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We report low-frequency 1/f noise measurements of degenerately doped Si:P \delta-layers at 4.2K. The noise was found to be over six orders of magnitude lower than that of bulk Si:P systems in the metallic regime and is one of the lowest values reported for doped semiconductors. The noise was found to be nearly independent of magnetic field at low fields, indicating negligible contribution from universal conductance fluctuations. Instead interaction of electrons with very few active structural two-level systems may explain the observed noise magnitude

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