  We theoretically investigate the Coulomb drag between the edge states of two
quantum spin Hall systems. Using an interacting theory of the one-dimensional
helical edge modes, we show that the drag vanishes at second order in the
inter-edge interaction, where it is typically finite in other systems, due to
the absence of backscattering within the edges. However, in the presence of a
small external magnetic field the drag is finite and scales as the fourth power
of the magnetic field, a behavior that sharply distinguishes it from other
systems. We obtain the temperature dependence of the drag for regimes of both
linear and quadratic edge dispersion in the presence of a finite field.
