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, the 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 density of states exhibits a gap at low energies. Its width $2E_0$ depends on the strength of interaction only logarithmically, $2E_0=(\hbar\omega_c/\nu)\ln (\nu e^2/\varepsilon\hbar v_F)$. The effects of temperature and disorder on the density of states are discussed.