We have measured low-temperature specific heat $C(T,H)$ of $\mathrm{La}{}_{1.9}\mathrm{Sr}{}_{0.1}\mathrm{Cu}{}_{1-x}\mathrm{Zn}{}_x\mathrm{O}{}_4$ ( $x=0\mathrm{}$, 0.01, and 0.02) in both zero and applied magnetic fields. A pronounced dip of $C/T$ below 2 K was 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 $N\left(E\right)$ in Zn-doped samples may be depressed below a small energy scale $E_0$. The present data can be well described by the model $N\left(E\right)=N\left(0\right)+\alpha E^{1/2}$, with a nonzero $N\left(0\right)$ and positive $\alpha$. Magnetic fields depress $N\left(0\right)$ and lead to an increase in $E_0$, while leaving the energy dependence of $N\left(E\right)$ unchanged. This novel depression of $N\left(E\right)$ below $E_0$ in impurity-doped cuprates cannot be reconciled with the semiclassical self-consistent approximation model. Discussions in the framework based on the nonlinear sigma model field theory and other possible explanations are presented.

• Received 3 September 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.5612