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It has been proposed that an extended version of the Hubbard model which potentially hosts rich possibilities of correlated physics may be well simulated by the transition metal dichalcogenide (TMD) moir{e} heterostructures. Motivated by recent reports of continuous metal insulator transition (MIT) at half filling, as well as correlated insulators at various fractional fillings in TMD moir{e} heterostructures, we propose a theory for the potentially continuous MIT with fractionalized electric charges. The charge fractionalization at the MIT will lead to experimental observable effects, such as a large universal resistivity jump and interaction driven bad metal at the MIT, as well as special scaling of the quasi-particle weight with the tuning parameter. These predictions are different from previously proposed theory for continuous MIT.
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It is well-known that magnetic impurities can change the symmetry class of disordered metallic systems by breaking spin and time-reversal symmetry. At low temperature these symmetries can be restored by Kondo screening. It is also known that at the Anderson metal-insulator transition, wave functions develop multifractal fluctuations with power law correlations. Here, we consider the interplay of these two effects. We show that multifractal correlations open local pseudogaps at the Fermi energy at some random positions in space. When dilute magnetic impurities are at these locations, Kondo screening is strongly suppressed. We find that when the exchange coupling J is smaller than a certain value J*, the metal-insulator transition point extends to a critical region in the disorder strength parameter and to a band of critical states. The width of this critical region increases with a power of the concentration of magnetic impurities.
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