  We theoretically study the power-law decay behavior of the local density of
states (LDOS) oscillations near a line defect in system with semi-Dirac points
by using a low-energy k.p Hamiltonian. We find that the LDOS oscillations are
strongly anisotropic and sensitively depend on the orientation of the line
defect. We analytically obtain the decay indexes of the LDOS oscillations near
a line defect running along different directions by using the stationary phase
approximation. Specifically, when the line defect is perpendicular to the
linear dispersion direction, the decay index is -5/4 whereas it becomes -1/4 if
the system is gapped, both of which are different from the decay index -3/2 in
isotropic Dirac systems. In contrast, when the line defect is perpendicular to
the parabolic dispersion direction, the decay index is always -1/2 regardless
of whether the system is gapped or not, which is the same as that in a
conventional semimetal. In general, when the defect runs along an arbitrary
direction, the decay index sensitively depends on the incident energy for a
certain orientation of the line defect. It varies from -5/4 to -1/2 due to the
absence of strict stationary phase point. Our results indicate that the decay
index -5/4 provides a fingerprint to identify semi-Dirac points in 2D electron
systems.
