A packet of vibration travelling through a crystal – the way its atoms jiggle together. Sound travelling through a solid is made of phonons. They also carry heat, slow electrons down by jostling them, and are what measures.
Going deeper
The phonon branches of a sheet. In-plane acoustic waves (LA, TA) rise linearly with wavevector; the flexural ZA wave, in which the sheet ripples out of plane, rises with its square, because bending a thin sheet costs little energy. These soft flexural modes are a signature of two-dimensional crystals.
Vibrations as particles
Atoms in a crystal are held by bonds that act like springs, so a push on one atom travels through the lattice as a wave. Quantum mechanics lets each wave gain or lose energy only in fixed steps, and those steps are phonons. A crystal with N atoms in its has 3N branches of them: three acoustic branches, in which neighbouring cells move together and the frequency falls to zero at long wavelengths, and 3N − 3 optical branches, in which atoms within a cell move against each other at a finite frequency.
A plot of frequency against wavevector is the phonon dispersion. It is measured across the whole Brillouin zone by or X-ray scattering, while Raman spectroscopy samples the optical phonons at its centre.
Flexural phonons, the 2D signature
A free-standing sheet has an unusual acoustic branch: the flexural or ZA mode, in which atoms move out of the plane and the sheet ripples. Bending a thin sheet costs little energy at long wavelengths, so the frequency grows with the square of the wavevector rather than linearly, and low-energy flexural phonons are plentiful.
In suspended graphene these modes carry a large share of the heat and help explain its very high ; they are also a main source of electron scattering in suspended devices near room temperature. Putting the sheet on a damps and scatters them, which is one reason supported graphene conducts heat several times less well than suspended graphene.
Phonons in measurements and devices
Scattering from phonons sets a ceiling on at room temperature that no amount of cleaning removes: calculations put it at a few hundred cm2/V·s for MoS2, far below graphene’s. Heat leaves a through phonons too, so the thermal conductivity of the channel and the thermal resistance of each interface decide how hot a scaled device runs.
Optical phonon frequencies are what Raman spectroscopy reads, and their shifts report , and layer number. Phonons also bind electrons into pairs in conventional such as NbSe2, drive when a mode softens towards zero frequency, and broaden lines as temperature rises.
For specialists
A quantised collective lattice vibration. host flexural (out-of-plane) acoustic modes with quadratic dispersion; scattering sets intrinsic mobility limits, and phonon frequencies measured by Raman spectroscopy report layer number, strain and doping.