ENERGY GAPS OF THE 2-DIMENSIONAL ELECTRON-GAS EXPLORED WITH EQUILIBRIUM TUNNELING SPECTROSCOPY

We detail our results revealing a new energy gap present in the two-di mensional electron gas (2DEG). The gap, seen in the tunneling spectrum of electrons in the 2DEG, develops only in the presence of a magnetic field applied perpendicular to the 2DEG plane. The experiments discus sed here consist of measurements of electron tunneling between a 2DEG in a quantum well and an n+ substrate using excitation voltages less t han k(B)T/e. At low temperatures and only with the magnetic field appl ied perpendicular to the plane of the electron gas in the well, the tu nneling rate develops an unusual temperature-dependent suppression. Th e suppression strength is roughly independent of Landau-level filling for densities 0.5 X 10(11) cm-2 to 6 X 10(11) cm-2. At low temperature s the application of an additional ac excitation voltage, with amplitu de larger than k(B)T, increases the tunneling conductivity. Using larg e enough excitation, the tunneling conductivity returns to its high-te mperature value. This behavior suggests the existence of a magnetic-fi eld-induced energy gap, at the Fermi level, in the tunneling spectrum of electrons in the 2DEG. The 2DEG density can be tuned continuously i n our samples. Oscillations are seen in the tunneling conductivity as the 2DEG density is varied, consistent with Landau-level structure obs erved in magnetocapacitance measurements on the same sample. While the amplitude of the magnetocapacitance structure is a strong function of temperature through the temperature range down to below 1 K, striking ly, contrast in the oscillations in the tunneling rate ceases to devel op as the sample temperature is decreased below the width of the gap. In other words, the presence of the gap density-of-states features of energy width smaller than the gap width. At zero magnetic field no tem perature dependence of the tunneling is observed except at 2DEG densit ies below 0. 5 X 10(11) cm-2. At these low densities, the tunneling co nductivity is also suppressed as the temperature is lowered. We believ e that this suppression arises due to an energy gap caused by localiza tion effects. For the lowest densities, this gap is likely a manifesta tion of the Coulomb gap. Interestingly, both the magnetic-field-induce d energy gap and the gap observed at low densities lead to similar tem perature dependencies of the tunneling conductivity.