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研究了一维Fibonacci准晶势调制下的p波超导体下的拓扑相变和局域化性质. 在Fibonacci准晶势调制下, 通过计算$Z_2$拓扑不变量确定了系统的拓扑相图. 分析相图指出在Fibonacci准晶势调制下, 系统可以由拓扑平庸超导相进入拓扑安德森超导相. 进一步分析发现, 在某些参数下, 系统会发生多次拓扑安德森超导相转变并伴随零能态的出现. 此外, 还研究了系统的局域化性质, 通过分析分形维度、平均逆参与率序参量, 发现Fibonacci准晶势诱导的拓扑安德森超导相, 其体态的波函数表现出多重分形行为, 这与随机无序诱导出来的传统拓扑安德森超导相完全不同. 该研究结果为一维p波超导体中拓扑相变和局域化转变的研究提供了一些新的理解和参考.
The topological phase transitions and localization properties in a 1D p-wave superconductor under Fibonacci quasi-periodic potential modulation are investigated in this work. By calculating the Z2 topological invariant, the topological phase diagram of the system is determined numerically. It is found that the system can transition from a topologically trivial phase to a topological Anderson superconductor phase through the Fibonacci quasi-periodic modulation. Moreover, under certain parameters, the system undergoes multiple topological Anderson superconductor phase transitions, accompanied by the emergence of zero-energy modes. However, in the case of strong disorder, the topological Anderson superconductor phase is destroyed, indicating that the topological Anderson superconductor phase can be induced only within a finite range of parameters. Furthermore, by calculating and analyzing the fractal dimension and the mean inverse participation ratio (MIPR) order parameter, the localization properties of the system are analyzed. The results show that regardless of how the disorder intensity increases, the fractal dimension values of most eigenstates always remain within a range of 0–1. Subsequently, the variations in the fractal dimensions of all eigenstates for different system sizes are studied. The results show that the fractal dimension values of most eigenstates are away from 0 and 1. These results indicate that the wavefunction in the bulk of the topological Anderson superconductor phase induced by Fibonacci quasi-periodic potential is a critical state wavefunction, with the system overall being in a critical phase. The stability of the critical phase is confirmed by scale behavior of MIPR as shown in Fig. (a). It differs from the traditional topological Anderson superconductor phase induced by random disorder or AA-type quasi-periodic disorder. The results provide new insights into and references for studying topological phase transitions and localization transitions in 1D p-wave superconductors. 
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