical enhancement expected from the Brinkmann-Rice picture. It is proposed that the metallic properties observed in this system near the Mott transition can be explained by considering the effect of a non-local electron correlation.Comment: 14 pages in a Phys. Rev. B camera-ready format with 10 EPS figures embedded. LaTeX 2.09 source file using "camera.sty" and "prbplug.sty" provided by N. Shirakawa. For OzTeX (Macintosh), use "ozfig.sty" instead of "psfig.sty". "ozfig.sty" can be also obtained by e-mail request to N. Shirakawa: . Submitted to Phys. Rev.

Electronic properties of bilayer and multilayer graphene

We study the effects of site dilution disorder on the electronic properties in graphene multilayers, in particular the bilayer and the infinite stack. The simplicity of the model allows for an easy implementation of the coherent potential approximation and some analytical results. Within the model we compute the self-energies, the density of states and the spectral functions. Moreover, we obtain the frequency and temperature dependence of the conductivity as well as the DC conductivity. The c-axis response is unconventional in the sense that impurities increase the response for low enough doping. We also study the problem of impurities in the biased graphene bilayer.Comment: 36 pages, 42 figures, references adde

Abelian gauge potentials on cubic lattices

The study of the properties of quantum particles in a periodic potential subject to a magnetic field is an active area of research both in physics and mathematics; it has been and it is still deeply investigated. In this review we discuss how to implement and describe tunable Abelian magnetic fields in a system of ultracold atoms in optical lattices. After discussing two of the main experimental schemes for the physical realization of synthetic gauge potentials in ultracold set-ups, we study cubic lattice tight-binding models with commensurate flux. We finally examine applications of gauge potentials in one-dimensional rings.Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM series 201