Resistivity saturation is observed in many metallic systems with large resistivities, i.e., when the resistivity has reached a critical value, its further increase with temperature is substantially reduced. This typically happens when the apparent mean free path is comparable to the interatomic separations -the Ioffe-Regel condition. Recently, several exceptions to this rule have been found. Here, we review experimental results and early theories of resistivity saturation. We then describe more recent theoretical work, addressing cases both where the Ioffe-Regel condition is satisfied and where it is violated. In particular we show how the (semiclassical) Ioffe-Regel condition can be derived quantum-mechanically under certain assumptions about the system and why these assumptions are violated for high-Tc cuprates and alkali-doped fullerides.
We extend the imaginary-time formulation of the equilibrium quantum many-body theory to steady-state nonequilibrium with an application to strongly correlated transport. By introducing Matsubara voltage, we keep the finite chemical potential shifts in the Fermi-Dirac function, in agreement with the Keldysh formulation. The formulation is applied to strongly correlated transport in the Kondo regime using the quantum Monte Carlo method.PACS numbers: 73.63. Kv, 72.10.Bg, 72.10.Di A coherent formulation of equilibrium and nonequilibrium is one of the ultimate goals of statistical physics. In the last two decades, this has become a particularly pressing issue with the advances in nanoelectronics. Although it has long been considered such Gibbsian description may exist in the steady-state nonequilibrium [1], implementation of time-independent nonequilibrium quantum statistics has produced limited success [2] without widely applicable algorithms.In nanoelectronics, the strong interplay between manybody interactions and nonequilibrium demands nonperturbative treatments of the quantum many-body effects. Perturbative Green function techniques [3,4] have been successful, but are often plagued by complicated diagrammatic rules and are limited to simple models. In the last few years, important advances have been made in this field to complement the diagrammatic theory. Timedependent renormalization group [5,6] and densitymatrix renormalization group method [7] were applied to calculate the real-time convergence toward the steadystate. Real-time methods [5,6,7] calculate the process toward the steady-state and therefore have clear physical interpretations. Unfortunately they often suffer from long-time behaviors associated with low energy strongly correlated states and finite size effects. Direct construction of nonequilibrium ensembles through the scattering state formalism [2,8,9, 10] and field theoretic approach [11] have provided new perspectives to the problem.The main goal of this work is to provide a critical step toward the time-independent description of equilibrium and steady-state nonequilibrium quantum statistics. In addition to the resolution of this fundamental problem, we provide a strong application. The steadystate nonequilibrium can be solved within the same formal structure as equilibrium, and therefore the powerful equilibrium many-body tools, such as the quantum Monte Carlo (QMC) method, can be easily applied to complex transport systems with many competing interactions. We demonstrate this point by applying this formalism to strongly correlated transport in the Kondo regime by using QMC. In contrast to the real-time methods, this approach starts from the steady-state and simulates the effect of many-body interaction. However, numerical analytic continuation and low temperature calculation, especially with the QMC application, are technical difficulties.In the following, we first construct a time-independent statistical ensemble of steady-state nonequilibrium [2] in the non-interacting limit with the i...
We analyze fulleride superconductivity at experimental doping levels, treating the electron-electron and electron-phonon interactions on an equal footing, and demonstrate that the Jahn-Teller phonons create a local (intramolecular) pairing which is surprisingly resistant to the Coulomb repulsion, despite the weakness of retardation in these low-bandwidth systems. The requirement for coherence throughout the solid then yields a very strong doping dependence to T(c), one consistent with experiment and much stronger than expected from standard Eliashberg theory.
Using Quantum Monte Carlo we compute thermodynamics and spectra for the orbitally degenerate Hubbard model in infinite spatial dimensions. With increasing orbital degeneracy we find in the one-particle spectra: broader Hubbard bands (consistent with increased kinetic energy), a narrowing Mott gap, and increasing quasi-particle spectral weight. In opposition, Hund's rule exchange coupling decreases the critical on-site Coulomb energy for the Mott transition. The metallic regime resistivity for two-fold degeneracy is quadratic-in-temperature at low temperatures. 75.30.Mb, 71.27.+a, 75.10.Dg The Hubbard Hamiltonian, the simplest model for strongly interacting many-electron systems, has been extremely popular in that, despite its simplicity, the model is considered to capture essential physics in electronic systems, ranging from a metal-insulator transition (MIT) and associated antiferromagnetism to possible d-wave superconductivity. Although most of the real systems displaying these phenomena have orbital degrees of freedom, most theoretical works have concentrated on the orbitally non-degenerate model for simplicity. Recently, with the advent of the colossal magnetoresistance materials [1], the proposed triplet pairing superconductivity in Sr 2 RuO 4 [2], and alkali-doped fullerides [3,4], attention has been turned to the multi-orbital Hubbard model (MOHM) [5,8,9].With on-site orbital degeneracy N deg > 1, one has to consider two additional aspects of the problem: first, the effect of orbital degrees of freedom on the mobility of electrons and second, the role of on-site exchange interactions between degenerate orbitals. In this paper, we concentrate on the MIT in MOHM motivated particularly by alkali-doped fullerides, A 3 C 60 (A=K, Rb, Cs etc.). We have studied the problem using Quantum Monte Carlo in a d = ∞ model on both Bethe and hypercubic lattices, with a focus on dynamical properties (obtained by analytic continuation of imaginary time data using the Maximum Entropy method [MEM]). We present the first systematic calculation of one-electron spectral functions at and away from particle-hole symmetry and the first calculation of the optical conductivity and d.c. resistivity for the two-orbital model.We find that the upper and lower Hubbard bands display a considerable broadening for N deg = 2, 3 relative to N deg = 1, which supports the idea of Gunnarsson, Koch, and Martin [5] and Lu [6] that orbital degeneracy serves to increase the effective hopping matrix element and thereby mitigate the efficacy of correlations in driving a MIT [7]. We also find that the quasiparticle spectral weight increases with N deg . We find that the inclusion of Hund's rule exchange serves to decrease the effective hopping, thereby decreasing again the critical value of on-site Coulomb interaction U = U c needed for the MIT, according to the approximate expressionwhere J is the Hund's rule exchange energy. Finally, we present a calculation of the optical conductivity σ(ω, T ) and resistivity ρ(T ) for the N deg = 2 case which...
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