Electron-electron interaction and instabilities in one-dimensional metals

The possible instabilities of a 1-dimensional itinerant electron gas are discussed, assuming electron-electron interaction to play the dominant role. As is well known, in the RPA, a 1-dimensional metal is prone to spin density wave (SDW), charge density wave (CDW) and Cooper pair (CP) instabilities. The spin channel decomposition of the irreducible scattering amplitude I is made and the spin channel projections are evaluated in terms of the matrix elements of bare electron-electron interactionV(x) for momenta of interest. It is found that if the bare electron interactionV(x) is repulsive and decreases monotonically with separation, only the SDW instability will occur. If the small separation (x?(2k _F )^?1) part of the interaction is greatly reduced or is made attractive,V(x) is non-monotonic,V _q (q?2k _F ) is negative, and a CDW instability is preferred. A CP instability is possible if the electron interaction is attractive,i.e., if [V _q (0<q<k _F )+V _q (q?2k _F )]<0. The above RPA results serve only as rough indicators, since in general there are important two-electron configurations with two-electron momentum close to zero and with electron hole momentum close to 2k _F , an example being the near Fermi energy configurationk ₁?k _F ,k ₂??k _F ,k ₃??k _F k ₄?k _F . Therefore as pointed out first by Bychkov, Gorkov and Dzhyaloshinskii (BGD), cross channel coupling is especially significant. It is shown that the cross channel coupling is constructive is some cases,eg., exchange of CD fluctuations leads to an effective electron-electron spin singlet attraction and vice-versa. A formalism for studying such effects is set up, and the particular example mentioned above is discussed. An RPA-like approximation is made for the form of the reducible singlet electron hole scattering amplitudeγ _s ^d and the resulting induced Cooper pair attraction is calculated to be $$\begin{gathered} [I_s ^e ]_{ind.} \rho _{{}^\varepsilon F} = [ln(\lambda \beta \omega _c )]^{ - 1} ln\{ [1 + 2\pi ^{ - 1} ln(\lambda \beta \omega _c )^2 ]/ \hfill \\ 1 + [8\pi ^{ - 1} \gamma _s ^d (q = 2k_F )^{ - 1} )^2 ]\} \hfill \\ \end{gathered} $$ where λ=1.14,β=(k _B T)^?1 andω ₀ is an electronic energy cut-off ～ε _F . The induced electron hole attraction due to the exchange of virtual Cooper pairs has a similar expression, but with a factor of (1/4) and withγ _s ^e (q=0) replacingγ _s ^d (q=2k _F ). The induced Cooper pair attraction is seen to be quite large over a broad range of temperatures close to but aboveT _CDW [i.e., aboveT such thatγ _s ^d (q=2k _F )^?1=0]. There is no requirement thatγ _s ^d (q=2k _F ) andγ _s ^e (q=0) become singular at the same temperature, as found by BGD. The BGD prediction is seen to arise from the neglect of real particle hole and particle-particle excitations while calculatingγ _s ^d andγ _s ^e . The effect of impurities, of electron-phonon coupling, of interchain coupling and of interaction between thermal order parameter fluctuations is discussed. The results are then applied to a discussion of the properties of TTF-TCNQ, where it is suggested that a CDW instability occurs becauseV _q (q=2k _F )<0,i.e., because the small separation electron repulsion is strongly reduced by the highly polarizable TTF. Because of substantial interchain coupling, the bulk CDW instability occurs close to the RPA instability temperature. The giant conductivity observed by Colemanet al is attributed to superconductive fluctuations in a 1-dimensional system with large mean field superconductive transition temperatureT _CP ^MF of order 300°K. Such a largeT _CP ^MF is shown to result from the induced Cooper pair attraction due to CD fluctuation exchange.     

OCCURRENCE OF PYRIMIDINE-RICH TRACTS IN ASCITES TUMOR DNA AND THE FORMATION OF UV-INDUCED THYMINE DIMERS

Abstract— Analysis of the distribution of pyrimidine-rich tracts (up to decanucleotides) in ascites tumor DNA revealed that these tracts occur predominantly in repetitive sequence of DNA. UV irradiation of ascites DNA resulted in preferential formation of thymine dimers in the pyrimidine-rich tracts as compared to other regions of DNA.     

Molecular Recognition of 1,5 Diamino Anthraquinone by <Emphasis Type="Italic">p</Emphasis>-tert-butyl-Calix(8)arene

The molecular recognition properties of p-tert-butyl-calix(8)arene with 1,5 -diamino anthraquinone (1,5 DAAQ) were studied by using UV–Visible and Fluorescence spectroscopic techniques. The binding constant was determined by using the Benesi-Hilde brand expression. It was found that the host–guest complex was formed between 1,5 DAAQ and p-tert-butyl- calix(8)arene in the 1:2 Stoichiometry ratio.     

A Facile Entry into Bicyclo[3.3.0] Octene System Via Anionic Oxy-Cope Rearrangement

The bicyclo[3.3.0] octene system has been synthesised from the readily available starting material 2-methyl-cyclohexane-1,3-dione, utilizing the base catalysed oxy-Cope rearrangement as a key step.     

Chirally Twisted Ultrathin Polydopamine Nanoribbons: Synthesis and Spontaneous Assembly of Silver Nanoparticles on Them

Polydopamine (PDA) is a synthetic polymeric material with immense potential in biomedical and surface functionalization applications. Herein, we have screened self-assemblies formed by Phenylalanine-based amphiphiles (Phe-AMPs) as soft templates for preparing chiral PDA nanostructures. Our study revealed that the amphiphile 2 endowed with a primary amine residue afforded chirally-twisted ultrathin nanoribbons of PDA under optimized conditions. The chirality at the Phe residue of 2 modulated the twist-chirality of the PDA nanoribbons; the l -2 resulted in nanoribbons with right-handed twist, whereas the d -2 induced a left-handed twist to the ribbons. The racemic mixture of these two amphiphiles produced flat, achiral tapes. The PDA ribbon thickness was ≈5.86±0.40 nm, whereas its width and length were ≈133.5±3.2 nm and >5000 nm, respectively. Upon dialysis, hollow PDA nanotubes were obtained due to curling of the PDA nanoribbons. These PDA-nanoarchitectures were employed to spontaneously form and assemble Ag-nanoparticles along the edges of the PDA nanoribbons. In this work we are reporting chirality controlled synthesis of PDA nanostructures for the first time.