we observe a slowing down in the structural relaxation for this temperature range. One can extract a characteristic time scale $\tau(T)$ which, for example, is defined as $C(t=\tau(T))=1/e$ for each temperature $T$. As Fig. 4b clearly shows, the temperature dependence of the relaxation time exhibits a non-Arrhenius behavior. We also checked whether the so-called time-temperature superposition holds for the above autocorrelation functions, which is shown in Fig. 4c. We clearly see that time-temperature superposition is systematically broken by the autocorrelation functions. This is consistent with the fact that the stretched exponents have dependence on temperature as is shown just below.

We find that the relaxation pattern of the correlation function $C(t)$ can be characterized by a power law relaxation $C(t)=1-A t^{b(T)}$ (known as the von Schweidler relaxation) in the early time regime and a stretched exponential relaxation $C(t)=C_0(T) \exp(-A't^{\beta(T)})$ in the late time regime. However, as the temperature gets higher, the regime of validity for early time power law relaxation was significantly reduced and we could better fit the early time relaxation with another stretched exponential form $C(t)=\exp(-A''t^{b'(T)})$. Of course for low temperature regime, we could get $b(T) \simeq b'(T)$.

Fig. 4d shows the temperature dependence of the fitted exponents. 