æ¥å人ïŒãçåè£ ææïŒéŠæž¯ç§æ倧åŠïŒ æ¥å人æèŠïŒ Inthis talk, I will start with the conventional wisdom of the Andersonlocalization transitions. Namely, allsystems can be classified into three ensembles: the Gaussian orthogonalensembles (GOE) when a system has both time-reversal and spin-rotational symmetries;the Gaussian unitary ensembles (GUE) when a system has neither time-reversalnor spin-rotational symmetries; and the Gaussian symplectic ensembles (GSE)when a system has time-reversal symmetry, but without spin-rotational symmetry.At the critical dimension of 2, no extended states exist in GOE at an arbitraryweak disorder, and extended states could exist in a GSE or a GUE when a strongperpendicular magnetic field is applied to drive the system into quantum Hallregion. Then I will argue the intrinsic inconsistency of this standardpicture. It turns out that spin-orbitinteractions play a crucial role. The types of Anderson-localizationtransitions (metal-insulator transitions) in a two-dimensional system aresensitive to the types and strength of spin-orbit interactions. I will presentseveral simple models that support Berezinskii-Kosterlitz-Thouless typetransition from a band of localized states to a band of critical states; or aBerezinskii-Kosterlitz-Thouless type transition from a band of conventionalextended states to a band of critical states. In contrast to the conventionalwisdom, I will also provide the evidences that support the existence ofextended states in a GUE at a weak magnetic field. This work is supported by the NationalNatural Science Foundation of China (Grants No. 11774296 and 1974296) and HongKong RGC (Grants No. 16301518, 16301619 and 16300117). æ¥å人ç®ä» çåè£ïŒéŠæž¯ç§æ倧åŠç»èº«ææïŒ1984幎æ¯äžäºæŠæ±å€§åŠç©çç³»ïŒ1990幎åšçŸåœçœåœ»æ¯ç¹å€§åŠ(Universityof Rochester)è·å士åŠäœã ç 究æ¹åïŒåèæç论ïŒç 究é¢åå
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