Direct Observation of Mono-, Bi-, and Tri-layer Charge Density Waves in 1T-TaS_2 by Transmission Electron Microscopy without a Substrate

Charge-density-waves (CDW) which occur mainly in low-dimensional systems have a macroscopic wave function similar to superfluids and superconductors. Kosterlitz-Thouless (KT) transition is observed in superfluids and superconductors, but the presence of KT transition in ultra-thin CDW systems has been an open problem. We report the direct real-space observation of CDWs with new order states in mono-, bi-, and tri-layer 1T-TaS_2 crystal by using a low voltage scanning-transmission-electron-microscope (STEM) without a substrate. This method is ideal to observe local atomic structures and possible defects. We clearly observed that the mono-layer crystal has a new triclinic stripe CDW order without the triple q condition q_1 + q_2 + q_3 = 0. A strong electron-phonon interaction gives rise to new crevasse (line) type defects instead of disclination (point) type defects due to the KT transition. These results reaffirm the importance of the electron-phonon interaction in mono-layer nanophysics.Comment: 5 figures, 1 tabl

The Nakano-Nishijima-Gell-Mann Formula From Discrete Galois Fields

The well known Nakano-Nishijima-Gell-Mann (NNG) formula relates certain quantum numbers of elementary particles to their charge number. This equation, which phenomenologically introduces the quantum numbers $I_z$ (isospin), $S$ (strangeness), etc., is constructed using group theory with real numbers $\mathbb{R}$. But, using a discrete Galois field $\mathbb{F}_p$ instead of $\mathbb{R}$ and assuring the fundamental invariance laws such as unitarity, Lorentz invariance, and gauge invariance, we derive the NNG formula deductively from Meson (two quarks) and Baryon (three quarks) representations in a unified way. Moreover, we show that quark confinement ascribes to the inevitable fractionality caused by coprimeness between half-integer (1/2) of isospin and number of composite particles (e.g. three).Comment: 14 pages, 4 figures, 2 table

Bose glass and Fermi glass

It is known that two-dimensional superconducting materials undergo a quantum phase transition from a localized state to superconductivity. When the disordered samples are cooled, bosons (Cooper pairs) are generated from Fermi glass and reach superconductivity through Bose glass. However, there has been no universal expression representing the transition from Fermi glass to Bose glass. Here, we discovered an experimental renormalization group flow from Fermi glass to Bose glass in terms of simple β-function analysis. To discuss the universality of this flow, we analyzed manifestly different systems, namely a Nd-based two-dimensional layered perovskite and an ultrathin Pb film. We find that all our experimental data for Fermi glass fall beautifully into the conventional self-consistent β-function. Surprisingly, however, flows perpendicular to the conventional β-function are observed in the weakly localized regime of both systems, where localization becomes even weaker. Consequently, we propose a universal transition from Bose glass to Fermi glass with the new two-dimensional critical sheet resistance close to R□=h/e2.Publisher PDFPeer reviewe