In condensed matter physics, second sound is a quantum mechanical phenomenon in which heat transfer occurs by wave-like motion, rather than by the more usual mechanism of diffusion.
[2] Normal sound waves are fluctuations in the displacement and density of molecules in a substance;[3][4] second sound waves are fluctuations in the density of quasiparticle thermal excitations (rotons and phonons[5]).
Second sound can be observed in any system in which most phonon-phonon collisions conserve momentum, like superfluids[6] and in some dielectric crystals[1][7][8] when Umklapp scattering is small.
Also gas molecules in a box conserve momentum (except at the boundaries of box), while quasiparticles can sometimes not conserve momentum in the presence of impurities or Umklapp scattering.
Umklapp phonon-phonon scattering exchanges momentum with the crystal lattice, so phonon momentum is not conserved, but Umklapp processes can be reduced at low temperatures.
For second sound, the Umklapp rate τu has to be small compared to the oscillation frequency ω ≪ 1/τu for energy and momentum conservation.
However analogous to gasses, the relaxation time τN describing the collisions has to be large with respect to the frequency ω ≫ 1/τN, leaving a window:[9] for sound-like behaviour or second sound.
In this sense, the second sound can also be considered as oscillations of the local temperature.
Second sound is a wave-like phenomenon which makes it very different from usual heat diffusion.
Helium II has the highest thermal conductivity of any known material (several hundred times higher than copper).
[14] Second sound is also observed in superfluid helium-3 below its lambda point 2.5 mK.
Second sound has been observed in solid 4He and 3He,[16][17] and in some dielectric solids such as Bi in the temperature range of 1.2 to 4.0 K with a velocity of 780 ± 50 m/s,[18] or solid sodium fluoride (NaF) around 10 to 20 K.[19] In 2021 this effect was observed in a BKT superfluid[20] as well as in a germanium semiconductor[21][22] In 2019 it was reported that ordinary graphite exhibits second sound at 120 K. This feature was both predicted theoretically and observed experimentally, and was by far the highest temperature at which second sound has been observed.
[23] However, this second sound is observed only at the microscale, because the wave dies out exponentially with characteristic length 1-10 microns.
Therefore, presumably graphite in the right temperature regime has extraordinarily high thermal conductivity but only for the purpose of transferring heat pulses distances of order 10 microns, and for pulses of duration on the order of 10 nanoseconds.
For more "normal" heat-transfer, graphite's observed thermal conductivity is less than that of, e.g., copper.
Measuring the speed of second sound in 3He-4He mixtures can be used as a thermometer in the range 0.01-0.7 K.[24] Oscillating superleak transducers (OST)[25] use second sound to locate defects in superconducting accelerator cavities.