Perturbation study of nonequilibrium quasiparticle spectra in an infinite-dimensional Hubbard lattice

Abstract

A model for nonequilibrium dynamical mean-field theory is constructed for the infinite-dimensional Hubbard lattice. We impose nonequilibrium by expressing the physical orbital as a superposition of a left $(L)$-moving and right $(R)$-moving electronic state with the respective chemical potentials ${\ensuremath{\mu}}_{L}$ and ${\ensuremath{\mu}}_{R}$. Using the second-order iterative perturbation theory we calculate the quasiparticle properties as a function of the chemical potential bias between the $L$ and $R$ movers, i.e., $\ensuremath{\Phi}={\ensuremath{\mu}}_{L}\ensuremath{-}{\ensuremath{\mu}}_{R}$. The evolution of the nonequilibrium quasiparticle spectrum is mapped out as a function of the bias and temperature. The quasiparticle states with the renormalized Fermi-energy scale ${\ensuremath{\epsilon}}_{QP}^{0}$ disappear at $\ensuremath{\Phi}\ensuremath{\sim}{\ensuremath{\epsilon}}_{QP}^{0}$ in the low-temperature limit. The second-order perturbation theory predicts that in the vicinity of the Mott-insulator transition at the Coulomb-parameter $U={U}_{c}$, there exists another critical Coulomb-parameter ${U}_{d}$ $(<{U}_{c})$ such that, for ${U}_{d}<U<{U}_{c}$, quasiparticle states are destroyed abruptly when ${({\ensuremath{\epsilon}}_{QP}^{0})}^{2}\ensuremath{\sim}a{(\ensuremath{\pi}{k}_{B}{T}_{c})}^{2}+b{\ensuremath{\Phi}}_{c}^{2}$ with the critical temperature ${T}_{c}$, the critical bias ${\ensuremath{\Phi}}_{c}$, and the numerical constants $a$ and $b$ on the order of unity.