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Disorder, in the form of impurities, defects, vacancies, etc., is inevitable in real materials, and can be of vital importance in certain physical systems. For example, the integer quantum Hall effect is born out of a conspiracy of disorder-induced localization and the phenomenon of Landau level quantization. And in the study of topological materials without Landau levels, i.e., the topological insulators, which have been the central focus of the condensed matter community in the past decades, researchers revealed a mechanism mediated by disorder that can drive an ordinary insulator into topological one. This phenomenon is termed as topological Anderson insulator. 

On the other hand, originated from TKNN theorem that shed light on the profound connection between integer numbers characterizing the topological properties of fiber bundle on some base manifold and Hall conductance of integer quantum Hall insulator, an entire classification theory has been established for gapped systems, and numerous efforts are devoted to experimental examination. However, the long-standing mystery of whether a gapless system can host a half-quantized topological number had remained inconclusive until a recent experiment by Mogi et al. provided convictive evidence.

In this talk, I will provide a brief overview of the study of disordered electronic systems, with a special focus on topological quantum systems. Building upon Mogi's experiments, I will demonstrate the impact of nonmagnetic impurities on the recently discovered half-integer quantum Hall metal phase. At the end of this talk, I will provide some remarks on the distinction between the half-integer quantum Hall metal and the integer quantum Hall insulator.