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We investigate through numerical simulations how a two-dimensional crystalyields and flows under an applied shear. We focus over a range that allows usto both address the response in the limit of an infinitesimal shear rate anddescribe the phase behavior of the system at a finite shear rate. In doing so,we carefully discuss the role of the topological defects and of the finite-sizeeffects. We map out the whole phase diagram of the flowing steady state in theplane formed by temperature and shear rate. Shear-induced melting of thetwo-dimensional crystal is found to proceed in two steps: first, the solidloses long-range bond-orientational order and flows, even for an infinitesimalshear rate (in the thermodynamic limit). The resulting flowing hexatic phasethen melts to a flowing, rather isotropic, liquid at a finite shear rate thatdepends on temperature. Finally, at a high shear rate, a third regimecorresponding to a strongly anisotropic string-like flowing phase appears.

Shear-Induced Phase Behavior and Topological Defects in Two-Dimensional Crystals