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A researcher who coauthored an examination of the Mott criterion across different metal-insulator transitions. The work treats the relation between the effective electronic size and critical carrier concentration as a common thread between doped semiconductors and correlated compounds. Its discussion of chromium-doped vanadium oxide highlights how magnetic order and conducting behavior can change together.^[ref]

A coauthor of a study of the Mott criterion and the metal-insulator transition. The paper considers vanadium oxides alongside doped semiconductors, testing whether a criterion based on electronic length and concentration remains informative in strongly interacting materials. Such comparisons help separate a useful organizing estimate from a complete microscopic explanation of a transition.^[ref]

A coauthor of a study examining how widely the Mott criterion applies to the metal-insulator transition. The criterion compares a characteristic electronic length with the spacing implied by the carrier concentration. The paper discusses both doped semiconductors and strongly interacting compounds, emphasizing that the same compact relation must be interpreted in the physical setting of each material.^[ref]

For a hydrogenic donor state, dielectric screening replaces ${ϵ}_0$ by ${ϵ}_r{ϵ}_0$ and the electron mass by the band effective mass. The characteristic orbital radius is thereforeUsing $a_0=0.0529177\mathrm{nm}$ givesA donor-state overlap estimate compares this radius with the mean dopant spacing $d\sim N_D^{-1/3}$. Taking $d\sim a^{\ast }$ yieldsThere is no sharp geometrical onset: hydrogenic wavefunctions have exponential tails. If “overlap” is defined by neighbouring orbital diameters touching, $d\sim 2a^{\ast }$, the corresponding estimate is $4.88\times 10^{23}{\mathrm{m}}^{-3}$, smaller by a factor of eight. These are conventions for the onset of appreciable orbital overlap, not an exact critical density for a metal-insulator transition.

A Peierls transition, named for Rudolf Peierls, is a metal-insulator transition caused by a Peierls distortion of an initially metallic chain.^[ref] A modulation at $2k_F$ mixes states near opposite Fermi points and can open a band gap at the Fermi energy. At half filling with one atomic orbital per chemical atom, this modulation doubles the original lattice period and alternates strong and weak bonds. In a weak-coupling zero-temperature description, the Peierls energy gain is proportional to $-({\delta }^2/t)\ln (t/|\delta |)$ whereas the elastic cost is proportional to ${\delta }^2$, where $t>0$ is the undistorted hopping strength and $\delta$ its small alternating change. The logarithm permits a distortion at arbitrarily weak coupling in the ideal model. Finite temperature, finite size, interchain coupling and thermal fluctuations matter for a real transition; strictly one-dimensional reasoning alone does not establish finite-temperature long-range order.