Effect Of Classical Chaos On Spin Transport In 2D Mesoscopic System

In resents decades,the problem that the correspondence and behavior of classical chaos in its quantum mechanics counterpart has been attracting common concern.The correspondence between the classical scattering process and the quantum transport in an open billiards is indeed one aspect of this research,and the latter can be investigated experimentally basing on micro-nano technology.We paid our main attention,in this thesis,to a theoretical study of the manifestation for the classical dynamics of a mesoscopic quantum dots with specific shape in a spin-polarized transport process.In the first chapter,we introduced the classical chaotic scattering,electronic transport and spin transport in two-dimensional mesoscopic system,and besides explained the unpredictability of deterministic system.We also showed the mesoscopic two-dimensional quantum system with spin-orbit interaction,with which we investigated the spin transport behavior of the electrons to capture the quantum“foot print” of the classical chaos on the spin degree of freedom.In the second chapter,we described the theoretical basis and calculation algorithm of spin-resolved ballistic quantum scattering and gave the spin-resolved scattering formalism.Specifically,in the front part,we gave the spin-resolved current and shot noise expressed,both of which can be expressed in terms of scattering matrix.We need to emphasize that all the properties of the transport process are encoded into the scattering matrix.In the latter two parts,two kinds of discrete algorithms were discussed for the purpose of the calculation of the scattering matrix.In the third chapter,we investigated the behavior of classical chaotic dynamics on spin polarization of scattering state.For four kinds of open quantum dots with different levels of classical chaos,we discussed the polarization property of the outgoing state for polarized electrons after scattering through these mesoscopic scattering cavities,respectively.The numerical results shown that for weak spinorbit interaction,the more chaotic the dynamic properties of the scattering cavity are,the better the polarization of the exit state is maintained,while for not too weak spin-orbit interaction,the more chaotic the dynamic properties of the scattering cavity are,the more the polarization of the exit state is destroyed.By these results,based on a piecewise cascade precession of spin polarization vector in a momentum-dependent equivalent “magnetic field”,we gave a semiclassical explanation which is consistent with the result of the quantum counterpart well.This fully confirms the explicit manifestation of classical chaos dynamics on the spin degree of freedom.In the fourth chapter,we mainly investigated the single particle spin-orbit entanglement and the important role of classically chaotic dynamics played in.We pointed out that the von Neumann entropy describing the entanglement degree of the spin-orbit and the physical quantity describing the coherence degree of the spin state,i.e.the purity,can both be expressed as a function of the norm of the spin polarization vector.After that,we directly investigated the cosine-shaped scattering cavity of which the classical dynamic properties can be changed continuously by changing the shape parameters,so that the spin polarization vector of the incident electrons after being scattered out differ from each other.We found that the more chaotic the system is,the more coherence is lost and the larger the entanglement entropy is increased.Our results provide a new understanding of the role of classical chaos played in spin quantum phenomena.In the fifth chapter,we generalized the Fano resonance encountered widely in transport process and gave the analytical formulas to describe the spin Fano resonance in theory.At the same time,we shown that both the spin-resolved transmission coefficient and the spin polarization vector can have the form of Fano resonance.Although our derivation was based on perturbation theory,the comparison between numerical results and theoretical results fully confirmed the rationality and efficiency of our theoretical results.Then,combining the shape dependence of transport properties and the different performance of Fano resonance on different classical dynamics,we studied the spin transport of polarized electrons in a bow-shaped quantum dot.A scheme to control the polarization of the outgoing state by changing its dynamic properties was proposed at last.This scheme is totally different from the ordinary scheme of spin control in principle,which can provide a different way of thinking for the design of spin devices.Finally,in the sixth chapter,we made a summary and a simple prospect.