Zero-bias tunneling anomaly in a clean 2D electron gas caused by smooth density variations

We show that smooth variations, \delta n({\bf r}), of the local electron concentration in a clean 2D electron gas give rise to a zero-bias anomaly in the tunnel density of states, \nu(\omega), even in the absence of scatterers, and thus, without the Friedel oscillations. The energy width, \omega_0, of the anomaly scales with the magnitude, \delta n, and characteristic spatial extent, D, of the fluctuations as (\delta n/D)^{2/3}, while the relative magnitude \delta\nu/\nu scales as (\delta n/D). With increasing \omega, the averaged \delta\nu oscillates with \omega. We demonstrate that the origin of the anomaly is a weak curving of the classical electron trajectories due to the smooth inhomogeneity of the gas. This curving suppresses the corrections to the electron self-energy which come from the virtual processes involving two electron-hole pairs