$d$-wave Pairing Amplitude and Particle-hole Asymmetry of the $t-J$ type models: Implication from the Spectral Weight Analysis

By using the projected variational wave functions (VWF), we study the quasiparticle spectral weight (QPSW) of hole-doped cuprates in the $t-J$ type models. The QPSW $Z^{+}$ for adding an electron shows a pocket structure outside the Fermi surface that is related to the momentum distribution function $n_{\mathbf{k}}$. Based on our VWF, $Z^{-}$ for removing an electron can be proven to have a simple relation among the pairing amplitude and $Z^{+}$. In addition, we also find that strong correlations mainly causes the particle- hole asymmetry of the low-energy tunneling spectra.