Numerical study of bound states for point charges shielded by the response of a homogeneous two-dimensional electron gas

We study numerically the existence and character of bound states for positive and negative point charges shielded by the response of a two-dimensional homogeneous electron gas. The problem is related to many physical situations and has recently arisen in experiments on impurities on metal surfaces with Shockley surface states. Mathematical theorems ascertain a bound state for two-dimensional circularly symmetric potentials V(r) with integral(infinity)(0)dr rV(r)<= 0. We find that a shielded potential with integral(infinity)(0)dr rV(r)> 0 may also sustain a bound state. Moreover, on the same footing we study the electron-electron interactions in the two-dimensional electron gas, finding a bound state with an energy minimum for a certain electron gas density.