Debye temperature, electron-phonon coupling constant, and three-dome shape of crystalline strain as a function of pressure in highly compressed La$_3$Ni$_2$O$_{7-\delta}$

Abstract

Besides ongoing studies of phase structural transitions, pairing mechanism, and physical properties of recently discovered highly compressed high-temperature superconductor La$_3$Ni$_2$O$_{7-\delta}$, here we explored a possibility for the electron-phonon pairing mechanism as an origin of the superconducting state and determined the microcrystalline strain, $\epsilon(P)$, in high pressure $Fmmm$-phase, and low-pressure $Ammm$-phase of this nickelate. To do this, we analyzed temperature dependent resistance and extracted pressure dependent Debye temperature, $\Theta_D(P)$, in La$_3$Ni$_2$O$_{7-\delta}$ with an approximate value of $\Theta_D(P = 25 GPa) = 550$ $K$. From this we established that the La$_3$Ni$_2$O$_{7-\delta}$ is strong-coupled superconductor with the electron-phonon coupling constant $\lambda_{e-ph}(P=22.4 GPa) = 1.75$. This value is close to $\lambda_{e-ph} = 1.70$ of ambient pressure superconductors $Nb_3R (R = Sn, Al)$. To address ongoing discussion that the lattice strain can be the origin for the emergence of high-temperature superconductivity in the La$_3$Ni$_2$O$_{7-\delta}$, we determined the microcrystalline strain, $0.011 < \epsilon(P)$, in the high-pressure $Fmmm$-phase, and $\epsilon(P) < 0.011$ of low-pressure $Fmmm$-phase. Our analysis showed that $\epsilon(P)$ has three-dome shape in the pressure range of $1.6 GPa < P < 41.2 GPa$. One of these two $\epsilon(P)$ deeps at $P \approx 15 GPa$ coincides with the pressure at which the $Ammm$-phase into the $Fmmm$-phase phase transition occurs. Based on our analysis, we proposed probable condition to observe the zero-resistance state in La$_3$Ni$_2$O$_{7-\delta}$.