  Under applied stress, the viscosity of many dense particulate suspensions
increases drastically, a response known as discontinuous shear-thickening
(DST). In some cases, the applied stress can even transform the suspension into
a solid-like shear jammed state. Although shear jamming (SJ) has been probed
for dense suspensions with particles having well-defined shapes, such a
phenomenon for fractal objects has not been explored. Here, using rheology and
in situ optical imaging, we study the flow behaviour of ultra-dilute fractal
suspensions of multi-walled carbon nanotubes (MWCNT) under confinement. We show
a direct transition from flowing to SJ state without a precursory DST in
fractal suspensions at an onset volume fraction, $\phi \sim$ 0.5\%,
significantly lower than that of conventional dense suspensions ($\phi \sim$
55\%). The ultra-low concentration enables us to demonstrate the fragility and
associated contact dynamics of the SJ state, which remain experimentally
unexplored in suspensions. Furthermore, using a generalized Wyart-Cates model,
we propose a generic phase diagram for fractal suspensions that captures the
possibility of SJ without prior DST over a wide range of shear stress and
volume fractions.
