Discovery of Lowest Density, Two Dimensional Fermion Liquid, Ever Found in Nature

7/27/2019 Discovery of Lowest Density, Two Dimensional Fermion Liquid, Ever Found in Nature

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Discovery of Lowest Density, Two Dimensional Fermion

Liquid, Ever Found in Nature

INTRODUCTION :

In the year 1978 Bidyut K. Bhattacharyya was working in Prof. Francis M. GasparinisCryogenics Laboratory to determine the behavior of He

3atoms on few atomic layers of He

4

sitting on multiple nuclepore filters[1]

papers which has an area about 104

m2

in about 10 or less

cubic centimeters in volume. It was observed that when the particle density of He3

is very low,

which is sitting on the top of He4

films, which is turn is sitting on the top of all the possible

surface areas of Nuclepore filter papers, behaves as a two dimensional gas, where the heat

capacity is constant and is equal to NkB, where N is the number of He3

atoms and kB is the

Boltzmann Constant. At that time the Bidyut K. Bhattacharyya and Prof. Francis Gasparini

were able to measure the lowest Heat capacity[2,3]

, ever measured in the History of the world, at

temperatures in the range of 30-300mK . The corresponding measured value of Heat Capacity

at that time (34 years back) was 0.009 ergs/mk. The continuation of the Heat Capacity

measurement of He3

on thinner He4

films eventually showed a kind of transition, which was

interpreted by Prof. Francis Gasparini as denser liquid like phase[3]

. This transition took place

around 80-120mK for He3

particle density which is less than or equal to one particle/nm2. This

was interpreted in this way, because Gaparini and his student Bhattacharyya observed that the

slope (=dCA/dT) of the heat capacity of He3

atoms increases with the increase of the He3

particles or with respect to the increase in He3

particle density. Later experiments[4]

by Pei-

Chung Ho et.alcould not confirm the presence of He3

liquid state , neither were they analyzed

according to the expected behavior of 2D Fermi Gas, just to understand from the effective mass

and effective surface area occupied by He

3

atoms. Possible support for the condensationhypothesis has come from separate measurements of the superfluid fraction in He

3and He

4films

[5]on Hydrogen. Thus there were controversies and that controversy was removed permanently

by Sato[7]

et.alfrom Tokyo, Japan group who showed directly the formation of puddling of He3

and they also showed their data is consistent with the Bhattacharyya[2,3]

et.al data taken 34

years back. Thus the formation of the lowest density quantum fluid is now discovered in nature.

RECENT DEVELOPMENT ON THIS SUBJECT:

In a recent development , the Tokyo groups work grew out of the previous efforts to elucidate

how magnetically disordered systems known as spin liquids transform to ferromagnetic states.

This is what was written in Physics Today article by Editor Ashley G. Smart [11]. Prof.Fukuyama and his colleagues sought to recreate such a transformation in the lab by gradually

increasing the density of a He3

monolayer adsorbed on graphite. Bidyut Bhattacharyya and

Prof. F.M. Gasparini used the base substrate as Nuclepore filter papers with high surface area in

small volumes. Before the transitions occurred , however, some He3

atoms leapt out of the

densely packed monolayers to form a new top layer. Those atoms, seemed, formed puddles

much like


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FIG.1. Mimicking two dimensions. When chilled to millikelvin temperatures, He 3 atoms atop a graphite substrate (top), a denseHe4 and He3 monolayers (bottom) closely approximate a 2D quantum fluid. In the multilayer films, the bottom monolayers ofHe4 serves to mitigate the effects of heterogeneities in the graphite substrate (Adopted from Ref.7)

the one, as observed by Bidyut Bhattachyya and Prof. Francis M. Gasparini, 34 years back. This

recent development was published[7]

by D.Sato et.al. in December 2012. This work was

elaborated by the Physics Today Editor Ashley G. Smart[11]

. In fig. 1 one shows mimicking two

dimensions. In this fig. 1 the top image , the He3

layer of interest was adsorbed directly onto a

graphite substrate; in a second picture (center), it was deposited on a dense monolayer of He4, in

the third picture (bottom) it was deposited atop two dense monolayers - a layer of He3

overlying

a layer of He4. According to A.G. Smart [editor of Physics Today] the He

4monolayers serve to

mitigate the effects of surface heterogeneities. The calorimetric data obtained by D. Sato et.al[7]

showed that below about 80mK, same as the State University of New York at Buffalo Physics

Department team , grows linearly with the particle density /nm2, for values of which is less

than one particle per nm2

or for small . This is exactly same as the SUNY at Buffalo team. In

fig. 2 the plot shows how changes with . In Buffalo experiment this linearity was predicted

to be the formation of dense 2D fermions liquid, even thought that density is less than oneparticle of He

3atom per nm

2. Which is basically the lowest density, 2D fermions liquid, ever

observed in nature. The Tokyo group also made the final interpretation of their date in terms of

the lowest density fermion fluids ever found in nature. Normally the zero point energy of these

fermion particles, which are He3

atoms, has very high energy and they do not get liquidity at

temperatures around 10-100mK temperature. Therefore it is unique and one of the most

fundamental discovery , discovered by SUNY at Buffalo and also the Tokyo, Japan group, to


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generate lowest density fermion 2D liquids. This is one of the amazing methods discover first by

Bidyut K Bhattacharyya and Francis M. Gasparini in 35 years back. The confirmation of this

work with Tokyo group D.Sato on graphite materials is also exciting and worth while for such an

important discovery. It basically shows that even though the zero point energy of Fermi particles

are high, which prevents these particles to be in any liquid state, but under some underlying force

on Z axis, Van der Wall force (normal to the surface where the He4

layers are residing ,fig.1),

one can liquefy the fermions particles in two dimensions while floating on superfluid He4. This is

one of the greatest and the amazing discovery for high zero points Fermi particles. The question

will be always why that happens to high energy fermion particles, which obeys Fermi-Dirac

distribution function with an assumption that no more than two particles can be in one energy

band! These particles are supposed to move freely on the 2D surface using Boltzmann

Distribution Function or Fermi-Dirac distribution functions depending on density and

temperature of He3

particles.

As in Buffalo experiment the linear growth region of Heat-Capacity data, is thought to be a

signal of puddling formation. Notably, the linear trend can be extrapolated to the origin, which

suggests that liquid phase is stable and the reality of this world in the infinitely diluted limit of

He3

density. That intercept will lead to the free mass of the He3particles. Buffalo group found

experimentally from the Heat - Capacity measurement the behavior of 2D classical gas for He3

particle at very low density, which is independent of the mass of the He3. Bhattacharyya et.al

[3]

measured flat heat capacity with respect to temperature at an extremely low density He3. But for

some other particle density the researchers the areal density inside the He3

puddles lies roughly

in the range of 0.6-0.9 particle per nm2

. This makes the low-density liquid ever discovered innature, with a mean interatomic spacing more than a nanometer, more than twice that of 3D

He3.

PROF. FRANCIS GASPARINIS VIEW OF SUCH 2D LIQUID

Prof. Francis Gasparini recently wrote an article[6]

in ViewPoint in American Physical Society

[(APS), Physics 5,136(2012)] stating the exact understanding of this liquid phase of He3

at the

top of superfluid liquid He4. He draws a picture which is shown in Fig.3 showing all the possible

configurations for graphite substrate. Prof. Gasparini in Viewpoint describes the experimental

set up as shown in Fig.3. In Fig. 3 (a), one might consider He4

surface as ideal substrate as one

could have-a superfluid and that at low temperature, is very nearly in its ground state andprovides no underlying crystalline structure that might affect the He

3behavior. Studies

[8]in

1970s of He3-on- He

4found no evidence of liquid formation in the measurement of the surface

tension and surface sound (a two dimensional density wave in He3) for He

3surface densities of

0.97-1.4 particles per nm2. That could be due to the fact that an extensive analysis to understand

the effective mass and activation energy of He3

particles were not done. Bidyut Bhattacharyyas

thesis calculates and perform a very complex data fit using BMDP[10]

program to determine all


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the possible energy states and effective mass of the system when one used the nuclepore filter

papers, with an assumption of constant chemical potential on the number of particles on the

surface and in space. The existence of the surface states was shown originally by Prof. F.M.

Gasparini and his student M.J.Di Pirro[9]

. The data were understood in terms of He3

as a 2D gas

with effective mass 1.3 times the bare He3

mass and the surface binding energy is about 2.3K.

FIG. 2. Calorimeter data for ultracold He3 atop a dense He4monolayer show signatures of a liquid phase. At low

coverage densities, -the slope of the heat capacity as afunction temperature-grows linearly with the averagecoverage density . In the regime, He3 collects into liquid

puddles of fixed, low density of 0.6/nm at which thepuddles presumably cover the entire substrate surface area grows linearly, indicating strengthen atomic interactions.Extrapolated to =0 (dot-dash line), the non linear branch

yields a thats roughly 25% larger than an ideal FermiGas value, indicated by the red line (Adapted from Ref.7]

FIG. 3: These illustrations show He3 (yellow) adsorbed ondifferent substrates: (a) on the surface of bulk He4represented in blue; (b) on the surface of graphiterepresented in gray; and (c) on a solid layer of He4 above a

graphite surface. Recent experimental evidence withgraphite and He4 on graphite indicate the formation of 2Dliquid phase in the adsorbed He-3 near absolute zero-

depicted in (d) (APS/Alan Stonebraker).

The nuclepore filter papers are not smooth , it has a path which is serpentine paths , but thegraphite substrate used by D. Sato and et.alis much smoother and uniform that the high surface

area formed by nuclepore filter papers. This is important as pointed out in the viewpoint by Prof.

F.M. Gasparini. Prof. F.M.Gasparini says that heterogeneity can mask the 2D behavior of

He3/Fermions High energy by providing the trapping sides for He

3. Under that circumstances one

may not see any transitions. The Tokyo Group adsorbed He3

on a graphite substrate , as shown in

Fig. 3b and measure the heat capacity at various temperature and various He3

densities under


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adiabatic calorimetric technique whereby the sample is thermally isolated from the surrounding.

The external heat input of the calorimeter, done by Prof. F.M. Gasparinis and his student

Bidyut K Bhattacharyya, was about 10-10

J/sec while measuring the lowest heat capacity (0.009

erg/mK) in the year 1978 using a dilution refrigerator and plated indium switch. The heat

capacity of the ideal 2D degenerates Fermi gas of a surface area A is given by CA=

(k2

BAm/3h2) T. This is independent of the number of He

3atoms, but the extensive nature of CA

is given by the proportionality to the occupied area A. In a measurement with a given calorimeter

the geometry area A will be fixed. However if there is a liquid or condensation of 2D He3

it will

occupy an area A0< A, see fig. 3d, under this assumption effective mass does not change but the

slope () of the heat capacity as a function of temperature will decrease, because A in the above

expression replaced by the smaller area A0.

The Heat Capacity

The data plotted by Tokyo Group is shown in fig. 4 from their Physical Review Paper

published in December 2012. In Fig. 5 Tokyo, Japan Group shows how the lowest density is

formed by the 2D He3

. This picture also shows that it condenses in the form of Puddles aspredicted by Francis M. Gasparini from the Heat Capacity data taken originally by Bidyut. K.

Bhattacharyya.

FIG. 4. Heat- Capacity data at various temperatures byTOKYO Group, Sato et.al. Buffalo group Bidyut

Bhattacharyya and Francis Gasparini also found similarcurve and they fitted the data two/three level of activation

energy, using BMDP

[10]

program.

FIG. 5. This Picture is created by a TOKYO group by C.Fukuyama Lab. This demonstrates how the 2D , He3 for alower density liquid ever found in nature, about 1 particle

or less per nm distance. Schematic view of self-boundpuddles of helium-3 (yellow) confined in a twodimensional space on a graphite surface near absolute zero.These puddles are the lowest density liquid in nature. Blue

dots are a solid monolayer of helium-4 which pre plates agraphite surface. .

CONCLUSION

It is interesting to see under some conditions, even any High Energy Fermions, can be

condensed in the puddle of liquid, which is the lowest density every found in nature. This kind of

understanding was never observed in any physical phenomena, particularly when considering

such low density of He3. This discovery of Physical Phenomena is made in two different


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substrate one in Nuclepore Filter papers and the other one is in Graphite. These two substrates

are different one is smooth and uniform (Graphite) and the other one is very complex like

sintered metals, it is in the form of serpentine and zig zag path. Both shows the formation of this

liquid state is universal and is the fundamental nature of this universe. This is same like

superconductivity where lattice helps electrons to pair up and in this case the substrate which

produces some amount of Van der Wall forces makes the Ferimons to form puddles of liquids as

shown in FIG.5. The measurement of Heat Capacity at those temperatures are very difficult ,

more than any other measurement of superfluity at The TOKYO groups work was worth while

to reveal the understanding of High Energy Zero points Ferimi Particles in two dimension. The

question will be next the behavior of these particles on some other conditions and understanding

the real effective mass of this system, since the area of the space occupied by the He3

is less.

Notes

[1] Some Properties of Nuclepore filters, Tar-pin Chen, Michael J. DiPirro, Bidyut

Bhattacharyya and Francis Gasparini, Review of Scientific Instruments 51, 846 (1980)][2] Thesis of Bidyut K. Bhattacharyya, can be found in Prof. Francis M. Gasparini Laboratory in

Fronzak Hall, Ground Floor in SUNY at Buffalo, NY, USA.[3] B.K. Bhattacharyya and F.M. Gasparini, Observation of Two-Dimensional Phase

Separation in3He-

4He Films, Phys. Ev. Lett. 49, 919(1982). Phase Transition of Two-

Dimensional3He from a dilute to a Dense Phase. Phy. Rev. B31, 2719(1985).

[4] Pei-Chung Ho and R.B. Hallock, Heat-Capacity studies of3He-

4He Mixture Films and the

Coverage Dependence of the Two-Dimensional3He Landau Fermi-Liquid Parameters., Phys.

Rev. Lett. 87,135301(2001), H. Akimoto and R.H. Hallock,Heat-Capacity Measurements of3

He-

4

He Mixture Films, J. Low Temp. Phys, 138,257(2004).[5] G.A. Csathy, E.Kim, and M.H.W. Chan, Condensation of3He and recentran Superfludity in

Submonolayer3He-

4He mixture Films on H2. Phys. Rev. Lett. 88,04530 (2002).

[6] Helium Puddles Near Absolute Zero, Francis M. Gasparini, Viewpoint , AmericanPhysical Society, Physics 5, 130 (2012).

[7] Observation of Self-Binding in monolayer He3. D.Sato, K. Naruse,T. Matsui nd Hiroshi

Fukuyama. Phys. Rev. Lett. 109, 235306(2012)- Published December 3,2012.

[8]Spin-Rotation Coupling in the Alkali-Rare Gas Van der Waals Molecule KAr, Phys. Rev.Lett 32,507(1974), D.O. Edwards , S.Y.Shen, J.R.Eckhardt,P.P Fatouros, and F.M.

Gsparini,Phys. Rev. B12,892(1975).

[9] Two-Dimensional3He in

4He films , M.J. Di Pirro and F.M. Gasparini, Phys.Rev. Lett.

44,69 (1980).[10] BMDP is a statistical package developed in 1965 at UCLA, USA, based on the older

BIMED program, developed in 1960 for biomedical applications, it used keyword parameters in

the input instead of fixed-ormat cards, so the letters P was added to the letters BMD. BMDP wasoriginally distribute for free, it is now offered by Statistical Solutions.http://en.wikipedia.org/wiki/BMDP

[11] Editor Ashley G. Smart . The corresponding article number is Phys. Today 66(1),16

(2013);doi:10.1063/PT.3.1842.
http://en.wikipedia.org/wiki/BMDPhttp://en.wikipedia.org/wiki/BMDP

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Discovery of Lowest Density, Two Dimensional Fermion Liquid, Ever Found in Nature