Thermoelectric transport and current noise through a multilevel Anderson impurity: Three-body Fermi liquid corrections in quantum dots and magnetic alloys

Abstract

We present a comprehensive Fermi liquid description for thermoelectric transport and current noise, applicable to multilevel quantum dots (QD) and magnetic alloys (MA) without electron-hole or time-reversal symmetry. Our formulation for the low-energy transport is based on an Anderson model with $N$ discrete impurity levels, and is asymptotically exact at low energies, up to the next-leading order terms in power expansions with respect to temperature $T$ and bias voltage $eV$. The expansion coefficients can be expressed in terms of the Fermi liquid parameters, which include the three-body correlation functions defined with respect to the equilibrium ground state in addition to the linear susceptibilities and the occupation number $N_d^{}$ of impurity electrons. We apply this formulation to the $\mathrm{SU}\left(N\right)$ symmetric QD and MA, and calculate the correlation functions for $N=4$ and 6, using numerical renormalization group approach. The three-body correlations are shown to be determined by a single parameter over a wide range of electron fillings $1\lesssim N_d^{}\lesssim N-1$ for strong Coulomb interactions $U$, and they also exhibit the plateau structures due to the $\mathrm{SU}\left(N\right)$ Kondo effects at integer values of $N_d^{}$. We find that the Lorenz number $L=\kappa /\left(T\sigma \right)$ for QD and MA, defined as the ratio of the thermal conductivity $\kappa$ to the electrical conductivity $\sigma$, deviates from the universal Wiedemann-Franz value ${\pi }^2/\left(3e^2\right)$ as the temperature increases from $T=0$, showing the $T^2$ dependence, the coefficient for which depends on the three-body correlations away from half filling. Furthermore, we find that the current noise for the SU(4) quantum dots and that for SU(6) show a pronounced difference at the quarter $N_d^{}/N=1/4$ and $3/4$ fillings. In particular, the linear noise for $N=4$ exhibits a flat peak while the peak for $N=6$ shows a round shape, reflecting the fact that, at these filling points, the $\mathrm{SU}\left(N\right)$ Kondo effects occur for $N\equiv 0$ (mod 4), whereas the intermediate-valence fluctuations occur for $N\equiv 2$ (mod 4). We also demonstrate the role of three-body correlations on the nonlinear current noise and the other transport coefficients.