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Hysteresis in the pinning-depinning transition in underdamped two-dimensional Frenkel-Kontorova model

Hysteretic phenomenon is studied in the 2D Frenkel-Kontorova model system. In the depinning process, two critical points Fs1 and Fs2 are found. In the pinning process, two critical points Fb1 and Fb2 are also found. The dependence of four critical forces Fs1, Fs2, Fb1, Fb2 on the system parameters such as external driving force, misfit angle, winding number, interatomic strength is investigated. The winding number b/a substantially affect the depinning forces of Fs1 and Fs2, but not the pinning forces of both Fb1 and Fb2. The pinning force of Fb2 linearly increases as the interatomic interaction strength (K) increase. The dependence of both Fb1 and Fb2 on the misfit angle θ is not in fractal structure which is different from the depinning force of Fs1.