  Controlling the vibrations in solids is crucial to tailor their mechanical
properties and their interaction with light. Thermal vibrations represent a
source of noise and dephasing for many physical processes at the quantum level.
One strategy to avoid these vibrations is to structure a solid such that it
possesses a phononic stop band, i.e., a frequency range over which there are no
available mechanical modes. Here, we demonstrate the complete absence of
mechanical vibrations at room temperature over a broad spectral window, with a
5.3 GHz wide band gap centered at 8.4 GHz in a patterned silicon nanostructure
membrane measured using Brillouin light scattering spectroscopy. By
constructing a line-defect waveguide, we directly measure GHz localized modes
at room temperature. Our experimental results of thermally excited guided
mechanical modes at GHz frequencies provides an eficient platform for
photon-phonon integration with applications in optomechanics and signal
processing transduction.
