Fluctuation spectroscopy of granularity in superconducting structures

We suggest to use `fluctuation spectroscopy' as a method to detect granularity in a disordered metal close to a superconducting transition. We show that with lowering temperature $T$ the resistance $R(T)$ of a system of relatively large grains initially grows due to the fluctuation suppression of the one-electron tunneling but decreases with further lowering $T$ due to the coherent charge transfer of the fluctuation Cooper pairs. Under certain conditions, such a maximum in $R(T)$ turns out to be sensitive to weak magnetic fields due to a novel Maki -- Thompson type mechanism.Comment: A final version, as published; the introduction and summary are considerably revise

Space-time dispersion of graphene conductivity

We present an analytic calculation of the conductivity of pure graphene as a function of frequency $\omega$, wave-vector $k$, and temperature for the range where the energies related to all these parameters are small in comparison with the band parameter $\gamma =3$ eV. The simple asymptotic expressions are given in various limiting cases. For instance, the conductivity for $kv_{0}\ll T\ll \omega$ is equal to $\sigma (\omega, k)=e^{2}/4\hbar$ and independent of the band structure parameters $\gamma$ and $v_{0}$. Our results are also used to explain the known dependence of the graphite conductivity on temperature and pressure.Comment: 4 pages, 1 figure, to be submitte

How the Phase Slips in a Current-Biased Narrow Superconducting Stripe?

The theory of current transport in a narrow superconducting channel accounting for thermal fluctuations is revisited. The value of voltage appearing in the sample is found as the function of temperature (close to transition temperature $T-T_{\mathrm{c}}$ $\ll T_{\mathrm{c}}$) and bias current $J<J_{\mathrm{c}}$ ( $J_{\mathrm{c}}$ is a value of critical current calculated in the framework of the BCS approximation, neglecting thermal fluctuations). It is shown that the careful analysis of vortex crossing of the stripe results in considerable increase of the activation energy.Comment: 6 pages, 2 figure

Electronic spectrum and tunnelling properties of multi-wall carbon nanotubes

We develop a general approach to calculations of the electron spectrum of metallic multi-wall carbon nanotubes (MWNT) with arbitrary number of coaxial layers. It is based on the model with singular attractive potential of equidistant conductive cylinders. The knowledge of one-electron spectrum allows to construct the corresponding Green function and then to calculate the entropy and density of states for MWNT. We analyze the tunnelling between the nanotube and normal metal electrode. The possibility of direct determination of one-electron density of states by measurements of the tunnelling conductivity at low temperatures is proved and the necessary restrictions on temperature are formulated. We discuss briefly the conflicting experimental observations of electronic properties of MWNT.Comment: 14 pages, 1 figur