High-field splitting of the cyclotron resonance absorption in strained $p\text{-InGaAs}/\text{GaAs}$ quantum wells

We report a systematic study of the cyclotron resonance (CR) absorption of two-dimensional holes in strained InGaAs/GaAs quantum wells (QWs) in the quantum limit. The energies of the CR transitions are traced as a function of magnetic field up to 55 T. A remarkable CR line splitting was evidenced when the resonant field exceeds 20 T. We analyze our data with a $4\times 4$ Luttinger Hamiltonian including strain and QW potentials using two different methods to calculate Luttinger parameters for ternary alloys. We found excellent agreement with the experiment when linear interpolation of the Luttinger parameters is used.

Figure 1

Selected transmission curves of ${\text{In}}_{0.14}{\text{Ga}}_{0.86}\text{As}/\text{GaAs}$ multiple quantum wells as a function of magnetic field, measured under FEL and QCL excitation. The excitation wavelengths are indicated on the left side, while the corresponding photon energies are given on the right side of the figure. Arrows 1 and 2 point to minima corresponding to the transitions $0s_1\to 1s_1$ and $3a_1\to 4a_1$, respectively, at the highest photon energy (see explanation in the text). Dotted lines are plotted to simplify the identification of the resonances.

Figure 2

(Color online) Energies of cyclotron resonance transitions as a function of magnetic field, calculated (lines) and measured (squares, circles, and triangles). The vertical arrow labeled $\nu =1$ indicates the magnetic field when the Landau-level filling factor $\nu$ is equal to unity. Solid lines correspond to the calculations made with linearly interpolated Luttinger parameters, while thin dashed lines represent results given by use of nonlinearly interpolated parameters. The inset shows the energies of the four lowest Landau levels versus magnetic field calculated using linearly interpolated Luttinger parameters. Arrows 1 and 2 indicate the transitions corresponding to lines 1 and 2 on the main figure, respectively.