Fragility of local moments against hybridization with flat bands

TL;DR

This work demonstrates that a δ-function–like peak in the hybridization function $Δ(ω)$ at the Fermi level can qualitatively suppress Kondo screening in the Anderson impurity model, even when its weight $α$ is only a small fraction of the total bath. By constructing a toy model with a tunable $δ$-peak atop a regular bath and analyzing with continuous-time QMC and perturbative RG, the authors identify four regimes of behavior as $α$ varies, including a rapid fragmentation of the Kondo resonance and an early loss of the local moment. The results reveal a surprising fragility of vertex corrections to singular bath features and show that flat-band baths can dominate screening despite a mostly non-singular background. The findings have implications for DMFT treatments of lattice systems and for twisted bilayer graphene, where flat-band physics in the bath can influence fluctuating local moments and possible ordering phenomena, especially near charge neutrality.

Abstract

The Kondo screening of a localized magnetic moment crucially depends on the spectral properties of the electronic bath to which it is coupled. Unlike textbook examples, realistic systems as well as dynamical mean-field theory of correlated lattice models force us to explicitly consider sharp features in the hybridization function near the Fermi energy. A case currently under the spotlight is twisted bilayer graphene, where the hybridization function of the heavy-fermion-like bands to the itinerant ones displays a divergence. We clarify how this impacts the screening mechanisms by means of a toy model with a tunable $δ$-peak in the hybridization function, superimposed to a regular part. Our analysis unveils an unexpectedly big impact on the Kondo screening already for a parametrically small weight of the flat band in the bath.

Figures (5)

• Figure 1: (main panel) Toy-model hybridization function (orange) of an AIM, Eq. \ref{['eq:Delta_toy_model']}, and corresponding non-interacting spectral function at the impurity site (green). The parameter $\alpha\,\in\,\left[0:1\right]$ tunes the weight of the $\delta$-like feature at the Fermi energy interpolating between a "box"-like hybridization function ($\alpha$=0) and an isolated flat band in the bath ($\alpha$=1). Left inset: schematics of the Moiré Brillouin zone of TBG. Right inset: hybridization function and non-interacting spectral function obtained projecting the Bistritzer-MacDonald model on the THF basis of TBG at $\theta=1.35^\circ$doi:10.1073/pnas.1108174108notesketchtoymodelrefsupplement.
• Figure 2: Local, static spin $\chi^{\text{spin}}_{zz}$ (a) and charge $\chi^{\text{charge}}$ (b) susceptibility for different $\alpha$. Corresponding impurity spectra at $T$=$\mathcal{D}$/1000 (c). Other parameters: $V$=0.2$\mathcal{D}$ and $U$=0.575$\mathcal{D}$.
• Figure 3: Effective moment $\mu_{\text{eff}}$ of the impurity for different values of $U$ from $\alpha$=0 (blue) to $\alpha$=1 (red).
• Figure 4: Local spin susceptibility $\chi^{\text{spin}}_{zz}$ (blue) together with the corresponding contributions of bubble (green) and vertex corrections (orange) at ${T\,=\,0.001\,\mathcal{D}}$. Inset: The corresponding ratios to $\chi^{\text{spin}}_{zz}$ show how the two contribution have a qualitatively different dependence on $\alpha$.
• Figure 5: Sketch of the RG flow of the dimensionless couplings $k$, $j$ and $m$ to the $\delta$-peak, the broad band and the hybridization between both, respectively, showing four regimes of the $\delta$-weight $\alpha$. (i) For large $\alpha$ the $\delta$-peak coupling $k$ dominates at any $T$. (ii,iii) At smaller $\alpha$ the couplings cross as function of $T$, implying a crossover which is located above or below the relevant temperature scale for the Kondo effect (red line). (iv) For very small $\alpha$ the $j$ coupling dominates at any $T$. The $m$ coupling is always in between the other couplings.