Electromechanical Noise in a Diffusive Conductor

Electrons moving in a conductor can transfer momentum to the lattice via collisions with impurities and boundaries, giving rise to a fluctuating mechanical stress tensor. The root-mean-squared momentum transfer per scattering event in a disordered metal (of dimension $L$ greater than the mean-free path $l$ and screening length $\xi$) is found to be reduced below the Fermi momentum by a factor of order $l/L$ for shear fluctuations and $(\xi /L{)}^2$ for pressure fluctuations. The excitation of an elastic bending mode by the shear fluctuations is estimated to fall within current experimental sensitivity for a nanomechanical oscillator.