We report on phase-coherent transport studies of a Bi$_2$O$_2$Se nanoplate and on observation of universal conductance fluctuations and spin-orbit interaction induced reduction in fluctuation amplitude in the nanoplate. Thin-layered Bi$_2$O$_2$Se nanoplates are grown by chemical vapor deposition (CVD) and transport measurements are made on a Hall-bar device fabricated from a CVD-grown nanoplate. The measurements show weak antilocalization at low magnetic fields at low temperatures, as a result of spin-orbit interaction, and a crossover toward weak localization with increasing temperature. Temperature dependences of characteristic transport lengths, such as spin relaxation length, phase coherence length, and mean free path, are extracted from the low-field measurement data. Universal conductance fluctuations are visible in the low-temperature magnetoconductance over a large range of magnetic fields and the phase coherence length extracted from the autocorrelation function is in consistence with the result obtained from the weak localization analysis. More importantly, we find a strong reduction in amplitude of the universal conductance fluctuations and show that the results agree with the analysis assuming strong spin-orbit interaction in the Bi$_2$O$_2$Se nanoplate.
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