Zero-Bias Tunnel-Conductance Minima Due to the Excitation of Collective Modes in the Barrier

Abstract

We evaluate the contribution to the tunnel conductance due to inelastic tunneling processes whereby the tunneling electron excites continuum modes in the barrier. For acoustical dispersion relations ${\omega }_{\overrightarrow{\mathrm{p}}}=v_{s}p+{\omega }_0$ of the continuum modes, the coherent inelastic contribution is usually proportional to ${\mathrm{}\left(\right|eV|-\hslash {\omega }_0)}^2\theta \mathrm{}\left(\right|eV|-\hslash {\omega }_0)\theta (\hslash {\omega }_{\mathrm{D}}-|\mathrm{eV}\left|\right)$, in which ${\omega }_{\mathrm{D}}=v_s{p}_{max}+{\omega }_0$. Comparison with experimental data suggests that certain zero-bias minima may be attributed to phonon excitation via inelastic tunneling.