Energy gaps of the two-dimensional electron gas explored with equilibrium tunneling spectroscopy

We detail our results revealing a new energy gap present in the two-dimensional 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 discussed here consist of measurements of electron tunneling between a 2DEG in a quantum well and an ${\mathit{n}}^{+}$ substrate using excitation voltages less than ${\mathit{k}}_{\mathit{B}}$T/e. At low temperatures and only with the magnetic field applied perpendicular to the plane of the electron gas in the well, the tunneling rate develops an unusual temperature-dependent suppression. The suppression strength is roughly independent of Landau-level filling for densities 0.5×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$ to 6×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$. At low temperatures the application of an additional ac excitation voltage, with amplitude larger than ${\mathit{k}}_{\mathit{B}}$T, increases the tunneling conductivity. Using large enough excitation, the tunneling conductivity returns to its high-temperature value. This behavior suggests the existence of a magnetic-field-induced energy gap, at the Fermi level, in the tunneling spectrum of electrons in the 2DEG. The 2DEG density can be tuned continuously in our samples. Oscillations are seen in the tunneling conductivity as the 2DEG density is varied, consistent with Landau-level structure observed 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, strikingly, contrast in the oscillations in the tunneling rate ceases to develop as the sample temperature is decreased below the width of the gap. In other words, the presence of the gap appears to blur density-of-states features of energy width smaller than the gap width. At zero magnetic field no temperature dependence of the tunneling is observed except at 2DEG densities below 0.5×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$. At these low densities, the tunneling conductivity is also suppressed as the temperature is lowered. We believe that this suppression arises due to an energy gap caused by localization effects. For the lowest densities, this gap is likely a manifestation of the Coulomb gap. Interestingly, both the magnetic-field-induced energy gap and the gap observed at low densities lead to similar temperature dependencies of the tunneling conductivity.