Transport of correlated electrons through disordered chains: A perspective on entanglement, conductance, and disorder averaging

Abstract

We investigate electron transport in disordered Hubbard chains contacted to macroscopic leads, via the non-equilibrium Green's functions technique. We observe a cross-over of currents and conductances at finite bias which depends on the relative strength of disorder and interactions. The finite-size scaling of the conductance is highly dependent on the interaction strength, and exponential attenuation is not always seen. We provide a proof that the Coherent Potential Approximation, a widely used method for treating disorder averages, fulfils particle conservation at finite bias with or without electron correlations. Finally, our results hint that the observed trends in conductance due to interactions and disorder also appear as signatures in the single-site entanglement entropy.PACS numbers: 72.15. Rn, 72.10.Bg, 71.10.Fd, 03.67.Mn In today's quest for novel electronics and quantuminformation technologies, materials with properties largely determined by electron correlations are an important asset [1]. Altogether, they exhibit a wide range of nontrivial phenomena, making them excellent potential candidates to exploit for cutting-edge functionalities and devices. However, materials behavior is often far from ideal because of uncontrolled, random inhomogeneities in the sample, i.e. disorder. Disorder can greatly affect the behavior of a solid (for example it can dramatically alter conduction properties) and thus it should be considered in a comprehensive theoretical description [2].Significant understanding of the behavior of noninteracting electrons in disordered solids is obtained in terms of a scaling theory of electron localization [3,4]. Interactions add great complexity to the picture, but the reverse is also true: describing electronic correlations in the presence of sample-to-sample statistical fluctuations is much harder than for the homogenous case. For this, one can either resort to straightforward but computationally expensive sums over configurations, or to analytical treatments of statistic fluctuations such as typical medium theory [5] or the Coherent Potential Approximation (CPA) [6,7]. Traditionally, CPA has been mostly used in static ab initio treatments of disordered metallic alloys [8], but, recently, it has also been used in nonequilibrium setups [9][10][11].On the whole, until now rigorous understanding of interacting electrons in strongly disordered systems has come primarily from numerical studies [4,12] in-and near-equilibrium regimes, by looking e.g. at linear conductances [13][14][15], spectral functions [5,16,17], the degree of localization via the inverse participation ratio [18], or signatures in the entanglement entropy [19,20].Out of equilibrium, the situation is less defined: Even for "simple" cases such as 1D wires in a quantum transport setup (for a recent review of work on 1D, see e.g.[21]), many issues are only partially or not-at-all settled. For example, how do interactions and disorder together affect conduction in a small wire when a finite electric bias is applied? And w...

Adiabatic Preparation of a Correlated Symmetry‐Broken Initial State with the Generalized Kadanoff–Baym Ansatz

“…Here we considered a periodic lattice system for which a solution of the KB and GKBA equations would be also possible directly in k-space. Our implementation in the localized lattice site basis has been tested to be in agreement with a k-space calculation, but for future studies the site basis implementation readily allows us to consider also disordered systems breaking the lattice periodicity, or realtime charge and thermal transport setups with lead environments [19,[72][73][74][75][76].…”

Disorder and interactions in systems out of equilibrium: The exact independent-particle picture from density functional theory

“…Born approximation, 27,65,68,69 , keeping all diagrams up to second order. While the numerical details depend on the chosen approximation, our conclusions do not, as discussed in more detail below.…”

“…2), for HF I vanishes at very large U . The non-monotonic behavior of I results from competing disorder and interactions 21,26,27 . Conversely, the density spread ∆n decreases monotonically as a function of U at both NQF and HF, i.e.…”

“…In equilibrium, interactions can increase or decrease conductivity in a disordered system 21,24,25 . Out of equilibrium, results for quantum rings 26 and quantum transport setups 27 suggest that at fixed disorder strength the current depends non-monotonically on interactions.…”

Effective bias and potentials in steady-state quantum transport: A NEGF reverse-engineering study

“…As approximations to Σ M B , we will make use of two standard approximations: 2nd Born (see e.g. [29,30]) that takes into account all diagrams of the self-energy up to second order, and the particle-particle T-Matrix Approximation (TMA) [31,32,33,34]. In these approximations, Σ…”