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.