Anomaly of the linear and quadratic Zeeman effect of an effective-mass acceptor: C in GaAs

The completely resolved Zeeman spectrum of a free-electron-effective-mass-hole transition is reported for the first time for GaAs: C and the hole Zeeman parameters $\tilde{\kappa }$, $\tilde{q}$, and $c_2$ are determined. The diamagnetic splitting $\Delta =0.075\mathrm{}\pm 0.075$ meV (at 18 T) is found to be 30 times smaller than predicted on the basis of a simple hydrogenic effective-mass theory, thus revealing the strong nonhydrogenic character of the acceptor wave function. A comparison with the larger diamagnetic splitting of the deeper acceptor Sn shows that its wave function has a larger extent due to an admixture of wave function from the ${\Gamma }_7$ split-off valence band. This admixture explains also the decrease of the isotropic hole $g$ value $\tilde{\kappa }$ from -0.30 for C to -0.39 for Sn, which is in contrast to the trend expected for increasing central-cell potentials.