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Peierls Instabilities in Covalent Structures

We study the instabilities of p-bonded systems with a particular emphasis on the structure of group-V and -VI elements. We show that the trivalency of As (respectively divalency of Se and Te) is due to the Peierls instability of a half-filled band (respectively two-third-filled band). A moment calculation shows that the periodicity is not a necessary condition for the Peierls instability. Consequently, the trivalency of As (respectively, divalency of Se, Te) also holds in disordered structures (liquid, amorphous structures), as has been shown experimentally. We also study the pressure dependence of the instability: a bifurcation point is observed for a given pressure, above which no distortion appears.