  It is well-known that (2+1)-dimensional Chern-Simons term may lead to
topological Meissner effect. However, we show that 3-dimensional Chern-Simons
term, which is different from (2+1)-dimensional Chern-Simons term, will instead
destroy traditional Meissner effect. This means that the presence of a
3-dimensional Chern-Simons term naturally guarantees the validity of
"pre-formed pairs" picture explaining high-T_c superconductivity, because such
a term breaks Meissner effect induced by paired electrons. In particular, if
3-dimensional Chern-Simons gauge fields indeed emerge in the "pre-formed pairs"
regime, our theory predicts that around the transition temperature T_c the Hall
conductivity {\sigma} should exhibit a scaling law {\sigma}->(T-T_c )^(2/D)
with D being the dimension of the superconducting material.
