phononrotons

Phononrotons are the collective excitations observed in certain quantum fluids, most prominently the superfluid phase of helium-4, described by the combined phonon and roton branches of the excitation spectrum. The term encapsulates the idea that the system supports two main types of quasiparticles in different momentum regions: long-wavelength phonons and short-wavelength rotons. The concept was introduced by Landau to explain the unique thermodynamic and dynamic properties of the superfluid.

In the dispersion relation of the excitations, energy ε is plotted against momentum p. Phonons dominate at small p, exhibiting a linear dispersion ε ≈ c p with c the speed of sound. Rotons appear at higher p, where the spectrum contains a local minimum at a finite momentum p0, accompanied by an energy gap Δ. For liquid helium-4, p0 is around 1.0 Å⁻¹ and Δ is of order 0.7 meV (roughly 8–9 K in temperature units). The roton minimum introduces a characteristic energy and momentum scale that influence the fluid’s thermodynamic and transport properties.

Experimental evidence for the phonon–roton spectrum comes from inelastic neutron scattering, which probes the dynamic structure factor S(k, ω) and reveals the distinct phonon branch at small wavevectors and the roton minimum at finite k. The roton feature affects properties such as specific heat, viscosity, and thermal conductivity, and it also sets a lower bound on the Landau critical velocity for superfluid flow.

Beyond helium-4, the phonon–roton framework is used to describe similar spectra in other quantum fluids and in ultracold atomic systems where roton-like minima can emerge due to interactions, confinement, or structured environments.