Zero-bias tunneling anomaly in a two-dimensional electron system with disorder

The temperature dependence of a zero-bias anomaly in the tunneling conductance of an Al/$\delta$-GaAs tunneling structure with a two-dimensional electron density in the $\delta$-layer of $3.5 \times 10^{12}$ cm$^{-2}$ has been investigated. It has been shown that the respective drop $\Delta\rho(\varepsilon,T)$ in the tunneling density of states $\rho$ near the Fermi level $E_{\mathrm F}$ of the two-dimensional electron system depends logarithmically on the energy $\varepsilon$ within the range of $2.7kT<|\varepsilon|<\hbar/\tau$, where $\varepsilon$ is measured with respect to $E_{\mathrm F}$ and $\tau$ is the momentum relaxation time of two-dimensional electrons. It has been found that the drop depth $\Delta\rho(0,T)/\rho$ is also proportional to $\ln(kT/\varepsilon_{0})$ in the temperature range $T = 0.1$–$20$ K and saturates below $0.1$ K.