Highly asymmetric superconducting dome and strange metallicity in La$_3$Ni$_2$O$_7$

The recent discovery of high-temperature superconductivity in La$_3$Ni$_2$O$_7$ under high pressure has stimulated intensive investigations concerning its paring mechanism and a correct description of its effective low-energy physics. Notable experimental observations include the right-triangle-shaped superconducting dome with the maximum $T_c$ of about 80 K and the strange metal behavior in the normal state above $T_c$. Here we apply the Schwinger boson approach to the bilayer $t$-$V$-$J$ model, which allows us to treat well both the magnetic correlations and the superconducting instability. We obtain a global phase diagram with both metallic and superconducting ground states separated by a quantum phase transition, and predict a minimal interlayer superexchange $J$ and a minimal $d_{z^2}$-hole concentration necessary for the superconductivity, with a highly asymmetric right-triangle-like shape for the $T_c$ curve as well as a maximum $T_c$ comparable with experiments. The normal state is featured with a pseudogap in the $d_{x^2-y^2}$ spectra associated with preformed Cooper pairs and non-Fermi liquid strange metal behavior due to hybridization-induced spinon-holon-electron scattering. Our work clarifies the key difference of the two-component scenario of the superconductivity from other mechanisms, and provides a consistent understanding of the high-temperature superconductivity and strange metallic properties of La$_{3}$Ni$_2$O$_7$ under high pressure.