NRG study of nonlinear susceptibilities appearing in low-energy transport through N-level quantum dots

We study nonequilibrium transport through an N-level Anderson impurity model at low-temperatures T and at low-bias voltages eV using a microscopic Fermi-liquid theory which is applicable to arbitrary cases of electron filling N_d[1,2]. The theory shows that the transport coefficients such as current, thermal conductivity, and current noise are determined by Fermi-liquid parameters: phase shifts, linear susceptibilities, and nonlinear susceptibilities. We calculate these parameters using Wilson numerical renormalization group(NRG) and 1\/(N-1) expansion[3]. The latter one is a large N theory which is exact in the limit of N→∞. The NRG results show that the nonlinear susceptibilities significantly contribute to the transport coefficients up to order of (eV)^3 as a position of the Kondo resonance peak deviates from the particle-hole symmetric point[4]. We also find that the nonlinear susceptibilities are determined by a single parameter in a range of 1≤N_d≤N-1 for strong interactions U. Such N_d dependence of the susceptibilities are experimentally observed[5]. Furthermore, we compare the NRG results with those obtained by 1\/(N-1) expansion and find that the three-body correlations are suppressed already for N=8.

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[2] A. Oguri and A. C. Hewson, Phys. Rev. B 97, 035435 (2018).
[3] A. Oguri, Phys. Rev. B 85, 155404 (2012).
[4] Y. Teratani, R. Sakano, and A. Oguri, Phys. Rev. Lett. 125, 216801 (2020).
[5] T. Hata, Y. Teratani, T. Arakawa, S. Lee, M. Ferrier, R. Deblock, R. Sakano, A. Oguri, and K. Kobayashi, Nature Communications 12, 3233 (2021).