Probing quasiparticle excitations in a doped Mott insulator via Friedel oscillations

TL;DR

This work investigates how impurities reveal the nature of charge carriers in a doped Mott insulator by analyzing impurity-induced Friedel oscillations within a strong-coupling Hubbard framework. Using a real-space Composite Operator Method with a holon-doublon decomposition, the authors show that weak impurities yield Friedel oscillations describable by an effective non-interacting model for holons and doublons, yet the oscillation wavevector encodes a violation of Luttinger's theorem due to non-canonical algebra. In the strong-impurity regime, nonperturbative effects drive phase separation into half-filled Mott regions and hole-rich metallic domains, arising from competition between holon kinetic energy and holon-doublon binding. The results provide insights into the emergent quasiparticles and charge-ordered phases in doped Mott systems, with implications for interpreting quasiparticle interference phenomena in correlated materials.

Abstract

In this work, we investigate impurity-induced Friedel oscillations in the doped two-dimensional Hubbard model, focusing on the role of holon and doublon excitations. We show that weak impurities, due to the non-fermionic nature of the underlying quasiparticles, induce Friedel oscillations whose behavior is consistent with an effective non-interacting theory for these quasiparticles, and whose wavevector reflects the violation of Luttinger's theorem. At larger impurity strength, the system transitions to a phase-separated state composed of coexisting Mott-insulating (half-filled) and hole-rich regions. Within the composite operator framework, this phase separation arises from a competition between the kinetic energy of holons and the tendency to form tightly bound holon-doublon pairs. Our results offer new insights into the nature of charge carriers and the emergent electronic phases in the doped Mott regime.

Figures (1)

• Figure 1: (A) Real-space distribution of the density of states at the Fermi level in the presence of a repulsive line impurity located at $x = 128$, for parameters $U = 8t$, $\delta = 0.16$, and impurity strength $V_{imp} = 1t$ (B) Absolute value of the Fourier transform, $|\delta\rho(\omega=0, q_x)|$, exhibiting a distinct peak at $q_{max}$, marked by the red dotted line, indicating the characteristic frequency of the Friedel oscillations. (C) Dependence of the Friedel-oscillation frequency $q_{max}$ at the Fermi level ($\omega=0$) on the electron density $n$ for various interaction strengths: $U = 8t$, $U = 12t$, and $U = 16t$. (D) Friedel-oscillation frequency as a function of the electronic density $n$ for a non-interacting band insulator at the Fermi level. (E) Equal energy contours for a non-interacting band insulator at half-filling. (F) Frequency of the Friedel oscillations for a non-interacting band insulator as a function of energy, with colors corresponding to the equal-energy contours shown in (E). The Friedel oscillation frequencies at positive and negative energies are marked by blue and red arrows respectively. The corresponding Fermi surface scattering vectors are illustrated in panel (E).