Angle Dependence of Landau Level Spectrum in Twisted Bilayer Graphene

In the context of the low energy effective theory, the exact Landau level spectrum of quasiparticles in twisted bilayer graphene with small twist angle is analytically obtained by spheroidal eigenvalues. We analyze the dependence of the Landau levels on the twist angle to find the points, where the two-fold degeneracy for twist angles is lifted in the nonzero modes and below/above which massive/massless fermion pictures become valid. In the perpendicular magnetic field of 10\,T, the degeneracy is removed at $\theta_{{\rm deg}}\sim 3^\circ$ %angles around 3 degrees for a few low levels, specifically, $\theta_{\rm deg}\simeq 2.56^\circ$ for the first pair of nonzero levels and $\theta_{\rm deg}\simeq 3.50^\circ$ for the next pair. Massive quasiparticle appears at $\theta<\theta_{{\rm c}}\simeq 1.17^\circ$ in 10\,T, %angles less than 1.17 degrees. which match perfectly with the recent experimental results. Since our analysis is applicable to the cases of arbitrary constant magnetic fields, we make predictions for the same experiment performed in arbitrary constant magnetic fields, e.g., for B=40\,T we get $\theta_{\rm c}\simeq 2.34^\circ$ and the sequence of angles $\theta_{\rm deg} = 5.11, 7.01, 8.42,...$ for the pairs of nonzero energy levels. The symmetry restoration mechanism behind the massive/massless transition is conjectured to be a tunneling (instanton) in momentum space.Comment: 8 pages, 7 figures, version to appear in PR

A New SX Phe Star in the Globular Cluster M15

A new SX Phe star (labelled SXP1) found from $BV$ CCD photometry is the first to be discovered in the globular cluster M15. It is a blue straggler and is located 102\arcsec.8 north and 285\arcsec.6 west of the center of M15 \citep{har96}. Mean magnitudes of SXP1 are = 18$\fm$671 and = 18\fm445. The amplitude of variability of SXP1 is measured to be $\Delta V \approx 0.15$. From multiple-frequency analysis based on the Fourier decomposition method, we detect two very closely separated pulsating frequencies: the primary frequency at $f_1=24.630$ c/d for both $B$- and $V$-bands, and the secondary frequency at $f_2=24.338$ c/d for the $B$-band and 24.343 c/d for the $V$-band. This star is the second among known SX Phe stars found to pulsate with very closely separated frequencies ($f_2/f_1\ge0.95$). These frequencies may be explained by excitation of nonradial modes; however, we have an incomplete understanding of this phenomenon in the case of SX Phe stars with relatively high amplitudes. The metallicity-period and the variability amplitude-period relations for SXP1 in M15 are found to be consistent with those for SX Phe stars in other globular clusters.Comment: 15 pages with 6 figures, accepted by the Astronomical Journal (scheduled May 2001

Fabrication of Multilayered Structure for Coherent Random Lasing

High powered lasers have many applications, including medical treatment and surgery. However, these lasers are extremely expensive and are therefore not widely available. The aim of this study was to demonstrate a method to create such a laser with significantly decreased overall cost and increased efficiency. In order to do this, we explored a phenomenon called random lasing which is a light amplification process. To start with, a low-cost pumping laser is directed at normal incidence toward a multi-layered sample with two alternating layers. At first pearl, a naturally found material that has many organic nano-scale layers (similar to the wavelength of visible light) was utilized and later fabricated using a spin coating technique. For the fabrication, two polymers, SU-8 with Rhodamine 6G (a fluorescent laser dye) and PMMA, were tested at different concentrations and spin coating speeds. It was necessary dissolve both polymers in a solvent so toluene composed about 25% of each solution. The spin coating speeds ranged from 1500 to 3000 rpm for both polymers to achieve layers approximately 500 nm thick. After the fabrication process, the pumping laser was directed at normal incidence onto the sample which increased the noise level and subsequently increased the degree of light localization. Light localization increases the amplification of the pumping laser and non-uniformity of the alternating layers increases this effect. Therefore, the lasing threshold was decreased which increases the lasers efficiency

Time dependent CP asymmetry in B0→ρ0γB^0 \to \rho^0 \gamma decay to probe the origin of CP violation

Since the CP violation in the $B$ system has been investigated up to now only through processes related to the $B$--$\bar{B}$ mixing, urgently required is new way of study for the CP violation and establishing its origin in the $B$ system independent of the mixing process. In this work, we explore the exclusive $B^0 \to \rho^0 \gamma$ decay to obtain the time-dependent CP asymmetry in $b \to d$ decay process in the standard model and the supersymmetric model. We find that the complex RL and RR mass insertion to the squark sector in the MSSM can lead to a large CP asymmetry in $b \to d \gamma$ decay through the gluino-squark diagrams, which is not predicted in the Standard Model induced by the $B$--$\bar{B}$ mixing.Comment: 10 pages, 4 eps figure