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

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 Nd^ of impurity electrons. We apply this formulation to SU(N) symmetric QD and MA, and calculate the correlation functions for $N=4$ and $6$, using the 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 Nd^ N-1 for strong Coulomb interactions U, and they also exhibit the plateau structures due to the SU(N) Kondo effects at integer values of Nd^. We find that the Lorenz number L=κ/(T σ) for QD and MA, defined as the ratio of the thermal conductivity κ to the electrical conductivity σ, deviates from the universal Wiedemann-Franz value π²/(3e²) as the temperature increases from $T=0$, showing the T² dependence, the coefficient for which depends on the three-body correlations away from half filling. We also demonstrate the role of three-body correlations on the nonlinear current noise and the other transport coefficients.