Two-gap superconductor ZrB$_{12}$ with dynamic stripes and charge density waves: Crystal structure, physical properties and pairing mechanism

A review of long-term studies of ZrB$_{12}$ and LuB$_{12}$ superconductors with very similar conduction bands and phonon spectra, but with radically different (by a factor of 15-20) critical temperatures and magnetic fields is presented. A detailed analysis of well-known studies in combination with new results of structural, thermodynamic and charge transport measurements obtained here for these metallic dodecaborides with Jahn-Teller instability of the rigid boron network and with dynamic charge stripes allows us to conclude in favor of the primary role of nanoscale effects of electron phase separation, leading to the formation of one-dimensional dynamic chains with different configurations of fluctuating charges, which in the case of ZrB$_{12}$ are predominantly $2p$-states, and for LuB$_{12}$-$5d$-$2p$ states. We propose a new plasmon-phonon pairing mechanism in ZrB$_{12}$, which may be common to different classes of high-$T_c$ superconductors.