  We study the injection current response tensor (also known as circular
photogalvanic effect or ballistic current) in ferrolectric monolayer GeS, GeSe,
SnS, and SnSe. We find that the injection current is perpendicular to the
spontaneous in-plane polarization and could reach peak (bulk) values of the
order of $10^{10}$A/V$^{2}$s in the visible spectrum. The magnitude of the
injection current is the largest reported in the literature to date for a two
dimensional material. To rationalize the large injection current, we correlate
the injection current spectrum with the joint density of states, electric
polarization, strain, etc. We find that various factors such as anisotropy,
in-plane polarization and wave function delocalization are important in
determining the injection current tensor in these materials. We also find that
compression along the polar axis can increase the injection current (or change
its sign), and hence strain can be an effective control knob for their
nonlinear optical response. Conversely, the injection current can be a
sensitive probe of the crystal structure.
