中文摘要：

拓扑绝缘体因其无能量耗散的拓扑表面输运而备受关注，揭示拓扑表面态因其π的贝利相位而产生的拓扑输运现象，将有助于拓扑绝缘体相关器件的应用开发．本文回顾了普适电导涨落（UCF）揭示拓扑绝缘体奇异输运性质的研究进展．通过调控温度、角度、门电压、垂直磁场和平行磁场等外部参量，实现了对拓扑绝缘体的UCF效应的系统研究，证实了拓扑绝缘体中二维UCF的输运现象，并通过尺寸标度规律获得了UCF的拓扑起源的实验证据，讨论了拓扑表面态的UCF的统计对称规律．从而实现了对拓扑绝缘体UCF效应的较为完整的理解．

英文摘要：

As an exotic quantum condensed matter, the topological insulator （TI） is a bulk-insulating material with a Dirac- type conducting surface state. Such a dissipationless transport of topological surface state （TSS） is protected by the time- reversal symmetry, which leads to the potential applications in spintronics and quantum computations. Understanding the topological symplectic transport of the Dirac fermions is a key issue to the study and design of the TI-based devices. There are many transport properties about Dirac fermions. And universal conductance fluctuation （UCF） is one of the most important transport manifestations of mesoscopic electronic interference. So the UCF effect in TI is a very meaningful research field It can provide an intriguing and special perspective to reveal the quantum transport of TSSs In this review, we introduce the research progress on the UCF of TSSs in a pedagogical way We review the achievements and the existing problems in order to inspire future research work. We start this review with the basic UCF theory and the experimental observation. The UCF has been observed in TI earlier, but weather it originates from TSS has not been further studied. Then a series of work is carried out to prove the topological nature of UCF in TI Firstly, the UCF phenomenon in TIs is demonstrated to be from two-dimensional （2D） interference by magnetoeonductance measurements. But the residual bulk state and the 2D electron gas （2DEG） on the surface can also bring about the 2D UCF The field-tilting regulation helps us exclude the distribution from the bulk And the classic self-averaging of UCF is investigated then to obtain the intrinsic UCF amplitude. By comparing with the theoretical prediction, the possibility has been ruled out that the 2D UCF may originate from the 2DEG So its topological nature is demonstrated. Secondly, we discuss the UCF effect in TI by a macroscopic perspective, i.e. the statistical symmetry of UCF, which should be more concise and reflect its universali