  We investigate the magnetic response in the quantized spin Hall (SH) phase of
layered-honeycomb lattice system with intrinsic spin-orbit coupling lambda_SO
and on-site Hubbard U. The response is characterized by a parameter g= 4 U a^2
d / 3, where a and d are the lattice constant and interlayer distance,
respectively. When g< (sigma_{xy}^{s2} mu)^{-1}, where sigma_{xy}^{s} is the
quantized spin Hall conductivity and mu is the magnetic permeability, the
magnetic field inside the sample oscillates spatially. The oscillation vanishes
in the non-interacting limit U -> 0. When g > (sigma_{xy}^{s2} mu)^{-1}, the
system shows perfect diamagnetism, i.e., the Meissner effect occurs. We find
that superlattice structure with large lattice constant is favorable to see
these phenomena. We also point out that, as a result of Zeeman coupling, the
topologically-protected helical edge states shows weak diamagnetism which is
independent of the parameter g.
