On the percolation induced conductivity in high-Tc superconducting materials

Electronic Phase Separation and Electron–Phonon Coupling in Cuprate Superconductors

“…This is one of the perspectives that has motivated early work on phase separation in hightemperature superconductors [8][9][10]. Another motivation was due to the fact that the phase separated electronic state may provide an electronic environment which is more supportive for the superconducting mechanism itself [2][3][4][5]11].…”

“…It is interesting to note that with regard to the parameter regime J/t < 1 relevant for cuprates, Emery and Kivelson refer in their paper to earlier works by Visscher [14] and by Ioffe and Larkin [15], who on the basis of the Hubbard model showed, that a very low density of holes is unstable to phase separation with the hole-rich phase being ferromagnetic. This kind of ferromagnetic clustering is at the heart of the second kind of scenario proposed by Hizhnyakov and Sigmund [2][3][4][5] which does not rely on a thermodynamic phase separation instability but starts with the question how the individual holes arrange when doped into the CuO 2 plane. In the SigmundHizhnyakov original proposal, a hole doped into the long-range antiferromagnetically ordered copper-oxygen plane and bound to its dopant ion, will locally distort the antiferromagnetic (AF) magnetic configuration.…”

“…It turns out that the interaction between the pairs is dominated by an anisotropic short-range core-core contribution which originates from the charge distribution of the localized holes. The percolative scenario described in [2][3][4][5] corresponds then to a head-to-tail aggregation of vortex-antivortex pairs that tend to form segments in such a way that only the vortex and the antivortex on the extremes contribute to the long range distortion of the magnetic structure. It has b) a) Parameters of the three-band model are taken from [22] been shown that a collection of such segments can induce a spiral distortion of the Cu spin configuration, the structure factor of which is in very good agreement with neutron scattering data of cuprate superconductors in the low doping regime, i.e.…”

“…One can start from the strongly overdoped [2][3][4][5]. The structure of the top left cluster is likely the model of choice for Alex Müller (essentially Fermi liquid like) regime and investigate the possibility of a phase separation instability upon lowering doping.…”

“…These efforts were supported by Vladimir Hizhnyakov from the University of Tartu, who together with Ernst Sigmund proposed an inhomogeneous doping mechanism for the cuprates in 1988 [2][3][4][5]. According to their picture the individual charge carriers form localized magnetic polarons in a fluctuating antiferromagnetic environment which then cluster together to form metallic regions (cf.…”