马约拉那零能模体系及其非阿贝尔统计的理论研究

Topological quantum computation based on nonabelian anyons has been designed to overcome quantum decoherence caused by local perturbation, hence is one of the most attractive schemes to realize fault-tolerant quantum computation. Its development, however, has been greatly hindered by the difficulty to control, or even find, elusive nonabelian anyons in real world. Majorana zero modes are one type of nonabelian anyons usually living in topological superconductors. In light of a series of recent experiments, performed on different platforms, which have confirmed the existence of Majorana zero modes, such systems have become the actual base for investigating topological quantum computation. Here, the next key development will be to demonstrate the nonabelian statistics associated with Majorana zero modes in laboratories. The proposed project will address several major theoretical questions closely related to this much-desired development. In particular, we will systematically study the origin of the low-energy quasi-particle excitations inside the topological superconducting gap universally seen in experiments, and further investigate their effect on the precision of nonabelian statistics measurement. We will also investigate the effect of interaction on Majorana zero mode systems in terms of their spectra and transport signatures. We expect that our investigations in this proposed project will have a significant impact on the development of Majorana zero mode systems towards realizing topological quantum computation.

基于非阿贝尔任意子的拓扑量子计算因其物理层面的纠错特性而成为实现高容错量子计算的一种极具吸引力的方案，但其发展却受限于非阿贝尔任意子的稀缺性。马约拉那零能模是非阿贝尔任意子的一类，其存在性已经于近期在不同的实验平台得到证实 。马约拉那零能模体系因此是现阶段研究拓扑量子计算的实际基础。而这方面研究的下一个关键是实际演示马约拉那零能模体系中的非阿贝尔统计。本申请项目旨在研究与此密切相关的理论问题，主要包括系统性探究马约拉那零能模体系的拓扑超导能隙内普遍存在的低能准粒子激发态的来源及其对非阿贝尔统计精度的影响，以及相互作用对马约拉那零能模体系的能谱和输运特征的影响。

本项目的主要目标是研究马约拉纳零能模系统在通向非阿贝尔编织统计演示实验的路径上存在的各种物理问题。这些问题包括对马约拉纳系统中带隙内量子态的深入研究、马约拉纳系统中的电子态退相干，以及用于测量该系统中多体量子态的输运特征和手段等。基于这些问题，在本项目支持下我们与合作者完成了数项工作，包括：1. 磁性原子体系中的Yu-Shiba-Rusinov能带理论，其能谱、拓扑与自旋特性，以及拓扑超导相下马约拉纳零能模的自旋性质；2. 通过无反射隧穿导致的零偏压电导峰对强自旋轨道耦合与超导的杂合体系中声子散射对电子相干性的影响的表征；3. 马约拉纳-约瑟夫森干涉仪与马约拉纳手征模式的量子相干性测量；4. 马约拉纳零能模在超导近邻与磁性杂化的拓扑螺旋边界态畴壁中的实现与首次实验观测。这些研究结果为我们进一步在总体目标方向上进行研究打下了良好的基础。