• T V Ramakrishnan

      Articles written in Pramana – Journal of Physics

    • Electron-electron interaction and instabilities in one-dimensional metals

      T V Ramakrishnan

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      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≳(2kF)−1) part of the interaction is greatly reduced or is made attractive,V(x) is non-monotonic,Vq(q≅2kF) is negative, and a CDW instability is preferred. A CP instability is possible if the electron interaction is attractive,i.e., if [Vq(0<q<kF)+Vq(q⋍2kF)]<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 2kF, an example being the near Fermi energy configurationk1kF,k2⋍−kF,k3⋍−kFk4kF. 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 amplitudeγsd 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=(kBT)−1 andω0 is an electronic energy cut-off ∼εF. 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 withγse(q=0) replacingγsd(q=2kF). The induced Cooper pair attraction is seen to be quite large over a broad range of temperatures close to but aboveTCDW [i.e., aboveT such thatγsd(q=2kF)−1=0]. There is no requirement thatγsd(q=2kF) andγse(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 calculatingγsdandγse. 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 becauseVq(q=2kF)<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 temperatureTCPMF of order 300°K. Such a largeTCPMF is shown to result from the induced Cooper pair attraction due to CD fluctuation exchange.

    • Density wave theory of freezing and the solid

      T V Ramakrishnan

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      The theory of the liquid to solid transition, in three as well as in two dimensions, is reviewed. The transition can be viewed either as the melting of the solid due to phonon or defect proliferation instabilities or alternatively as freezing of the liquid into a density wave state with crystalline symmetry. A theory due to Yussouff and the author, based on the latter idea, is discussed and its predictions are compared with experiment. It is shown that the theory leads to a new approach to the properties of a deformed (e.g., sheared) solid and of defects such as grain boundaries and dislocations in a solid. The approach brings out explicitly the structural nature of these properties, and is not restricted to small deviations from perfect periodicity (harmonic approximation) since the solid, the liquid and anything in between can be handled theoretically.

    • Some open problems in the physics of disordered systems

      T V Ramakrishnan

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      Some problems in the physics of disordered systems are pointed out; most of these arise from experiments.

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