Most books on strongly correlated electrons claim that when the number of itinerant electrons is small and the screening length is large, that the system becomes "strongly correlated", (i.e. the independent electron approximation breaks down). If this is the case, why isn't doped silicon (or some other semiconductor/insulator) a strongly correlated electron system at low temperature where there are no thermal carriers? What are the critical ingredients that make a system unwilling to abide by the independent electron approximation?
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Strong correlation usually come with localized $d$ or $f$ orbitals in (or close to) a Mott insulating state, where the charge degrees of freedom is gapped by interaction, and the system become insulating even at half-filling. Silicon has no localized orbitals and it is a band insulator. Its valence band is fully filled, not half-filled, which means it can never approach to any Mott phase, and hence not strongly correlated. The doped electrons/holes in the silicon are just fermions with residual interactions, which can be well understood by free-fermion band theory, no fractionalization phenomenon (like spin-charge separation) is expected in silicon.
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$\begingroup$ Is this another way of saying that because Si has p-orbitals, the electron wavefunction overlap between sites is high and therefore the electrons will necessarily have a higher kinetic energy (than d-orbitals)? And that this kinetic energy will not give rise to any sort of localization even if the Thomas-Fermi wavelength is large? $\endgroup$– XcheckrNov 18, 2014 at 6:29
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$\begingroup$ @Xcheckr More itinerancy and better screening is just part of the story. The most important point to me is that Si is a fully filled band insulator, instead of a half-filled Mott insulator (or a partially filled orbital selective Mott insulator). The electron filling is important, because a fully filled band insulator effectively has no low-energy degrees of freedom from the electron sector, but strong correlation basically means a lot of different low-energy degrees of freedoms inter-winded together, which can not be realized with a band insulator. $\endgroup$ Nov 20, 2014 at 3:12
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$\begingroup$ This is why I was wondering in particular about doped Si. Doped Si does have low energy degrees of freedom. But my guess is that it is because the band is a p-band that it is not "strongly correlated". Anyway, thanks a lot for you help. $\endgroup$– XcheckrNov 20, 2014 at 16:24