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 ͑L͒-moving and right ͑R͒-moving electronic state with the respective chemical potentials L and 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., ⌽ = L − 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 QP 0 disappear at ⌽ ϳ 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 ͑ϽU c ͒ such that, for U d Ͻ U Ͻ U c , quasiparticle states are destroyed abruptly when ͑ QP 0 ͒ 2 ϳ a͑k B T c ͒ 2 + b⌽ c 2 with the critical temperature T c , the critical bias ⌽ c , and the numerical constants a and b on the order of unity.In recent years significant experimental progress has been made in the fabrication of sophisticated electronic heterostructures utilizing strongly correlated electronic materials. These systems have given rise to the discovery of rich novel phenomena. These include: ballistic transport of electrons through heterostructures of superconductors, 1 ferromagnets, 2 magnetic tunneling junctions, 3,4 and oxides. 5-8 With this vast array of strongly correlated heterostructures it is very important to theoretically understand how the strongly correlated materials in the bulk limit will behave under nonequilibrium conditions. In this work we formulate the nonequilibrium problem in the lattice and present significant progress toward a more complete understanding of strongly correlated lattices out of equilibrium.We are interested in heterostructures of strongly correlated materials under a finite source-drain bias where the voltage drop occurs mainly at the interface of the strongly correlated material and the source/drain leads, as considered previously. 9,10 By this construction this model may not be sufficient to describe nonequilibrium in true-bulk systems. However, we speculate that this model is relevant to nanoscale devices where the nonequilibrium is established by unequal statistics between ballistic electrons from source and drain. This study will give an insight on how the lattice effects manifest in such systems. Our focus here is to investigate the evolution of strongly correlated quasiparticle spectra due to nonequilibrium driven by an imbalance in the chemical potentials. In this work we gain qualitative understanding on how the enhanced dephasing by the new particle-hole decay channel due to nonequilibrium modifies the spectral properties.One of the most practical and powerful theoretical techniques for studying strongly correlated lattices is the dynamical mean-field theo...

Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach

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Nonequilibrium dynamical mean-field theory and its applications

“…The weak-coupling perturbation theory has been used for a long time as an impurity solver in equilibrium DMFT calculations (Georges and Kotliar, 1992;Zhang, Rozenberg, and Kotliar, 1993;Freericks, 1994;Freericks and Jarrell, 1994;Georges et al, 1996), and in the nonequilibrium DMFT context, it has enabled a range of studies of the Hubbard model (Schmidt and Monien, 2002;Heary and Han, 2009;Eckstein and Werner, 2011a;Amaricci et al, 2012;Aron, Kotliar, and Weber, 2012;Tsuji et al, 2012;Tsuji, Eckstein, and Werner, 2013) and of the FalicovKimball model (Turkowski and Freericks, 2007a).…”

Nonequilibrium dynamical mean-field theory and its applications

“…Perturbation theory for nonequilibrium impurity problems (Fujii and Ueda, 2003;Hershfield et al, 1991Hershfield et al, , 1992) is a straightforward generalization of the equilibrium perturbation theory formulated on the Matsubara branch (Abrikosov et al, 1975;Mahan, 2000;Yosida andYamada, 1970, 1975). The weak-coupling perturbation theory has been used for a long time as an impurity solver in equilibrium DMFT calculations (Freericks, 1994;Freericks and Jarrell, 1994;Georges and Kotliar, 1992;Georges et al, 1996;Zhang et al, 1993), and in the nonequilibrium DMFT context, it has enabled a range of studies of the Hubbard model (Amaricci et al, 2012;Aron et al, 2012;Eckstein et al, 2010a;Eckstein and Werner, 2011a;Heary and Han, 2009;Schmidt and Monien, 2002;Tsuji et al, 2013bTsuji et al, , 2012Tsuji and Werner, 2013) and of the Falicov-Kimball model (Turkowski and Freericks, 2007a).…”