Interlayer screening effect in graphene multilayers with ABA and ABC stacking

We study the effect of perpendicular electric fields on the band structures of ABA and ABC graphene multilayers, and find that the electronic screening effect is significantly different between them. In ABA multilayers, the field produces a band overlap and gives a linear screening, while in ABC multilayers, in contrast, it opens an energy gap in the surface-state band at low energy, leading to a strong screening effect essentially non-linear to the field amplitude. The energy gap of a large ABC stack sharply rises when the external field exceeds a certain critical value.Comment: 8 pages, 6 figure

Integer quantum Hall effect and Hofstadter's butterfly spectra in three-dimensional metals in external periodic modulations

We propose that Hofstadter's butterfly accompanied by quantum Hall effect that is similar to those predicted to occur in 3D tight-binding systems by Koshino {\it et al.} [Phys. Rev. Lett. {\bf 86}, 1062 (2001)] can be realized in an entirely different system -- 3D metals applied with weak external periodic modulations (e.g., acoustic waves). Namely, an effect of two periodic potentials interferes with Landau's quantization due to an applied magnetic field \Vec{B}, resulting generally in fractal energy gaps as a function of the tilting angle of \Vec{B}, for which the accompanying quantized Hall tensors are computed. The phenomenon arises from the fact that, while the present system has a different physical origin for the butterfly from the 3D tight-binding systems, the mathematical forms are remarkably equivalent.Comment: 4 pages, 2 figure

Electronic structure of an electron on the gyroid surface, a helical labyrinth

Previously reported formulation for electrons on curved periodic surfaces is used to analyze the band structure of an electron bound on the gyroid surface (the only triply-periodic minimal surface that has screw axes). We find that an effect of the helical structure appears as the bands multiply sticking together on the Brillouin zone boundaries. We elaborate how the band sticking is lifted when the helical and inversion symmetries of the structure are degraded. We find from this that the symmetries give rise to prominent peaks in the density of states.Comment: RevTeX, 4 pages, 6 figure

Duality and integer quantum Hall effect in isotropic 3D crystals

We show here a series of energy gaps as in Hofstadter's butterfly, which have been shown to exist by Koshino et al [Phys. Rev. Lett. 86, 1062 (2001)] for anisotropic three-dimensional (3D) periodic systems in magnetic fields \Vec{B}, also arise in the isotropic case unless \Vec{B} points in high-symmetry directions. Accompanying integer quantum Hall conductivities $(\sigma_{xy}, \sigma_{yz}, \sigma_{zx})$ can, surprisingly, take values $\propto (1,0,0), (0,1,0), (0,0,1)$ even for a fixed direction of \Vec{B} unlike in the anisotropic case. We can intuitively explain the high-magnetic field spectra and the 3D QHE in terms of quantum mechanical hopping by introducing a ``duality'', which connects the 3D system in a strong \Vec{B} with another problem in a weak magnetic field $(\propto 1/B)$.Comment: 7 pages, 6 figure

Full Quantum Analysis of Two-Photon Absorption Using Two-Photon Wavefunction: Comparison with One-Photon Absorption

For dissipation-free photon-photon interaction at the single photon level, we analyze one-photon transition and two-photon transition induced by photon pairs in three-level atoms using two-photon wavefunctions. We show that the two-photon absorption can be substantially enhanced by adjusting the time correlation of photon pairs. We study two typical cases: Gaussian wavefunction and rectangular wavefunction. In the latter, we find that under special conditions one-photon transition is completely suppressed while the high probability of two-photon transition is maintained.Comment: 6 pages, 4 figure

Orbital diamagnetism in multilayer graphenes: Systematic study with the effective mass approximation

We present a theoretical study on the orbital magnetism in multilayer graphenes within the effective mass approximation. The Hamiltonian and thus susceptibility can be decomposed into contributions from sub-systems equivalent to monolayer or bilayer graphene. The monolayer-type subband exists only in odd layers and exhibits a delta-function susceptibility at $E_F=0$. The bilayer-type subband appearing in every layer number gives a singular structure in the vicinity of $E_F=0$ due to the trigonal warping as well as a logarithmic tail away from $E_F=0$. The integral of the susceptibility over energy is approximately given only by the layer number.Comment: 12 pages, 5 figure

Electronic structure of periodic curved surfaces -- continuous surface versus graphitic sponge

We investigate the band structure of electrons bound on periodic curved surfaces. We have formulated Schr\"{o}dinger's equation with the Weierstrass representation when the surface is minimal, which is numerically solved. Bands and the Bloch wavefunctions are basically determined by the way in which the ``pipes'' are connected into a network, where the Bonnet(conformal)-transformed surfaces have related electronic strucutres. We then examine, as a realisation of periodic surfaces, the tight-binding model for atomic networks (``sponges''), where the low-energy spectrum coincides with those for continuous curved surfaces.Comment: 4 page