【作者】 杨宁；

【导师】 朱嘉麟；

【作者基本信息】 清华大学 ， 物理学， 2007， 博士

【摘要】 低维纳米结构中相互作用电子态的研究可以建立从少体到多体物理的桥梁,为未来量子器件利用和调控体系量子特性提供物理基础。本文研究磁场下半导体量子点结构中少电子基态及低能激发态的量子特性,揭示了磁场下量子点中少电子态由电子液体到电子晶体的转变特征,及其在电子自旋关联、纠缠和涡旋结构等量子特性上的反映;阐明了电子态涡旋结构与电子相互作用的关系;讨论了在双垒纳米环中通过电场调控电子间纠缠的基本方法。论文采用模型哈密顿量和精确对角化方法研究了无塞曼效应( Lande g因子为0)情况下,包含四个和五个电子的量子点在磁场下的量子行为。结果表明,自旋自由度给量子点中少电子由液体态到晶体态的转变带来新的特征:一是表现在体系的能谱结构上,不同自旋态在强磁场下形成自旋窄带,不同自旋最低态在强磁场下的角动量转变各自具有依赖于自旋的确定的关系;二是表现在电荷与自旋关联的特性上,发现自旋关联揭示出电子间的磁耦合,强磁场下不同自旋最低态的磁耦合存在规则的振荡,这是包含自旋自由度的旋转Wigner晶体态的特征;三是电子间的纠缠熵随磁场的变化在液-晶两相中有着不同的特征,两相中不同自旋态角动量成份的差别是造成纠缠特征不同的原因。论文对量子点中少电子态的涡旋结构进行了系统的分析,给出了在包含自旋自由度后利用条件单粒子波函数正确分析涡旋结构的方法。分析了不同种类涡旋的行为与电子间相互作用的关系,由此确定了其在降低电子间相互作用上的不同效果。揭示了孤立涡旋对降低短程相互作用没有任何效果的涡旋,是造成液相中特定角动量态缺失即角动量转变不规则的原因。论文从局域的Hartree-Fock轨道出发,构造了包含自旋的旋转Wigner晶体态的试探波函数,通过与精确对角化结果的比较,证明了这些解析的波函数可以准确地反映结晶态在磁场下的角动量转变和自旋关联特征。论文通过对双垒纳米环中两电子纠缠的研究,揭示了纳米结构中全同粒子纠缠的基本特性,分析了体系的对称性对纳米结构中粒子纠缠及其调控的重要作用,提出了利用纳米体系的结构和外电场参数对纠缠进行调控的基本方法,并分析了体系远红外谱测量在今后纠缠调控实验中的作用。更多还原

【Abstract】 The investigation on interacting electronic states in nanostructures can serve as abridge between few-body to many-body physics, and it is also the basis of controllingand utilizing quantum behaviors of the system in future quantum devices. In this thesis,we study the quantum behaviors of ground and low-lying excited states in few-electronquantum dots in magnetic fields. We investigate the characters of the few-electronstates in the transition from the electronic liquid to crystal states and mainly focus on thespin correlations, entanglements between electrons and the vortex structures in differentstates. The effects of the interaction between electrons on the vortex structures arestudied in detail. And the methods of controlling the entanglements between electronsin double-barrier nanorings by electric fields are also discussed.We employ the model Hamiltonian and the method of exact diagonalization tostudy the quantum behaviors of four- and five-electron quantum dots in magnetic fieldswith negligible Zeeman effect. It is found that the spin degree of freedom brings newcharacters to the liquid-crystal transition of the states. Without the Zeeman splitting,different spin states gradually form a narrow band within the process of crystalliza-tion due to the decreasing differences in exchange interactions of the states. With thechange of the magnetic field, the angular momentum transitions of the ground statesand the lowest states with different spins have corresponding rules. The spin corre-lations reveal the magnetic couplings between electrons and it is found that there areregular oscillations of the couplings in strong fields. The characters of entanglement en-tropies in liquid and crystal states are different due to their different angular momentumcomponents.The vortex structures of few-electron states in quantum dots are investigated byconditional single-particle wavefunctions. We present the methods of analyzing thevortex structures with the spin degree of freedom. By adjusting the interaction range,we can study the behaviors of different vortices and then reveal their different effectson reducing the interactions between electrons. It is found that the separated vorticeswhich have no use in reducing the short-range interactions may result in the absences of certain electronic states in the angular momentum transitions.Based on the unrestricted Hartree-Fock orbits, we construct the trial wavefunc-tions for the rotating Wigner crystals of electrons in quantum dots with spin degree offreedom. Comparing with the results of exact diagonalization, it can be demonstratedthat the trial functions satisfy the rules of angular momentum transitions and spin cor-relations of crystal states in magnetic fields.We also study the entanglements between two electrons in double-barrier nanor-ings to reveal the characters of entanglements between indistinguishable particles innanostructures. We analyze the symmetries of wavefunctions and present the methodsof controlling the entanglements by electric fields. The far-infrared spectroscopies ofthe system may provide the information of the energy level structures and be useful inthe experiments of controlling the entanglements.更多还原