Crossover exponents in percolating superconductor–nonlinear-conductor mixtures

摘要: The nonlinear response is studied in a two-component composite with concentration p of superconductor (S) and 1-p normal conductor (N) the form J=${\mathrm{\ensuremath{\sigma}}}_{1}$E+${\mathrm{\ensuremath{\chi}}}_{1}$${\mathit{E}}^{\mathrm{\ensuremath{\beta}}}$ (\ensuremath{\beta}\ensuremath{\gtrsim}1). Below percolation threshold ${\mathit{p}}_{\mathit{c}}$ superconductor, can be represented by 〈J〉=${\mathrm{\ensuremath{\sigma}}}_{\mathit{eE}}$+${\mathrm{\ensuremath{\chi}}}_{\mathit{eE}}^{\mathrm{\ensuremath{\beta}}}$, where 〈...〉 represents spatial averages. magnitude crossover field ${\mathit{E}}_{\mathit{c}}$, defined as electric at which linear become comparable, found to have power-law dependence ${\mathit{E}}_{\mathit{c}}$\ensuremath{\sim}(${\mathit{p}}_{\mathit{c}}$-p${)}^{\mathit{M}(\mathrm{\ensuremath{\beta}})}$, corresponding current ${\mathit{I}}_{\mathit{c}}$ similar ${\mathit{E}}_{\mathit{c}}$\ensuremath{\sim}(${\mathit{p}}_{\mathit{c}}$-p${)}^{\mathit{W}(\mathrm{\ensuremath{\beta}})}$ approached from below. By using connection between random problem conductance fluctuation explicit expressions for M(\ensuremath{\beta}) W(\ensuremath{\beta}) are calculated. We prove that both monotonically decreasing functions \ensuremath{\beta}, special values M(${1}^{+}$)=W(${1}^{+}$)=+\ensuremath{\infty}, M(3)=[\ensuremath{\kappa}\ensuremath{'}(2)+s/2], W(3)=[\ensuremath{\kappa}\ensuremath{'}(2)-s/2], M(+\ensuremath{\infty})=(2-d)\ensuremath{\nu}/2\ensuremath{\le}0, W(+\ensuremath{\infty})=-(s+${\mathrm{\ensuremath{\zeta}}}_{\mathit{G}}$)/20. ${\mathit{E}}_{\mathit{c}}$ discussed \ensuremath{\beta} some interesting effects reported this paper. \textcopyright{} 1996 American Physical Society.