Brittle yielding in supercooled liquids below the critical temperature of mode coupling theory

Molecular Dynamics (MD) computer simulations of a polydisperse soft-sphere model under shear are presented. Starting point for these simulations are deeply supercooled samples far below the critical temperature, $T_c$, of mode coupling theory. These samples are fully equilibrated with the aid of the swap Monte Carlo technique. For states below $T_c$, we identify a life time $\tau_{\rm lt}$ that measures the time scale on which the system can be considered as an amorphous solid. The temperature dependence of $\tau_{\rm lt}$ can be well described by an Arrhenius law. The existence of transient amorphous solid states below $T_c$ is associated with the possibility of brittle yielding, as manifested by a sharp stress drop in the stress-strain relation and shear banding. We show that brittle yielding requires on the one hand low shear rates and on the other hand, the time scale corresponding to the inverse shear rate has to be smaller or of the order of $\tau_{\rm lt}$. Both conditions can be only met for large life time $\tau_{\rm lt}$, i.e.~for states far below $T_c$.