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

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 $\left(L\right)$-moving and right $\left(R\right)$-moving electronic state with the respective chemical potentials ${\mu }_L$ and ${\mu }_R$. 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., $\Phi ={\mu }_L-{\mu }_R$. 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 ${\epsilon }_{QP}^0$ disappear at $\Phi \sim {\epsilon }_{QP}^0$ 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 $U_d$ $\left(<U_c\right)$ such that, for $U_d<U<U_c$, quasiparticle states are destroyed abruptly when ${\left({\epsilon }_{QP}^0\right)}^2\sim a{\left(\pi k_B{T}_c\right)}^2+b{\Phi }_c^2$ with the critical temperature $T_c$, the critical bias ${\Phi }_c$, and the numerical constants $a$ and $b$ on the order of unity.

Figure 1

The Bethe lattice where the (physical) $d$ state is given as a superposition of a left $\left(L\right)$- and a right $\left(R\right)$- moving state with the corresponding chemical potentials ${\mu }_L=\Phi /2$ and ${\mu }_R=-\Phi /2$.

Figure 2

(Color online) Interacting local spectral functions for $U=2$, inverse temperature $\beta =300$ and half-bandwidth $D=1$ plotted for a range of chemical potential biases, $\Phi$. At this value of the Coulomb-interaction $U$ the quasiparticle peak is destroyed continuously as $\Phi$ is increased.

Figure 3

(Color online) Interacting local spectral functions for $U=2.3$, 2.5, 2.6, and 2.8 at inverse temperature $\beta =300$ and bandwidth $D=1$. These plots depict the sudden disappearance of the quasiparticle peak at the critical voltage ${\Phi }_c$. The spectral functions are plotted at $\Phi =0$, at $\Phi$ just before the quasiparticle destruction, and at $\Phi ={\Phi }_c$.

Figure 4

(Color online) Quasiparticle-energy ${\epsilon }_{QP}$ as a function of the chemical potential bias $\Phi$ at $\beta =300$ and $D=1$. The quasiparticle energy is scaled to the quasiparticle energy at zero bias, ${\epsilon }_{QP}^0$, and the chemical potential bias is scaled to the critical bias at which the quasiparticle peak is destroyed, ${\Phi }_c$. For small bias, $\Phi \lesssim 0.4{\Phi }_c$, the quasiparticle energies scale to a single curve. In this range of values for $U$ the disappearance of the quasiparticle peak is strongly discontinuous.

Figure 5

(Color online) Quasiparticle-energy ${\epsilon }_{QP}$ as a function of the chemical potential bias $\Phi$ at $U=2.8$ and $D=1$ for different values of the inverse temperature $\beta$. As the temperature is increased, the disappearance of quasiparticles remains discontinuous and the critical bias ${\Phi }_c$ is lowered. The inset gives the temperature dependence of the critical bias. The data (filled circles) were fit (solid curve) to the function, ${\left({\epsilon }_{QP}^0\right)}^2\sim a{\left(\pi k_B{T}_c\right)}^2+b{\Phi }_c^2$, where $a=1.1$ and $b=0.54$.

Figure 6

The critical bias ${\Phi }_c$ is plotted as a function of the Coulomb-interaction $U$ at inverse temperature $\beta =300$ and bandwidth $D=1$. We have also plotted the renormalized Fermi-energy ${\epsilon }_{QP}^0$ at $\Phi =0$. In the region $U_d<U<U_c$ the quasiparticle peak is destroyed discontinuously at ${\Phi }_c$. When $U<U_d$ the quasiparticle peak disappears smoothly with increasing chemical potential bias. At this temperature ${\Phi }_c\sim {\epsilon }_{QP}^0$.