Gapless State of Bismuth-Type Semimetals

It is shown that in semimetals of the bismuth type under certain conditions the direct energy gap in the vicinity of the L point of the Brillouin zine can be closed. The energy spectrum is found for values of the parameters near the gap annihilation point (gamma = gamma 0): epsilon = P-z(2)/2M(1) +/- root[gamma - gamma(0) + (p(z)(2)/2m(2))](2) + (v(x)P(x))(2) + (v(y)p(y))(2) + lambda(2) where the parameter gamma - gamma(0) can be altered by variation of the external pressure or of the alloy concentration; m(1) > m(2); the z axis corresponds to the direction of "elongation" of electron "ellipsoid"; and lambda similar to (gamma(o) - gamma)(3/2) for gamma(o) - gamma > 0. It is shown that it is permissible to assume gamma - gamma(o) approximate to for pure bismuth. The qualitative and quantitative characteristics of the spectrum, including the optical properties, are well explained in this case. The role of the interaction of electrons in the gapless state is analyzed (the energy maximum at the T point is below the band contact level in the vicinity of the L point). The carrier mobility in the gapless and semiconducting states is found as a function of the temperature, the parameter gamma - gamma(o), and the number of carriers injected by alloying.