Keywords: 
• 拓扑绝缘体 /
• 量子输运 /
• 普适电导涨落 /
• 贝利相位

Abstract: 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 magnetoconductance 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 universality. For a single TSS, the applied magnetic field will drive the system from a Gaussian symplectic ensemble into a Gaussian unitary ensemble. It results in a √2 fold increase of the UCF amplitude. However, the experiment reveals that the UCF amplitude is reduced by 1/√2. This is contradictory to the theoretical prediction. Actually, there are two TSSs and they are coherently coupled to each other in TIs since the sample’s thickness is smaller than its bulk dephasing length. This leads to a Gaussian orthogonal ensemble of the intersurface coupling system without an external field. In such a case, the UCF amplitude will be reduced by 1/√2 with field increasing. It is consistent with the experimental result. Finally, the other progress on UCFs is discussed, and the general outlook is also mentioned briefly.