Full Counting Statistics Of Electron Transport Thought Single-molecule Magnet

With the development of the micro-fabrication techniques and ingenious experimental schemes for the setup of single-molecule devices, the feasibility of single-molecule devices has been experimentally demonstrated, and the corresponding experimental control over these systems is also rapidly improving. Especially, the coupling between electron and the spin degrees of freedom of single-molecule magnet (SMM) has experimentally confirmed by Heersche et al., which has opened up a new field--molecular spintronics, which combining the promising concepts of molecular electronics and spintronics, and the magnetic single-molecule transistors have been proposed as candidates for the experimental realization of molecular spintronics. Interestingly, the presence of specific internal molecular degrees of freedom can lead to numerous novel quantum transport phenomena that go beyond the physics observed in larger nano-structural objects such as quantum dots or carbon nanotubes, and provide the opportunity to study and understand the related electronic transport properties on a fundamental level. In addition, SMM, which has a long coherence time, has also proposed as candidates for realizing quantum qubits in quantum computation. Therefore, the electron transport through SMM has attracted much attention and become an active subject of molecular electronics due to the hope of applications in molecular spintronics and quantum information technology.Alternatively, compared with the conductance measurements, the current noise can sometimes provide deep insight into the nature of transport mechanisms, in particular, full counting statistics can provide the full information about the electron transport through the system, i.e., all zero frequency current-correlation functions, and new techniques based on carbon nanotubes have been proposed for the possible realization of real-time measurement of single-electron transfers through an individual SMM. Thus, the FCS of electron transport through a SMM or molecular junction has been attracting much interest. However, the investigations of current noise spectrum and FCS in SMM are still at primary stage due to the complexity of the SMM's internal level structure. Therefore, the study of FCS of electron transport through SMM has important scientific significance because that may provide the opportunity to understand the related quantum transport phenomena and reveal new physical effects on the molecular level. The predictions regarding of high order current cumulants may be helpful in designing magnetic molecular functional devices and allow for experimental tests in the near future. In this thesis, we theoretically study the FCS of electron transport through a SMM weakly coupled to two metallic electrodes above the sequential tunneling threshold by means of an efficient particle-number-resolved quantum master equation and the Rayleigh-Schro-dinger perturbation theory. We put emphasis on the effects of the external conditions (the magnetic field, gate voltage, left-right asymmetry of the SMM-electrode coupling), the Coulomb interaction between two electrons in the lowest unoccupied molecular orbital, the angle between the external magnetic field and easy-axis of the SMM, and the transverse anisotropy on the FCS in SMM, in particular super-Poissonian noise, and explain the origin of the related physical mechanisms. Our main results are as follows:Firstly, it is demonstrated that for the case of U→∞the internal level structure of the SMM and the left-right asymmetry of the SMM-electrode coupling play a crucial role in the super-Poissonian statistics of electron transport. In particular, above the sequential tunneling threshold the shot noise depends not only on the gate voltage by which the internal level structure of the SMM can be tuned but also on the left-right asymmetry of the SMM-electrode coupling. Moreover, it was found that the temperature dependence of super-Poissonian shot noise also depends on the left-right asymmetry of the SMM-electrode coupling. The occurrence-mechanism of super-Poissonian shot noise can be qualitatively attributed to the competition between fast and slow transport channels.Secondly, for a realistic SMM system, the Coulomb interaction is usually finite and thus one should consider the effect of the finite Coulomb interaction on FCS. For finite U the FCS, differing from U→∞, shows a symmetric gate-voltage-dependence when the coupling strengths with two electrodes are interchanged, which can be observed experimentally just by reversing the bias-voltage. Moreover, we find that the effect of finite U on shot noise depends on the internal level structure of the SMM and the coupling asymmetry of the SMM with two electrodes as well. When the coupling of the SMM with the incident-electrode is stronger than that with the outgoing-electrode, the super-Poissonian shot noise in the sequential tunneling regime appears under relatively small gate-voltage and relatively large finite U, and dose not for U→∞; while it occurs at relatively large gate-voltage for the opposite coupling case. The formation mechanism of super-Poissonian shot noise can be qualitatively attributed to the competition between fast and slow transport channels.Lastly, we consider a more universal model of the SMM. In the present actual break-junction and electromigration experiments, the angle of the external field with respect to the easy axis of the SMM is unknown and cannot be controlled. If the angle between the easy axis and magnetic field is not small, the transverse Zeeman energy may compare with the easy-axis anisotropy energy. This implies that the molecular eigenstates are not approximate eigenstates of the spin component along any axis, which leads to the failure of the perturbation calculation. Therefore, we have studied theoretically the FCS of electron transport through a single-molecule magnet (SMM) with an arbitrary angle between the applied magnetic field and the SMM's easy axis based on the exact numerical diagonalization of the SMM Hamiltonian and the completely numerical calculation of the high order current cumulants in terms of the Rayleigh-Schrodinger perturbation theory. In the absence of the small transverse anisotropy, when the coupling of the SMM with the incident-electrode is stronger than that with the outgoing-electrode, i.e.,ΓL>>ΓR, the maximum peak of shot noise firstly increase and then decrease with increasingθfrom 0 toπ/2. In particular, the shot noise can reach up to super-Poissonian value from sub-Poissonian when considering the small transverse anisotropy. ForΓL<<ΓR, the maximum peaks of the shot noise and skewness can be reduced from super-Poissonian to sub-Poissonian value with increasingθfrom 0 toπ/2;the super-Poissonian behavior of the skewness is more sensitive to the small 9 than shot noise, which is suppressed when taking into account the small transverse anisotropy. These characteristics of shot noise can be qualitatively attributed to the competition between the fast and slow transport channels. The predictions regarding of theθ-dependence of high order current cumulants are very interesting for a better understanding electron transport through SMM, and will allow for experimental tests in the near future.