A pseudopotential calculation of the Fermi surface and of magnetic breakdown effects in thallium

Abstract

We have parameterized the Fermi surface of thallium by using a local pseudopotential model Hamiltonian with spin effects included in the initial matrix elements. The pseudopotential coefficients are adjusted to fit the existing de Haas-van Alphen (dHvA) data and we find U_10macron10 = -0.1058, U₀₀₀₂ = -0.0603, U_10macron11 = -0.0429, U_10macron12 = -0.0195, λ_5p = 0.1130, all in Ryd. These values give a band structure which agrees very well with experiment, having a maximum error of 3 × 10^-3 Ryd at a Fermi energy of 0.6110 Ryd. The interpretation by Capocci et al. of their recent dHvA data as due to a fifth zone dumbbell at H is confirmed, and the very small orbits which they observed are reliably assigned to fourth zone pockets along capital GammaM. Recent cyclotron resonance data by Shaw and Everett are shown to agree well with our model. We use our model to calculate magnetic breakdown fields for breakdown across the AHL plane and obtain values reasonably consistent with the existing dHvA data, but much larger than those deduced from the magnetoresistance. We find B₀ = 90 kG for the open orbit along [11macron20], whereas Young finds B₀ = 10.3 kG by fitting his magnetoresistance data. Our calculations confirm that the fourth zone posts do not contact the capital GammaKM plane, but we find that they are sufficiently close to it for breakdown across the capital GammaKM plane to occur at fields of several hundred kilogauss, thus creating open orbits along [0001].