  Within a relativistic quantum formalism we examine the role of second-order
corrections caused by the application of magnetic fields in two-dimensional
topological and Chern insulators. This allows to reach analytical expressions
for the change of the Berry curvature, orbital magnetic moment, density of
states and energy determining their canonical grand potential and transport
properties. The present corrections, which become relevant at relatively low
fields due to the small gap characterizing these systems, unveil a zero-field
diamagnetic susceptibility which can be tuned by the external magnetic field.
