Pinning of a two-dimensional Wigner crystal by charged impurities

The magnitude of pinning of the classical Wigner crystal as a function of the distance between the crystal and a charged impurity is calculated numerically. The pinning magnitude is shown to be very asymmetric with respect to the sign of the impurity charge. Donors are found to pin effectively only in a narrow layer at a finite distance from the crystal, whereas acceptors pin strongly in a relatively wide region adjacent to the crystal plane. It is shown that pinning of the crystal by a close acceptor cannot be described by the conventional model of periodic coupling because at small distances the acceptor is built into the lattice.