Resistivity minimum emerges in Anderson impurity model modified with Sachdev-Ye-Kitaev interaction

Abstract

We investigate a modified Anderson model at the large-$N$ limit, where Coulomb interaction is replaced by Sachdev-Ye-Kitaev random interaction. The resistivity of conduction electron $\rho_{c}$ has a minimum value around temperature $\widetilde{T}_{K}$, which is similar to the Kondo system, but the impurity electron's density of state $A_{d}(\omega)$ elucidates no sharp-peak like Kondo resonance around the Fermi surface. The impurity electron's entropy $S_{d}$ and specific heat capacity $C_{\textrm{v}}$ illustrate a crossover from Fermi liquid to the non-Fermi liquid. The system is a non-Fermi liquid at temperature $T^{\star}<T<\widetilde{T}_{K}$, a Fermi liquid for $T<T^{\star}$, and becomes a Fermi gas if $T>\widetilde{T}_{K}$. The non-Fermi liquid at intermediate-$T$ regime does not occur in standard Anderson model. With renormalization group analysis, we elucidate a crossover from Fermi liquid to the non-Fermi liquid, coinciding with transport and thermodynamics. The resistivity minimum and the Kondo resonance are two characteristics of Kondo effect. However, the resistivity minimum emerges in our model when the system behaves as a NFL rather than FL, and the impurity electron's density of state without the Kondo resonance.