We analyze inelastic cotunneling through an interacting quantum dot subject to an ambient magnetic field in the weak tunneling regime under a non-adiabatic time-dependent bias-voltage. Our results clearly exhibit photon-assisted satellites and an overall suppression of differential conductance with increasing driving amplitude, which is consistent with experiments. We also predict a zeroanomaly in differential conductance under an appropriate driving frequency. PACS numbers: 72.40.+w, 73.23.Hk, 73.63.Kv, 03.65.Yz Recently, cotunneling 1 through discrete levels, i.e., a quantum dot (QD), has attracted much attention since it determines the intrinsic limitation of accuracy of single-electron transistors due to leakage, and since it also involves correlation effects, such as the Kondo effect. 2 It has also been reported experimentally 3 and theoretically 4,5,6,7 that external microwave irradiation can induce the occurrence of Kondo satellites and an overall suppression of the Kondo peak. However, there are few studies so far concerning time-dependent secondorder cotunneling in the weak tunneling regime at temperatures above the Kondo temperature. About ten years ago, Flensberg presented an analysis for coherent photon-assisted cotunneling in a double-junction Coulomb blockade device in the adiabatic limit. 8 In this letter, we will further study the cotunneling in an interacting QD when an ac bias-voltage is applied between two electrodes in the non-adiabatic regime.We employ the s-d exchange Hamiltonian to model inelastic cotunneling through a QD in an ambient magnetic field, B, in the weak-coupling regime:where c † ηkσ (c ηkσ ) is the creation (annihilation) operator for electrons with momentum k, spin-σ in lead η (= L, R). The energies ε ηk (t) = ε 0 ηk + eV η (t) include a rigid shift of the Fermi energy of the electrons in the leads due to the applied time-dependent bias-voltage V η (t) = V 0 η + v η cos(Ωt) with V 0 η (v η ) being the amplitude of the dc(ac) part of the bias-voltage. Here, we assume that the Fermi energies of two leads are zero at equilibrium andis the static magnetic-field B-induced Zeeman energy. S ≡ (S x , S y , S z ) are Pauli spin operators of electrons in the QD [S ± ≡ S x ± iS y ], and J is the exchange coupling constant. H dir is the potential scattering term with 2J d = J. As in our previous paper, 9 we can rewrite the tunneling term, H I in Eq. (1), as a sum of three products of two variables:with the generalized coordinates Q z(±) of reservoir variables asand Q1 = H dir . In the following, we will use units where = k B = e = 1. As in our previous studies of inelastic cotunneling through an interacting QD in the weak tunneling limit, we employ a generic quantum Langevin equation approach 10,11,12 to establish a set of quantum Bloch equations for the description of the dynamics of a single spin [modeled by Eq. (1)] explicitly in terms of the response and correlation functions of free reservoir variables. This procedure provides explicit analytical expressions for the nonequilibriu...
