  We reveal the existence of asymmetric vortex solitons in ideally symmetric
periodic lattices, and show how such nonlinear localized structures describing
elementary circular flows can be analyzed systematically using the
energy-balance relations. We present the examples of rhomboid, rectangular, and
triangular vortex solitons on a square lattice, and also describe novel
coherent states where the populations of clockwise and anti-clockwise vortex
modes change periodically due to a nonlinearity-induced momentum exchange
through the lattice. Asymmetric vortex solitons are expected to exist in
different nonlinear lattice systems including optically-induced photonic
lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical
lattices.
