  Breakdown of Stokes-Einstein relation in supercooled liquids is believed to
be one of the hallmarks of glass transition. The phenomena is studied in depth
over many years to understand the microscopic mechanism without much success.
Recently it was found that violation of Stokes-Einstein relation in supercooled
liquids can be tuned very systematically by pinning randomly a set of particles
in their equilibrium positions. This observation suggested a possible framework
where breakdown of Stokes-Einstein relation in the dynamics of supercooled
liquids can be studied with precise control. We have done extensive molecular
dynamics simulations to understand this phenomena by analyzing the structure of
appropriately defined set of dynamically slow and fast particles clusters. We
have shown that the Stokes-Einstein breakdown actually become predominant once
the cluster formed by the slow particles percolate the entire system size.
Finally we proposed a possible close connection between fractal dimensions of
these clusters and the exponents associated with the fractional Stokes-Einstein
relation.
