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, u(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 u/ u scales as (delta n/D). With increasing omega, the averaged delta u 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