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 nextleading 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 SU(N ) 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 ≲ N d ≲ 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 N d .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 π 2 /(3e 2 ) 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 SU(N ) Kondo effects occur for N ≡ 0 (mod 4), whereas the intermediate-valence fluctuations occur for N ≡ 2 (mod 4).We also demonstrate the role of three-body correlations on the nonlinear current noise and the other transport coefficients.