基于多带超导体的超导-绝缘相变及量子同步研究

This is a research proposal aimed to investigate the superconducting-insulating phase transition and quantum synchronization in multi-band superconductors, such as the magnesium-boron, the high Tc cuprate, and the iron-based superconductors. By diagonalization the Bogoliubov-de Gennes model Hamiltonian self-consistently, we will show that different orderings, in particular, the equal spin triplet and the spin-singlet correlations can coexist due to the intra- and inter-band coupling associated spin-split and spin-flip scatterings, and the spin-orbit interactions. Driven by external magnetic fields and the bias voltage/current, an electronic texture- superconducting domains with correlation wave functions of different orderings immersed into a weak-link matrix forms. The system can be described in terms of two characteristic energy scales, that is, the Josephson tunneling energy and the Coulomb blockade energy. While the system is expected to undergo a superconducting-insulating quantum phase transition by tuning the magnetic fields and the bias voltages, the phase boundary separating the superconducting and insulating phases is in need to be specified. More profound, in the vicinity of the transition, a stable domain structure forms when the synchronization of the phase of the pair correlations at the domains across the whole system is realized. Therefore, a spin-triplet state with total spin projection of zero must exist at the domain boundaries. Such a bound state with an even orbit quantum number has to be an odd symmetry in frequency, as required by the Pauli exclusion principle, implying the existences of the zero energy bound states that have particle-hole symmetry. We will prove that the zero energy bound states can be classified as to the Majorana fermions(MF) states in the doped superconductors with the Fermi surface having an odd number of time-reversal invariant k points in the Brillouin zone where the zero energy mode excitation present. We will clarify that the MF state is stable against interactions with nodal excitations and with impurities and has a topological invariant Berry flux of half the superconducting flux quanta. As a well-separated pair of Majorana bound states defines a degenerate two-level system-a qubit. The 2N Majorana bound states define N qubits that store the quantum information nonlocally. Implementing unitary operations on the state vectors enable adiabatically interchanging the quantum information. Bringing vortices i and j back together allows the quantum state associated with each pair to be measured. We expect these can provide a physical platform that has profound implications for quantum information processing or quantum computation.

本项目主要研究基于多带超导体的超导-绝缘量子相变与量子同步问题。将建立描述多带超导如MgB2、YBa2Cu3O7、 铁基超导体的模型哈密顿形式表述；并由此推导对不同序的关联函数及其量子态时间演化方程(Bogliubov-de Gennes方程)和自洽迭代条件. 通过自洽叠代将模型哈密顿对角化. 研究在物理参量空间(如磁场、偏置电流、工作温度) 量子态演化过程. 深刻理解支配多带超导-超绝缘量子相变物理过程,揭示其输运规律. 探索实现量子态相位非局域量子同步的物理条件.将明确回答零能Majorana束缚态、分数量子磁通和涡旋-反涡旋基态存在性问题; 建议并论证基于零能本征束缚对态的量子比特及其量子态调控方案；为拓扑量子计算提供物理演示平台.

本项目重点研究多带超导体中量子态随磁场、电场和温度等物理参量的演化规律及其量子相变和同步。从Gor’kov 传播子方程出发，推导了适合硼化镁双带超导体的微观Ginzburg-Landau 方程；基于双带紧束缚模型哈密顿的推导出适合高温超导体d-波的Bogliubov de Gennes 方程。理论分析和数值模拟得到一系列重要结论；主要包括：（1）预言了硼化镁双带超导体中涡旋-反涡旋对和半整数量子磁通存在性；揭示了外磁场下涡旋态三角格子与四方格子共存和相变。（2）揭示了d-波超导环中磁场诱导的超导-绝缘相变过程和Majorana 粒子态的存在性问题；同时，在d-波超导/半金属/超导结中重点考虑自旋-轨道相互作用过程以描述自旋单态配对态与奇频三重态配对态间转换机制；明确了自旋三重态零能模与界面散射的关系。（3）对自旋三重态p波超导体的BdG方程的自洽求解， 通过引入双带超导序相互竞争机制，预言并很好解释了实验上观测到的反常量子振荡现象。此外，证明了对应涡旋束缚态的零能峰以及各能级占据态的粒子密度空间分布分别与所建议的奇频超导配对应能级的分布完全吻合；强有力地支持奇频自旋三重偶宇称超导配对的存在。（4）表面非局域散射效应将诱导自旋-轨道相互作用和自旋倒易过程，进而在超导环环边界形成相反手性的边缘态和自旋流。手性边缘态和自旋单态配对态之间的相互竞争会导致一系列依赖于轴向磁场的量子相变和间隙性巨涡旋超导态。有趣的是，相邻角动量量子数（或称环绕数）的巨涡旋态发生相变时，系统的等效磁矩跳跃量总表现为一个常量，为波尔磁矩的四分之一。. 上述研究成果促进了人们深入理解多带超导体中量子态演化与相变、 对称破缺诱导的Majorana束缚态条件和判据有着重要的价值；对进一步的依据多带超导体中新奇量子态，如Majorana束缚态的操纵和相应自旋电子器件的研制具有参考意义。