Quantum Transport Through Large Spin Systems:Hubbard Green Function Approach

Single molecular magnets (SMMs), characterized by a large spin, a large magnetic anisotropy barrier and transverse anisotropy terms, which allows this spin to tunnel through the barrier, have attracted much attention in the last two decades for showing fundamental properties, such as the macroscopic quantum coherence and macroscopic quantum tunneling, which test the border of quantum and classical physics. Recently, individual magnetic molecule Mn12acetate was reported to be trapped in a typical field effect transistor geometry, allowing electronic transport to be measured on a SMM. Since then physicists have devoted great efforts to the electron transport through a SMM and a number of fascinating transport properties were observed or theoretically predicted, such as negative differential conductance, Kondo effect, current-induced switching, and Berry phase blockade. On the other hand, one naturally bethinks of the artificial counterparts to a SMM. Recently, Mn-doped QD, such as a CdTe QD doped with a single Mn ion with spin S=5/2, is proposed as an artificial single-molecule magnet (ASMM). The rich physics of the artificial single-molecule magnets is reflected in the transport properties through the system.Our main results in this work are as follows:Firstly, we study the transport through a SMM by nonequilibrium Green’s function method with the help of Hubbard operators. The large spin and the total Hamiltonian are reformulated in the language of Hubbard operators. Equation of motion scheme is presented for the Hubbard Green’s functions and an analytical formula for the retarded Green’s function is derived in the sequential tunneling regime. In Kondo tunneling regime we also get the analytical result for the retarded Green’s function. In numerical discussions we present the probabilities of eigenstates and differential conductance for SMM and compare these results with master equation method.Secondly, we study the transport properties of an ASMM in the sequential and Kondo regimes. In the sequential tunneling regime,(2S+1) peaks occur in the differential conductance spectrum, corresponding to resonance tunneling via (2S+1) sublevels. At low temperature, Kondo physics dominates transport. The differential conductance and local density of states (DOS) exhibit (2S+1) Kondo peaks, which is different from the Kondo effects in the molecular magnet induced by the quantum tunneling of the moment and also differs from Kondo effects in a half-integer-spin or an integer-spin QD. It originates from the exchange interaction between the hole spin and the impurity spin in ASMM. The exchange interaction splits the initial singly-occupied level into (2S+1) sublevels. The holes in the leads and on the sublevel form a spin-singlet state via higher-order processes, which leads to the Kondo effects depending on the parallel and antiparallel spin pair states.Lastly, we address inelastic quantum transport through an ASMM coupled to a single phonon mode in the low-temperature regime. At low temperature, the model exhibits Kondo-like physics which is different from QD and molecular magnet. The local density of states (DOS) presents not only main Kondo-like peaks but also phonon-induced satellite peaks. These peaks originate from the Kondo-like effect discussed in the main text. Moreover, they are related to the (2S+1) spin pair states in ASMM and the process of emitting phonons.