Shot Noise Of Coherent Transport In A Quantum Coupled Device

The research on shot noise in mesoscopic size devices has always been a very active research field.With the rapid development of electronic science and technology this research field is more closely related to our actual life.In recent years,many kinds of mesoscopic devices have been successfully prepared in the laboratory.Such as quantum dots,quantum wires,ferromagnetic-semiconductor-ferromagnetic heterojunctions,and carbon nanotubes.Some of the new phenomena and effects of these low dimensional mesoscopic systems have aroused people's interest and attention.At the end of last century,the discovery and the successful preparation of carbon nanotubes provide a new material for nano devices.With the development of the research on carbon nanotubes,it is found that carbon nanotubes have excellent properties in mechanics,thermodynamics,optics,electromagnetism and acoustics.These make carbon nanotubes have a very broad application prospects.Electronic Science and technology is highly developed now.The design and research of carbon nanotube based electronic devices is particularly important.With the continuous discoveries of new materials,various research fields in Physics is expanding constantly.Further research on graphene,topological insulator and topological superconductor,make Majorana fermion,which is predicted by Italy physicist Ettore Majorana,into more people's field of vision.In the study of the electrical properties of materials,systems,or devices,the current,conductance and shot noise in the system are usually studied.And compared with the conductance,the noise can give more detailed information of the system we studied.So we focus our attention on the study of the shot noise in the system or device.In this paper,we first introduce several concepts related to our research.Then the theoretical methods used in the analysis and calculation are given.After that we introduce the current,conductance,shot noise and Fano factor in different systems.Finally,the paper is summarized,and the future development in this field is prospected.In the first chapter of this paper,we first introduce the basic concepts of mesoscopic transport.After that a brief review of the discovery of carbon nanotubes is described,and the structure and properties of carbon nanotubes are summarized and summarized.In the third section of this chapter the development and research of Majorana fermions were simply introduced.In the fourth section,the concepts of thermal noise and shot noise are introduced.In the fifth section,the framework of the whole paper is given.In the second chapter,we introduce the theoretical methods that used in our work.From the definition of Green's function,the non-equilibrium Green's function is introduced.The perturbation theory of non-equilibrium statistics is based on the Green's function in the complex series.Because the current,conductance and other observable measurements are related to real time Green's function,we introduce the Langrenth theorem which is the bridge connecting the two as well as the relevant Dyson equation.After that,we briefly explain the solving process of Green's function by employing the equation-of-motion.Based on these,at the end of this chapter,we detail describes the general idea to find out the shot noise of the system.Based on the Hamiltonian of the system,using the continuity equation and Heisenberg movement equation,fund the current operator in the system,then with the Current association function and the Green's function,eventually find the expression of shot noise.In the third chapter,the shot noise in a toroidal carbon nanotube interferometer under the perturbation of a rotating magnetic field has been investigated.A general shot noise formula has been derived by calculating the current correlation.It was found that photon absorption and emission induce novel features of dynamic shot noise.The oscillatory behavior of shot noise and Fano factor vary with the Aharonov-Bohm(AB)magnetic flux,and they are sensitively dependent on the Zeeman energy,frequency of RMF,and source-drain bias.By adjusting the Zeeman energy,the AB oscillation structures of shot noise and Fano factor show valley-to-peak transformation.The shot noise increases nonlinearly with increasing the Zeeman energy and photon energy.The enhancement and asymmetry of shot noise can be attributed to the spin-flip effect.In the fourth chapter,the shot noise of a toroidal carbon nanotube interferometer coupled with Majorana fermions is deduced from evaluating the current correlation.Many novel channels are opened for electrons to transport,and the energy gap of the semiconducting toroidal carbon nanotube becomes narrower.The Majorana fermions cause additional current correlations among the normal tunneling currents and Andreev reflection currents,and hence the shot noise and Fano factor are enhanced.The conductance,current,and shot noise are modified by Majorana fermions to exhibit different oscillation and resonance structures.The detailed behaviors of these quantities are quite different from the metal and semiconducting toroidal carbon nanotubes.In the fifth chapter,the dynamic properties of a quantum dot(QD)coupled with Majorana fermions under the perturbation of microwave fields(MWFs)have been investigated through the nonequilibrium Green's function(NGF)technique.The photon-assisted differential conductance,current,shot noise,and Fano factor have been evaluated in the Nambu representation.In the absence of MWFs,three steps exhibit in the current-voltage characteristics to show the electron tunneling through normal channel and Andreev reflection induced channels.Correspondingly,the differential conductance displays tree large resonant peaks,where the Andreev reflections dedicate to each resonant peak evidently.As the photon irradiation is imposed on the Majorana fermion coupled system,each photon-induced side channel is accompanied with Andreev reflection induced channels,and novel current steps are generated.The photon perturbation induces side resonant conductance peaks and the Andreev reflections induce novel peaks around the photon-assisted peaks.The irradiation of photons suppresses the central conductance,while by providing novel side conductance peaks as compensation.The shot noise formula has been derived through evaluating the current correlation,where the current correlations among normal transmission,local and cross Andreev reflections contribute to the total noise.The perturbation of MWFs induces dynamic effect in shot noise,which is nonzero when the source-drain bias is removed.The interaction of Majorana fermions enhances shot noise evidently compared with the system without the interaction of Majorana fermions.The shot noise is enhanced by increasing the interaction strength of Majorana fermions evidently.The photon perturbation induces photon-assisted Andreev reflections,and the shot noise is suppressed compared with the system without MWFs.Under the irradiation of MWFs,the Fano factor exhibits novel suppressing steps due to the photonassisted Andreev reflections.