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A charge density wave (CDW) ground state is observed in polycrystallineCu$_2$Se below 125 K, which corresponds to an energy gap of 40.9 meV and anelectron-phonon coupling constant of 0.6. Due to the polycrystalline structure,the Peierls transition process has been expanded to a wide temperature rangefrom 90 to 160 K. The Hall carrier concentration shows a continuous decreasefrom 2.1$\times$10$^{20}$ to 1.6$\times$10$^{20}$ cm$^{-3}$ in the temperaturerange from 160 K to 80 K, while almost unchanged above 160 K and below 90 K.After entering the CDW ground state, a wave-like fluctuation was observed inthe I-V curve near 50 K, which exhibits as a periodic negative differentialresistivity in an applied electric field due to the current. We alsoinvestigated the doping effect of Zn, Ni, and Te on the CDW ground state. BothZn and Ni doped Cu$_2$Se show a CDW character with increased energy gap andelectron-phonon coupling constant, but no notable Peierls transition wasobserved in Te doped Cu$_2$Se. Similar wave-like I-V curve was also seen inCu$_{1.98}$Zn$_{0.02}$Se near 40 K. The regular fluctuation in $\it{dc}$ I-Vcurve was not magnetic field sensitive, but temperature and sample sizesensitive.

Anomalous CDW ground state in Cu$_2$Se: a wave-like fluctuation of $\it{dc}$ I-V curve near 50 K