Exchange enhancement of the electron $g$-factor in a two-dimensional semimetal in HgTe quantum wells

The exchange enhancement of the electron $g$-factor in perpendicular magnetic fields to 12 T in HgTe/CdHgTe quantum wells 20 nm wide with a semimetal band structure is studied. The electron effective mass and $g$-factor at the Fermi level are determined by analyzing the temperature dependence of the amplitude of Shubnikov–de Haas oscillation in weak fields and near odd Landau-level filling factors $\nu\le$ 9. The experimental values are compared with theoretical calculations performed in the one-electron approximation using the eight-band $\mathrm{kp}$ Hamiltonian. The found dependence of $g$-factor enhancement on the electron concentration is explained by changes in the contributions of hole- and electron-like states to exchange corrections to the Landau-level energies in the conduction band.