Tunneling into a Two-Dimensional Electron Liquid in a Weak Magnetic Field

We study the spectral density function of a two-dimensional electron liquid in a weak magnetic field, filling factor $\nu \gg 1$. A hydrodynamic model for low-energy excitations of the liquid is developed. It is found that even at $\nu \gg 1$ the tunneling density of states exhibits a gap at low energies. Its width ${2E}_0$ depends on the strength of interaction only logarithmically, ${2E}_0=(ħ{\omega }_c/\nu )\ln (\nu e^2/\varepsilon ħv_F)$. The effects of temperature and disorder on the density of states are discussed.