Screening of a single impurity and Friedel oscillations in Fermi liquids

Abstract

Abstract.We numerically study Friedel Oscillations and screening eect around a single impurity in one-and two-dimensional interacting lattice electrons. The interaction between electrons is accounted for by using a momentum independent self-energy obeying the Luttinger theorem. It is observed in one-dimensional systems that the amplitude of oscillations is systematically damped with increasing the interaction while the period remains unchanged. The variation of screening charge with the impurity potential is discussed. We see that the screening charge is suppressed by the interactions. In case of two-dimensional systems the surface oscillations around the impurity are more localized with increasing the interactions.

Friedel oscillation in non-Fermi liquid: Lesson from exactly solvable Hatsugai-Kohmoto model

“…31 When involving electron-electron interaction, both the Luttinger liquid in one spatial dimension (d = 1) and the Landau Fermi liquid (FL) show such characteristic oscillation. [32][33][34][35][36][37] The origin of FO is generally believed to tie to the 2k F singularity of densitydensity correlation in the system with sharp Fermi surface, thus even quantum spin liquid with ghost (spinon) Fermi surface may show signature of FO. 38,39 Consequently, FO can act as diagnosis for fermionic system with well-defined Fermi surface whatever its FL or NFL nature and may shed light on how to detect putative NFL state in realistic quantum materials proposed by existing effective field theory or slave-particle theory.…”

Friedel oscillation in non-Fermi liquid: lesson from exactly solvable Hatsugai–Kohmoto model

“…the Friedel oscillation (FO) [31]. When involving electron-electron interaction, both the Luttinger liquid in one spatial dimension (d = 1) and the Landau Fermi liquid (FL) show such characteristic oscillation [32][33][34][35][36][37]. The origin of FO is generally believed to tie to the 2k F singularity of density-density correlation in the system with sharp Fermi surface, thus even quantum spin liquid with ghost (spinon) Fermi surface may show signature of FO [38,39].…”

Real-space dynamical mean-field theory of Friedel oscillations in strongly correlated electron systems

“…After the initial prediction [1,2] further theoretical investigations were performed to understand FOs in crystals with non-spherical Fermi surfaces [18][19][20][21][22][23][24][25], in model systems with an impurity on which the electrons can interact [26][27][28][29][30], in one dimensional quantum wires where interacting electrons form a Luttinger liquid [31][32][33][34][35][36][37], in two or three-dimensonal Hubbard models with electrons forming either the Fermi liquid or the Mott insulator [38][39][40][41][42][43], or in system with interacting and disordered electrons such as amorphous alloys and quasicrystals [44]. Recent theoretical progress was made in understanding spin dependent FOs [45], as well as understanding FOs in topological insulators [46,47], in graphane [48][49][50], in cold atoms [51], in systems with charge density waves [52] or with presence of the transport currents [53].…”

“…Different studies of FOs in Fermi liquids revealed that the oscillations are renormalized due to the electronic interactions. Though, the charge FOs in the Hubbard model and the spin liquid at the Mott transition were studied [38][39][40][41][42][43], a comprehensive quantitative analysis of the FOs at the Mott transition is still an open prob-lem. In particular, we would like to address quantitatively the questions: How does the oscillation amplitude A change with the interaction strength?…”