  We present a new exact solution to the defocusing modified Korteweg-de Vries
equation to describe the interaction of a dark soliton and a traveling periodic
wave. The solution (which we refer to as to the dark breather) is obtained by
using the Darboux transformation with the eigenfunctions of the Lax system
expressed in terms of the Jacobi theta functions. Properties of elliptic
functions including the quarter-period translations in the complex plane are
applied to transform the solution to the simplest form. We explore the
characteristic properties of these dark breathers and show that they propagate
faster than the periodic wave (in the same direction) and attain maximal
localization at a specific parameter value which is explicitly computed.
