Superconductivity in single crystals of a quasi-one dimensional infinite chain cuprate Sr$_x$Ca$_{1-x}$CuO$_2$ at 90 K

Although there is no complete theory of high temperature superconductivity, the importance of CuO$_2$ planes in cuprate superconductors is confirmed from both theory and experiments. Strong Coulomb repulsion between electrons on the CuO$_2$ plane makes the resultant electron system highly correlated and a difficult problem to solve since exact solutions of many-body Hamiltonian in two dimensions do not exist. If however, superconductivity can arise in structures having chains rather than planes and having a high critical temperature, then the high temperature superconductivity problem could become more tractable since exact solutions in one dimension do exist. In this paper, we report the observation of bulk superconductivity in single crystals of a cuprate Sr$_x$Ca$_{1-x}$CuO$_2$ at very high critical temperature, T$_c$, of $\sim$ 90 K whose structure reveals the presence of infinite double chains of Cu-O-Cu-O instead of CuO$_2$ planes, thus, ensuring quasi-one dimensional superconductivity. Bulk superconducting behaviour was observed in \textit{dc} magnetisation, \textit{ac} susceptibility as well as resistance measurements. The observation of bulk superconductivity in Sr$_x$Ca$_{1-x}$CuO$_2$ having chains of Cu-O-Cu-O rather than planes of CuO$_2$ at a high T$_c$ of 90 K is expected to profoundly impact our understanding of high temperature superconductivity.