  We have measured low-temperature specific heat C(T, H) of
La1.9Sr0.1Cu1-xZnxO4 (x=0, 0.01, and 0.02) both in zero and applied magnetic
fields. A pronounced dip of C/T below 2 K was first observed in Zn-doped
samples, which is absent in the nominally clean one. If the origin of the dip
in C/T is electronic, the quasiparticle density of states N(E) in Zn-doped
samples may be depressed below a small energy scale E0. The present data can be
well described by the model N(E)=N(0)+alphaE^1/2, with a non-zero N(0) and
positive alpha. Magnetic fields depress N(0) and lead to an increase in E0,
while leaving the energy dependence of N(E) unchanged. This novel depression of
N(E) below E0 in impurity-doped cuprates can not be reconciled with the
semi-classical self-consistent approximation model. Discussions in the
framework based on the non-linear sigma model field theory and other possible
explanations are presented in this Letter.
