(has a lower flow velocity than the sound velocity, but this model is useful to illustrate the concept.)
Landau also showed that the sound wave and other excitations could equilibrate with one another and flow separately from the rest of the called the "condensate".
From the momentum and flow velocity of the excitations he could then define a "normal fluid" density, which is zero at zero temperature and increases with temperature. At the so-called Lambda temperature, where the normal fluid density equals the total density, the is no longer superfluid.
To explain the early specific heat data on superfluid , Landau posited the existence of a type of excitation he called a "roton", but as better data became available he considered that the "roton" was the same as a high momentum version of sound.
Bijl in the 1940s, and Feynman around 1955, developed microscopic theories for the roton, which was shortly observed with inelastic neutron experiments by Palevsky.
Landau thought that vorticity entered superfluid by vortex sheets, but such sheets were shown to be unstable.
Onsager and, independently, Feynman showed that vorticity enters by quantized vortex lines. They also developed the idea of quantum vortex rings.
Superfluids, such as supercooled helium-4, exhibit many unusual properties. A superfluid acts as if it were a mixture of a normal component, with all the properties associated with normal fluid, and a superfluid component. The superfluid component has zero viscosity, zero entropy, and infinite thermal conductivity. (It is thus impossible to set up a temperature gradient in a superfluid, much as it is impossible to set up a voltage difference in a superconductor.) Application of heat to a spot in superfluid helium results in a wave of heat conduction at the relatively high velocity of 20 m/sec, called second sound.
One of the most spectacular results of these properties is known as the thermomechanical or "fountain effect". If a capillary tube is placed into a bath of superfluid helium and then heated, even by shining a light on it, the superfluid helium will flow up through the tube and out the top as a result of the Clausius-Clapeyron relation. A second unusual effect is that superfluid helium can form a layer, a single atom thick, up the sides of any container in which it is placed.
A more fundamental property than the disappearance of viscosity becomes visible if superfluid is placed in a rotating container. Instead of rotating uniformly with the container, the rotating state consists of quantized vortices. That is, when the container is rotated at speed below the first critical velocity (related to the quantum numbers for the element in question) the liquid remains perfectly stationary. Once the first critical velocity is reached, the superfluid will very quickly begin spinning at the critical speed. The speed is quantized, i.e. it can only spin at certain speeds.
Recently in the field of chemistry, superfluid helium-4 has been successfully used in spectroscopic techniques, as a quantum solvent. Referred to as Superfluid Helium Droplet Spectroscopy (SHeDS), it is of great interest in studies of gas molecules, as a single molecule solvated in a superfluid medium allows a molecule to have effective rotational freedom, allowing it to behave exactly as it would in the "gas" phase.
Superfluids are also used in high-precision devices such as gyroscopes, which allow the measurement of some theoretically predicted gravitational effects (for an example see the Gravity Probe B article).
Recently, superfluids have been used to trap light and slow its speed. In an experiment performed by Lene Hau, light was passed through a Bose-Einstein condensed gas of sodium (analagous to a superfluid) and found to be slowed to 17 metres per second from its normal speed of 299,792,458 metres per second in vacuum. This does not change the absolute value of c, nor is it completely new: any medium other than vacuum, such as water or glass, also slows down the propagation of light to c/n where n is the material's refractive index.
Additionally, supersolids may also have been discovered in 2004 by physicists at Penn State University. When helium-4 is cooled below about 200 mK under high pressures, a fraction (~1%) of the solid appears to become superfluid.