Electron mass in a HgTe quantum well: Experiment versus theory

The energy spectrum of the conduction band in HgTe/Cd_xHg_1−xTe quantum wells with a width d=(4.6−20.2)nm has been experimentally studied in a wide range of electron density. For this purpose, the electron density dependence of the effective mass was measured by two methods: by analyzing the temperature dependence of the Shubnikov–de Haas oscillations and by means of the quantum capacitance measurements. There was shown that the effective mass obtained for the structures with d<d_c, where d_c≃6.3nm is a critical width of quantum well corresponding to the Dirac-like energy spectrum, is close to the calculated values over the whole electron density range; with increasing width, at d>(7−8)nm, the experimental effective mass becomes noticeably less than the calculated ones. This difference increases with the electron density decrease, i.e., with lowering the Fermi energy; the maximal difference between the theory and experiment is achieved at d=(15−18)nm, where the ratio between the calculated and experimental masses reaches the value of two and begins to decrease with a further d increase. We assume that observed behavior of the electron effective mass results from the spectrum renormalization due to many-body effects.