  In the present study, we performed molecular-dynamics simulations and
investigated dynamical heterogeneity in a supercooled liquid under a steady
shear flow. Dynamical heterogeneity can be characterized by three quantities:
the correlation length $\xi_4(t)$, the intensity $\chi_4(t)$, and the lifetime
$\tau_\text{hetero}(t)$. We quantified all three quantities by means of the
correlation functions of the particle dynamics, i.e., the four-point
correlation functions, which are extended to the sheared condition. Here, to
define the local dynamics, we used two time intervals $t=\tau_\alpha$ and
$\tau_{\text{ngp}}$; $\tau_\alpha$ is the $\alpha$-relaxation time, and
$\tau_{\text{ngp}}$ is the time at which the non-Gaussian parameter of the Van
Hove self-correlation function is maximized. We discovered that all three
quantities ($\xi_4(t)$, $\chi_4(t)$, and $\tau_\text{hetero}(t)$) decrease as
the shear rate $\dot{\gamma}$ of the steady shear flow increases. For the time
interval $t=\tau_\alpha$, the scalings $\xi_4(\tau_\alpha) \sim
\dot{\gamma}^{-0.08}$, $\chi_4(\tau_\alpha) \sim \dot{\gamma}^{-0.26}$, and
$\tau_\text{hetero}(\tau_\alpha) \sim \dot{\gamma}^{-0.88}$ were obtained. The
steady shear flow suppresses the heterogeneous structure as well as the
lifetime of the dynamical heterogeneity. In addition, our results demonstrated
that the $\alpha$-relaxation time $\tau_\alpha$ dependences of three quantities
coincide with those at equilibrium. This means that all three quantities of the
dynamical heterogeneity can be mapped onto those in the equilibrium state
through $\tau_\alpha$.
