Multiple energy scales and emerging quasiparticles in a doped Mott insulator

We recognize two temperature scales relevant to formation of quasiparticles but distinct from the Brinkman-Rice scale in a doped Mott insulator. $T_{qp}$ marks the formation of incoherent quasiparticles, while a smaller scale $T_{FL}$ indicates the onset of Fermi-liquid coherence. Below $T_{qp}$, the scattering rate evolves linearly with temperature and the quasiparticle weight is also strongly $T$-dependent. Furthermore, the imaginary part of self energy is particle-hole asymmetric at low energy. These facts lead to non-Fermi liquid behaviors in transport properties. The Fermi liquid scale $T_{FL}$ is characterized by a smooth saturation of quasiparticle weight and emerging particle-hole symmetry in self energy. We compute transport properties and find that non-Fermi liquid behavior of longitudinal and Hall resistivity persist down to well below $T_{FL}$ while Hall angle and Nernst effect have revealed Fermi-liquid behavior above $T_{FL}$. We also discuss the validity of relaxation time approximation in interpreting non-Fermi liquid behaviors.