Abstract
We have studied the $1/f$ noise in underdoped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ (YBCO). The YBCO material being studied is the conducting layer in a three-terminal gated device. In sufficiently underdoped devices, the carriers are localized and the main transport mechanism is variable range hopping. In this regime, the normalized power spectrum ${S}_{I}{/I}^{2}$ is observed to be linearly proportional to the device resistance R. This scaling is observed as we change R by changing the temperature of the device, the amount of oxygen doping, or the gate voltage. The observed noise is interpreted as being the result of the motion of oxygen atoms in the ${\mathrm{CuO}}_{x}$ (basal) planes of the YBCO.
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