Gapless state of bismuth-type semimetals

Abstract

It is shown that in semimetals of the bismuth type under certain conditions the direct energy gap in the vicinity of theL point of the Brillouin zine can be closed. The energy spectrum is found for values of the parameters near the gap annihilation point (γ=γ_t0):

$$\varepsilon = p_z^2 /2m_1 \pm \sqrt {\left[ {\gamma - \gamma _0 + ({\text{p}}_{\text{z}}^{\text{2}} /2m_2 )} \right]^2 + (v_x p_x )^2 + (v_y p_y )^2 + \lambda ^2 } $$

where the parameter γ−γ₀ can be altered by variation of the external pressure or of the alloy concentration;m ₁>m ₂; thez axis corresponds to the direction of “elongation” of electron “ellipsoid”; and γ∼(γ₀−γ)^3/2 for γ₀−γ>0. It is shown that it is permissible to assume γ−γ₀≈0 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 theT point is below the band contact level in the vicinity of theL point). The carrier mobility in the gapless and semiconducting states is found as a function of the temperature, the parameter γ−γ₀, and the number of carriers injected by alloying.