Superfluid film
Encyclopedia
Superfluidity and superconductivity are macroscopic manifestations of quantum mechanics
. There is considerable interest, both theoretical and practical, in these quantum phase transitions. There has been a tremendous amount of work done in the field of phase transitions and critical phenomenon in two dimensions . Much of the interest in this field is because as the number of dimensions increases, the number of exactly solvable models diminishes drastically. In three or more dimensions one must resort to a mean field theory approach. The theory of superfluid transitions in two dimensions is known as the Kosterlitz-Thouless (KT) theory. The 2D XY model
- where the order parameter is characterized by an amplitude and a phase - is the universality class for this transition.
s in thin films, specifically helium
, the two main experimental signatures are the superfluid
fraction and heat capacity
. If either of these measurements were to be done on a superfluid film in a typical open container, the film signal would be overwhelmed by the background signal from the container. Therefore, when studying superfluid films, it is of paramount importance to study a system of large surface area as to enhance the film signal.
There are several ways of doing this. In the first, a long thin strip of material such as PET film
is rolled up into a “jelly roll” configuration. The result is a film that is a long continuous plane, referred to as a planar film . A second way is to have a highly porous material such as porous gold, Vycor
, or Aerogel
. This results in a multiply connected film where the substrate is much like Swiss cheese with the holes interconnected . These porous materials all have an extremely high surface area to volume ratio. A third method is to separate two extremely flat plates by a thin spacer, again resulting in a large surface area to volume ratio.
One can measure the superfluid response of the film by measuring the moment of inertia
. An indispensable tool for this is the Torsional Oscillator, and early design was first used by Andronikashvili to detect superfluid in bulk fluid 4He and later modified by John Reppy and co-workers at Cornell in the 1970’s. In the torsional oscillator, the experimental volume is suspended by a torsion rod and made to oscillate at resonance via capacitive coupling with a fin or pair of fins, depending on the configuration (shown below in grey). When part of the film becomes superfluid, it no longer has any viscosity and will remain at rest in the lab frame, lowering the moment of inertia of the cell. Recall that the resonant period of a torsional oscillator is
. Therefore, lowering the moment of inertia reduces the resonant period of the oscillator. By measuring the period drop as a function of temperature, and total loading of the film from the empty cell value, one can deduce the fraction of the film that has entered the superfluid state. A typical set of data clearly showing the superfluid decoupling in helium films is shown in ref. 2.
A typical torsional oscillator has a resonant frequency on the order of 1000 Hz. This corresponds to a maximum velocity of the substrate of micrometres per second. The critical velocity of helium films is reported to be on the order of 0.1 m/s . Therefore, in comparison to the critical velocity, the oscillator is almost at rest. To probe theories of dynamical aspects of thin film phase transitions one must use an oscillator with a much higher frequency. The quartz crystal microbalance
provides just such a tool having a resonant frequency of about 10 kHz. The operating principles are much the same as for a torsional oscillator. When the thin film is adsorbed onto the surface of the crystal, the resonant frequency of the quartz crystal drops. As the crystal is cooled through the superfluid transition, the superfluid decouples and the frequency increases.
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. There is considerable interest, both theoretical and practical, in these quantum phase transitions. There has been a tremendous amount of work done in the field of phase transitions and critical phenomenon in two dimensions . Much of the interest in this field is because as the number of dimensions increases, the number of exactly solvable models diminishes drastically. In three or more dimensions one must resort to a mean field theory approach. The theory of superfluid transitions in two dimensions is known as the Kosterlitz-Thouless (KT) theory. The 2D XY model
XY model
The classical XY model is a model of statistical mechanics. It is the special case of the n-vector model for n=2.-Definition:...
- where the order parameter is characterized by an amplitude and a phase - is the universality class for this transition.
Experimental methods
In looking at phase transitionPhase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
s in thin films, specifically helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
, the two main experimental signatures are the superfluid
Superfluid
Superfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...
fraction and heat capacity
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...
. If either of these measurements were to be done on a superfluid film in a typical open container, the film signal would be overwhelmed by the background signal from the container. Therefore, when studying superfluid films, it is of paramount importance to study a system of large surface area as to enhance the film signal.
There are several ways of doing this. In the first, a long thin strip of material such as PET film
PET film (biaxially oriented)
BoPET is a polyester film made from stretched polyethylene terephthalate and is used for its high tensile strength, chemical and dimensional stability, transparency, reflectivity, gas and aroma barrier properties and electrical insulation.A variety of companies manufacture boPET and other...
is rolled up into a “jelly roll” configuration. The result is a film that is a long continuous plane, referred to as a planar film . A second way is to have a highly porous material such as porous gold, Vycor
Vycor
Vycor is a glass with high temperature and thermal shock resistance, made by Corning Incorporated. Vycor is 96% silica, but unlike pure fused silica it can be readily manufactured in a variety of shapes....
, or Aerogel
Aerogel
Aerogel is a synthetic porous material derived from a gel, in which the liquid component of the gel has been replaced with a gas. The result is a solid with extremely low density and thermal conductivity...
. This results in a multiply connected film where the substrate is much like Swiss cheese with the holes interconnected . These porous materials all have an extremely high surface area to volume ratio. A third method is to separate two extremely flat plates by a thin spacer, again resulting in a large surface area to volume ratio.
| Material | Surface area (m2/g) | Pore Size (nm) |
|---|---|---|
| Vycor Glass | 250 | 4 |
| Porous gold | 100-200 | 100 |
| Aerogel | 200-1000 | 20 |
One can measure the superfluid response of the film by measuring the moment of inertia
Moment of inertia
In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass, is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation...
. An indispensable tool for this is the Torsional Oscillator, and early design was first used by Andronikashvili to detect superfluid in bulk fluid 4He and later modified by John Reppy and co-workers at Cornell in the 1970’s. In the torsional oscillator, the experimental volume is suspended by a torsion rod and made to oscillate at resonance via capacitive coupling with a fin or pair of fins, depending on the configuration (shown below in grey). When part of the film becomes superfluid, it no longer has any viscosity and will remain at rest in the lab frame, lowering the moment of inertia of the cell. Recall that the resonant period of a torsional oscillator is
. Therefore, lowering the moment of inertia reduces the resonant period of the oscillator. By measuring the period drop as a function of temperature, and total loading of the film from the empty cell value, one can deduce the fraction of the film that has entered the superfluid state. A typical set of data clearly showing the superfluid decoupling in helium films is shown in ref. 2.A typical torsional oscillator has a resonant frequency on the order of 1000 Hz. This corresponds to a maximum velocity of the substrate of micrometres per second. The critical velocity of helium films is reported to be on the order of 0.1 m/s . Therefore, in comparison to the critical velocity, the oscillator is almost at rest. To probe theories of dynamical aspects of thin film phase transitions one must use an oscillator with a much higher frequency. The quartz crystal microbalance
Quartz crystal microbalance
A quartz crystal microbalance measures a mass per unit area by measuring the change in frequency of a quartz crystal resonator. The resonance is disturbed by the addition or removal of a small mass due to oxide growth/decay or film deposition at the surface of the acoustic resonator...
provides just such a tool having a resonant frequency of about 10 kHz. The operating principles are much the same as for a torsional oscillator. When the thin film is adsorbed onto the surface of the crystal, the resonant frequency of the quartz crystal drops. As the crystal is cooled through the superfluid transition, the superfluid decouples and the frequency increases.
Some results
The KT theory has been confirmed in a set of experiments by Bishop and Reppy in planar films, ie. Helium films on mylar . Specifically, they found that the transition temperature scaled with film thickness and the superfluid transition is found in films as thin as 5% of a monolayer. More recently, it has been found that near the transition temperature when the correlation lengths exceed any relevant length scale in the system, a multiply connected film will behave as a 3D system near its critical point.See also
- SuperfluidSuperfluidSuperfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...
- Bose–Einstein condensateBose–Einstein condensateA Bose–Einstein condensate is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near absolute zero . Under such conditions, a large fraction of the bosons occupy the lowest quantum state of the external potential, at...
- SuperconductivitySuperconductivitySuperconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
- Quantum vortexQuantum vortexIn physics, a quantum vortex is a topological defect exhibited in superfluids and superconductors. Superfluids and superconductors are states of matter without friction. They exist only at very low temperatures. The existence of these quantum vortices was independently predicted by Richard Feynman...
- SupersolidSupersolidA supersolid is a spatially ordered material with superfluid properties. Superfluidity is a special quantum state of matter in which a substance flows with zero viscosity.-Background:...
- Phase TransitionPhase transitionA phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....