Quantum Ripples in Strongly Correlated Metals

Abstract

We study how well-known effects of the long-ranged Friedel oscillations are affected by strong electronic correlations. We first show that their range and amplitude are significantly suppressed in strongly renormalized Fermi liquids. We then investigate the interplay of elastic and inelastic scattering in the presence of these oscillations. In the singular case of two-dimensional systems, we show how the anomalous ballistic scattering rate is confined to a very restricted temperature range even for moderate correlations. In general, our analytical results indicate that a prominent role of Friedel oscillations is relegated to weakly interacting systems.

Dynamical Mean-field Theories of Correlation and Disorder

“…Besides, strong interactions also give rise to large inelastic scattering effects, and it is unclear if these are strong enough to mask the anomalous temperature dependence. The full analysis shows two things (Andrade et al, 2010). • The interaction suppression of scattering (disorder screening), eqn (6.66), acts to weaken both elastic and inelastic contributions from impurities, but does not destroy the non-Fermi-liquid, anomalous behavior.…”

Screening of a single impurity and Friedel oscillations in Fermi liquids

“…Hasegawa et al observed FO at 5K on Si(111)Ag surface [5]. Most of the theoretical and experimental studies have been conducted for non-interacting or weakly interacting systems till now [6,7,8,9,10,11]. An exception is the study of one-dimensional Luttinger liquid where a strong renormalisation of FO has been found theoretically by Matveev et al [12].…”

Non-Gaussian Spatial Correlations Dramatically Weaken Localization

“…A perturbative calculation shows that the correlations among the v i 's are given by v i v j ∼ r −1 ij , for r ij 1, where r ij = |r i − r j | [13,17]. These long-ranged correlations of the effective disorder potential come from the usual Friedel oscillations.…”

“…In principle, interactions could modify either the amplitude or the form of spatial correlations [6] of the renormalized disorder potential. The former mechanism is known to be significantly enhanced by strong correlation effects [9] and to survive even in high dimensions, while the latter is more pronounced [13] in the weak-coupling regime and in low dimensions [4].Despite this progress, several important questions remained unanswered: (1) What is the dominant physical mechanism for disorder screening, and can it qualitatively modify the noninteracting picture? (2) Can the interaction effects overcome Anderson localization and stabilize the metallic phase in low dimensions?…”

“…To cross-check our HF predictions within a theory that is able to capture strong correlation effects, we repeated the same calculations using the slave boson (SB) mean-field theory (i.e. the Gutzwiller approximation) of Kotliar and Ruckenstein [9,14], generalized to disordered systems [13]. The SB theory features two local variational parameters: the renormalized site energies v i and the quasiparticle weight Z i (Z i = 1 within HF) [15][16][17].…”