Quantum oscillations of the resistivity and hall coefficient and the quantum limit in Bi0.93Sb0.07 alloys in a magnetic field along the trigonal axis

Abstract

The dependences of the electrical resistivity ρ and the Hall coefficient R on the magnetic field have been measured for single-crystal samples of the n-Bi0.93Sb0.07 semiconductor alloys with electron concentrations in the range 1 × 1016 cm−3 < n < 2 × 1018 cm−3. It has been found that the measured dependences exhibit Shubnikov-de Haas quantum oscillations. The magnetic fields corresponding to the maxima of the quantum oscillations of the electrical resistivity are in good agreement with the calculated values of the magnetic fields in which the Landau quantum level with the number N intersects the Fermi level. The quantum oscillations of the Hall coefficient with small numbers are characterized by a significant spin splitting. In a magnetic field directed along the trigonal axis, the quantum oscillations of the resistivity ρ and the Hall coefficient R are associated with electrons of the three-valley semiconductor and are in phase with the magnetic field. In the case of a magnetic field directed parallel to the binary axis, the quantum oscillations associated both with electrons of the secondary ellipsoids in weaker magnetic fields and with electrons of the main ellipsoid in strong magnetic fields (after the overflow of electrons from the secondary ellipsoids to the main ellipsoid) are also in phase. In magnetic fields of the quantum limit ħωc/2 ≥ EF, the electrical conductivity increases with an increase in the magnetic field: σ22(H) ∼ Hk. A theoretical evaluation of the exponent in this expression for a nonparabolic semiconductor leads to values of k close to the experimental values in the range 4 ≤ k ≤ 4.6, which were obtained for samples of the semiconductor alloys with different electron concentrations. A further increase in the magnetic field results in a decrease of the exponent k and in the transition to the inequality σ22(H) ≤ σ21(H).