Superfluidity of ⁴He confined in nanoporous media
We have examined superfluid properties of ⁴He confined to a nanoporous Gelsil glass that has nanopores 2.5 nm in diameter. The pressure–temperature phase diagram was determined by torsional oscillator, heat capacity and pressure studies. The superfluid transition temperature Tc approaches zero at...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1169152017-05-19T03:02:36Z Superfluidity of ⁴He confined in nanoporous media Shirahama, K. Yamamoto, K. Shibayama, Y. Жидкий гелий We have examined superfluid properties of ⁴He confined to a nanoporous Gelsil glass that has nanopores 2.5 nm in diameter. The pressure–temperature phase diagram was determined by torsional oscillator, heat capacity and pressure studies. The superfluid transition temperature Tc approaches zero at 3.4 MPa, indicating a novel quantum superfluid transition. By heat capacity measurements, the nonsuperfluid phase adjacent to the superfluid and solid phases is identified to be a nanometer-scale, localized Bose condensation state, in which global phase coherence is destroyed. At high pressures, the superfluid density has a T-linear term, and Tc is proportional to the zero-temperature superfluid density. These results strongly suggest that phase fluctuations in the superfluid order parameter play a dominant role on the phase diagram and superfluid properties. 2008 Article Superfluidity of ⁴He confined in nanoporous media / K. Shirahama, K. Yamamoto, Y. Shibayama // Физика низких температур. — 2008. — Т. 34, № 4-5. — С. 350–356. — Бібліогр.: 30 назв. — англ. 0132-6414 PACS: 67.25.D–;81.07.–b http://dspace.nbuv.gov.ua/handle/123456789/116915 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Жидкий гелий Жидкий гелий |
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Жидкий гелий Жидкий гелий Shirahama, K. Yamamoto, K. Shibayama, Y. Superfluidity of ⁴He confined in nanoporous media Физика низких температур |
| description |
We have examined superfluid properties of ⁴He confined to a nanoporous Gelsil glass that has nanopores
2.5 nm in diameter. The pressure–temperature phase diagram was determined by torsional oscillator, heat
capacity and pressure studies. The superfluid transition temperature Tc approaches zero at 3.4 MPa, indicating
a novel quantum superfluid transition. By heat capacity measurements, the nonsuperfluid phase adjacent
to the superfluid and solid phases is identified to be a nanometer-scale, localized Bose condensation state, in
which global phase coherence is destroyed. At high pressures, the superfluid density has a T-linear term, and
Tc is proportional to the zero-temperature superfluid density. These results strongly suggest that phase fluctuations
in the superfluid order parameter play a dominant role on the phase diagram and superfluid properties. |
| format |
Article |
| author |
Shirahama, K. Yamamoto, K. Shibayama, Y. |
| author_facet |
Shirahama, K. Yamamoto, K. Shibayama, Y. |
| author_sort |
Shirahama, K. |
| title |
Superfluidity of ⁴He confined in nanoporous media |
| title_short |
Superfluidity of ⁴He confined in nanoporous media |
| title_full |
Superfluidity of ⁴He confined in nanoporous media |
| title_fullStr |
Superfluidity of ⁴He confined in nanoporous media |
| title_full_unstemmed |
Superfluidity of ⁴He confined in nanoporous media |
| title_sort |
superfluidity of ⁴he confined in nanoporous media |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2008 |
| topic_facet |
Жидкий гелий |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/116915 |
| citation_txt |
Superfluidity of ⁴He confined in nanoporous media / K. Shirahama, K. Yamamoto, Y. Shibayama // Физика низких температур. — 2008. — Т. 34, № 4-5. — С. 350–356. — Бібліогр.: 30 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT shirahamak superfluidityof4heconfinedinnanoporousmedia AT yamamotok superfluidityof4heconfinedinnanoporousmedia AT shibayamay superfluidityof4heconfinedinnanoporousmedia |
| first_indexed |
2025-07-08T11:18:42Z |
| last_indexed |
2025-07-08T11:18:42Z |
| _version_ |
1837077388551258112 |
| fulltext |
Fizika Nizkikh Temperatur, 2008, v. 34, Nos. 4/5, p. 350–356
Superfluidity of 4He confined in nanoporous media
Keiya Shirahama, Keiichi Yamamoto, and Yoshiyuki Shibayama
Department of Physics, Keio University, Yokohama 223-8522, Japan
E-mail: keiya@rk.phys.keio.ac.jp
Received December 5, 2007
We have examined superfluid properties of
4
He confined to a nanoporous Gelsil glass that has nanopores
2.5 nm in diameter. The pressure–temperature phase diagram was determined by torsional oscillator, heat
capacity and pressure studies. The superfluid transition temperature Tc approaches zero at 3.4 MPa, indicat-
ing a novel quantum superfluid transition. By heat capacity measurements, the nonsuperfluid phase adjacent
to the superfluid and solid phases is identified to be a nanometer-scale, localized Bose condensation state, in
which global phase coherence is destroyed. At high pressures, the superfluid density has a T-linear term, and
Tc is proportional to the zero-temperature superfluid density. These results strongly suggest that phase fluc-
tuations in the superfluid order parameter play a dominant role on the phase diagram and superfluid pro-
perties.
PACS: 67.25.D– Superfluid phase;
81.07.–b Nanoscale materials and structures: fabrication and characterization.
Keywords: nanoporous glass, torsional oscillator, superfluid transition.
Introduction
4He confined or adsorbed in nanoporous media is an
interesting model system of strongly correlated bosons
under external potential. Recently, we have investigated
the superfluid and thermodynamic properties of 4He in
nanoporous Gelsil glass, and have found that the strong
confinement into the nanopores causes a dramatic change
in the phase diagram [1–8]. We show the obtained P–T
phase diagram in Fig. 1. With increasing pressure, the
superfluid transition temperature Tc approaches zero at
3.4 MPa. Measurements of isochoric pressure have sug-
gested that the freezing pressure is at or above 3.4 MPa
[2,3]. These behaviors indicate a quantum phase transi-
tion (QPT) among superfluid, nonsuperfluid and solid
phases induced by pressure as an external parameter.
The QPT behavior and the existence of a nonsuper-
fluid phase between the superfluid and solid phases are in
striking contrast to the case of bulk 4He. To investigate
the nature of the nonsuperfluid phase and to understand
the mechanism of QPT, we have made measurements of
heat capacity and isochoric pressure [3,5]. In this paper,
we summarize the recent experimental results and pro-
pose an interpretation that will provide a novel per-
spective to the physics of 4He in porous media: The con-
finement of 4He to nanopores fluctuates the phase of
superfluid order parameter, and the phase fluctuations re-
sult in the localization of Bose–Einstein condensates
(BEC) and a quantum phase transition.
2. Results: phase diagram and superfluid properties
Here we summarize the results of the measurements of
pressure and heat capacity, and describe in more detail
about the torsional oscillator studies, focusing on the tem-
perature dependence of the superfluid fraction. The de-
tails of the results have been described elsewhere [1–8].
We have employed a porous Gelsil glass [9], which is
manufactured by the sol-gel process. Gelsil has
three-dimensionally (3D) interconnected nanopores, sim-
ilarly to Vycor. The nominal pore diameter of our glass
samples is 2.5 nm. Since various pore sizes are available,
Gelsil has been recently used in helium studies. The con-
trollability and wide variety of the pore size were not
available in Vycor. It was first employed for 4He study by
Miyamoto and Takano (MT) [10]. They found that the
superfluid transition in a 2.5-nm Gelsil sample was de-
pressed to 0.9 K at ambient pressure.
We have constructed a heat capacity cell having a ca-
pacitance pressure gauge [4,5]. This cell enables us to
measure the pressure and heat capacity for the same glass
sample. The sample cell contains four Gelsil disk samples
© Keiya Shirahama, Keiichi Yamamoto, and Yoshiyuki Shibayama, 2008
(5.5 mm diameter, 2.3 mm thick) which are taken from the
same batch as the one used in the torsional oscillator
experiments.
2.1. Phase diagram
In the pressure study [2,3], we measure pressure P T( )
along isochores. The rates of cooling and warming of the
cell are also recorded simultaneously. Both data show
some signatures that are related to freezing and melting of
4He in the nanopores. The freezing and melting occur at
different temperatures and in finite temperature ranges,
unlike the first order transition of bulk 4He. We have
identified P T( ) at which 4He starts and terminates to
freeze and thaw. The four data sets are plotted in Fig. 1.
The reduction of freezing and melting temperatures ob-
served above 3.7 MPa. Below 3.4 MPa, no signatures in-
dicating freezing and melting were observed. The liq-
uid-solid boundary below 0.8 K should therefore be
located between 3.7 and 3.4 MPa, meaning that the freez-
ing line is nearly flat and the entropy difference between
the solid and nonsuperfluid phases is small. This fact
strongly suggests that the nonsuperfluid phase is a sort of
an ordered state.
To clarify the nature of the low-entropy nonsuperfluid
state, we have conducted the heat capacity measurement
[4,5]. Figure 2,a shows the heat capacity data, in which
Superfluidity of 4He confined in nanoporous media
Fizika Nizkikh Temperatur, 2008, v. 34, Nos. 4/5 351
Pc
1 20
2
4
6
Solid
Superfluid
Localized
BEC
Normal
Tc
TB
TMO
TMT
TFT
TFO
P
,
M
P
a
T, K
Fig 1. P T� phase diagram. The superfluid transition tempera-
tures Tc (green dots) are obtained by torsional oscillator stu-
dies [1], and the localized BEC temperatures TB (red dots) and
the melting points (red crosses) are by heat capacity [4,5].
Pressure and thermal response measurements [2,3] give the
melting and freezing lines: melting onset TMO, melting termi-
nation TMT , freezing onset TFO, freezing termination TFT . Ar-
row indicates the critical pressure Pc at which Tc tends to 0 K.
T, K
0.76
1.27
1.77
2.28
3.02
3.30
3.58
TB
1 20
0.02
0.04
40
30
20
10
-
2000150010005000
0.34 MPa
1.06
1.77
2.30
b
4
3
2
1
6005004003002001000
T, mK
2.59 MPa
2.72
2.95
c
(
a
H
ea
t
ca
p
ac
it
y,
J/
K 0.25MPa
�
f,
1
0
H
z
3
�
f,
1
0
H
z
3
Fig. 2. (a) Heat capacity of liquid
4
He in the Gelsil nanopores
for eight pressures. Arrows indicate the peak temperatures TB
that are interpreted as the LBEC formation temperatures. See
recent publications [4,5] for the method of extraction of the
heat capacity in the nanopores. (b) Torsional oscillator fre-
quency shifts �f T( ) at pressures below the bulk melting pres-
sure. The shifts starting around 2 K are the contribution from
bulk liquid in the sample cell. (c) �f T( ) at pressures above the
bulk melting pressure. The n-shaped anomalies are anti-cross-
ing resonances resulting from the coupling to superfluid fourth
sound.
4He in the nanopores is liquid. A broad, but substantial
peak is found in each heat capacity. The peak temperature
TB indicated by arrows and the peak height decrease as P
increases. We plot TB on the phase diagram of Fig. 1. Ob-
viously, the TB line is located about 0.2 K below the �
line, and is parallel to the � line.
The heat capacity peak is reminiscent of the superfluid
size effect in 4He in various restricted geometries [12].
However, the system exhibits no superfluid transition at
and just below TB . This is clearly seen in Fig. 2,b, the data
of the frequency shift in the torsional oscillator measure-
ment. In Fig. 2,b, small upturns seen in both data around
2 K are due to the superfluid transition of the bulk liquid
in the open space of the cell. The large, abrupt increase at
lower temperatures indicates the superfluid transition of
4He confined in the nanopores. The superfluid transition
temperature Tc is much lower than TB , and it decreases
progressively with increasing pressure. The remarkable
difference in the behaviors of two characteristic tempera-
tures is obviously seen in Fig. 1.
2.2. Superfluid properties
Torsional oscillator technique [13] is based on a sim-
ple relationship that the frequency shift �f is proportional
to the superfluid density �s . Therefore, �f T( ) should con-
tain essential information for understanding the nature of
superfluidity. In the next section we focus on the behavior
of �s T( ). Here we mention some features in the �f T( )
curves in two density regions: (1) adsorbed films to filled-
pore states, (2) pressurized states at 0 3 4� �P . MPa.
2.2.1. Film states
The adsorbed film shows the superfluid response
when the coverage exceeds the critical coverage nc �
= 19.9 �mol / m 2. The superfluid transition temperature
Tc increases almost linearly with the superfluid coverage
n nc� , and has a maximum at n full
2mol / m� 33 � , at
which the pore is filled with 4He. It should be noted that
the amount of the nonsuperfluid (i.e., inert) layers adja-
cent to the pore walls is larger than that of superfluid
liquid under ambient pressure. The effective pore diame-
ter for the superfluid part is therefore reduced to about
1.5 nm.
From the slope of f n( ) in the nonsuperfluid and
superfluid states, we obtained the ratio of detected
superfluid mass to total superfluid mass to be 0.1. This
value is much smaller than 0.33 in the case of Vycor, but
larger than the obtained value by MT for the similar Gelsil
glass, 0.06. These results indicate that the nanopores in
Gelsil are more tortuous than the pores in Vycor.
In Fig. 3, we show the typical superfluid frequency
shift normalized by the shift at 0 K, � �f T f( ) / ( )0 , which
is equal to the superfluid fraction � �s T( ) / , together with
the similar data of 4He film in 2.5-nm Gelsil by MT and in
Vycor. The �f data set at various coverages are shown in
the inset of Fig. 3,a. There exists substantial difference in
the temperature dependence of � �s T( ) / among three ex-
periments. Our Gelsil data lie between the Vycor data and
Gelsil data by MT, and possess the features of these two
systems. In the Vycor case, �s T( ) is proportional to T 2 at
low temperatures, and show a bulk-like critical behavior
near Tc [11]. The T 2 behavior suggests that one-dimen-
sional phonons are the dominant low-energy excitations.
In the Gelsil experiment by MT [10], � �s T( ) / is also
fitted to T 2 at low temperatures at T � 0 4. –0 8. Tc . As
shown in Fig. 3,b, also in our Gelsil the normal fluid den-
sity obeys approximately T 2 law at low-temperature re-
gions. This behavior is shown in the inset. Near Tc , our
�s T( ) resembles the Vycor data, although the data are not
enough to accurately determine the critical exponent.
352 Fizika Nizkikh Temperatur, 2008, v. 34, Nos. 4/5
Keiya Shirahama, Keiichi Yamamoto, and Yoshiyuki Shibayama
0 .5 1 .00
0 .5
1 .0
Vycor (430 mK)
Gelsil (400)
Gelsil, MT (340)
a
�
f,
H
z
0.03
0.02
0.01
0 0.5 1.0 1.5
T, K
T/Tc
�
�
s
/
�
�
n
/
b
20.4 mol/m�
2
0.01 0.1 1.0
T, K
20 22 24
3
2
1
n, mol/m�
2
�
21.5
23.0
24.2
1
10
–2
10
–3
10
–4
10
–1
Fig. 3. Torsional oscillator results in the adsorbed film states.
(a) Comparison of the normalized superfluid fraction (� �s /
versus T Tc/ ) to the data of
4
He in other 2.5-nm Gelsil [10] and
in Vycor [11]. The adopted data have similar Tc. Inset: Fre-
quency shift �f T( ) for eight coverages. (b) Log-log plots of the
normal fluid fraction � �n T( ) / for four coverages. The solid
lines are the best powerlaw fittings. Inset: Powerlaw exponents
� obtained in the fitting � � �
n T aT( ) / � as a function of n.
2.2.2. Liquid under pressure
Next we mention the results obtained in the pressur-
ized states, where liquid 4He fills the nanopores [1]. Fi-
gures 2,b and c show the �f T( ) data. The data in Fig. 2,b
are obtained by subtraction of the empty cell background
at bulk superfluid trantision temperatures.
We have found that also in pressurized liquid �f T( )
obeys powerlaw at low temperatures. At P � 17. MPa the
normal fluid fraction � �n / is best fitted by � �
n T/
with the exponent ranging from 2.3 to 2.5. At higher
pressures, a T -linear behavior emerges. In order to see the
crossover from the nearly parabolic to linear temperature
dependence, we have fitted the normal fraction to the sum
of T -linear and square terms, � �n aT bT/ � � 2. The ob-
tained coefficients a and b are plotted in Fig. 4. Obvi-
ously, the T -linear term dominates � �n / above 2.3 MPa.
We will discuss the origin of the T -linear term in the next
section.
3. Discussion: localized BEC and phase fluctuation
3.1. The localized BEC
We have proposed in the previous publications that the
QPT behavior, i.e., the anomalous reduction in superfluid
Tc , results from the localization of Bose–Einstein con-
densates in the nonsuperfluid state [6–8]. We believe that
this conjecture is now proven by the heat capacity measu-
rement [4,5].
The idea of the localized BEC (LBEC) is shown in a
cartoon of Fig. 5: When liquid 4He is confined in the
nanopores, the BEC transition temperature should be re-
duced below bulk T� due to the size effect. Around a cer-
tain temperature below T�, many BECs grow from large
pores or intersections of pores, in which 4He atoms can
exchange frequently their positions. The heat capacity
peak is attributed to the formation of LBECs. The size of
the BECs is roughly limited to the pore size. The atom ex-
changes between the BECs via the narrow regions of the
pores are interrupted, because 4He atom has a hard core.
For the movement of one 4He atom, the surrounding 4He
atoms act as a potential. The lack of the atom exchanges
causes fluctuations in phase of the superfluid order pa-
rameter. Therefore, no phase coherence exists among the
BECs, and the whole system has also no global phase co-
herence and does not exhibit superfluidity that can be de-
tected by macroscopic and dynamical measurements such
as torsional oscillator. As the temperature is further de-
creased, the phase coherence between the localized BECs
grows, and macroscopic superfluidity, which is detected
by torsional oscillator technique, is realized when most of
the BECs coalesce.
The heat capacity peak provides a definite evidence
for the formation of LBECs at TB . Broad peak structure in
heat capacity is a common feature of 4He in restricted ge-
ometries, and was recognized as a manifestation of
superfluidity and BEC. The temperature dependence of
the heat capacity (the shape of the peak) of 4He in Gelsil
agrees semi-quantitatively with that in restricted geome-
tries such as Vycor. In our 4He-Gelsil system, however,
the superfluid Tc is much lower than the peak temperature
TB , so the nanoscale BEC occurs around TB without mac-
roscopic superfluid transition.
Superfluidity of 4He confined in nanoporous media
Fizika Nizkikh Temperatur, 2008, v. 34, Nos. 4/5 353
0 1 2 3
0.001
0.002
0.003
0.004
0.005
0.006
0.007
a
b
P, MPa
0
0.002
0.004
0.006
0.008
0.010
0.012
a,
H
z/
K
b
,
H
z/
K
2
Fig. 4. The coefficients a and b obtained from the linear-parab-
ola fitting � �f f T aT bT( ) ( )0 2� � � for the data taken at nine
pressures.
Glass
substrate
BEC
Fig. 5. A cartoon showing the formation of localized BECs
(shown as white) in a porous glass substrate (dark grey).
4
He
atoms form many small BEC’s at the wider regions (especially
intersections of the pores), where the atoms can exchange ac-
tively. The phase of each BEC is illustrated by thick arrows.
Since no phase coherence exist among the LBECs due to the
hard core of
4
He suppressing the spatial exchanges at the nar-
rower regions (light grey), the whole system exhibits no
superfluidity on macroscopic length scale. As temperature is
lowered, thermal phase fluctuations are diminished, and the
system should undergo a macroscopic superfluid transition at
some temperature Tc .
Heat capacity peak without macroscopic superfluidity
has been observed in liquid 4He droplets formed in metal
foils [14]. In this case each droplet that is several
nanometers in diameter is perfectly independent, and the
droplets never exhibit superfluidity in macroscopic sense.
The situation of 4He in nanoporous Gelsil is rather similar
to this droplet system.
In the abovementioned LBEC scenario, the smallness
of the pore size is only essential to the QPT behavior. It
has been pointed out that disorder or randomness in po-
rous structures produces boson localization called Bose
glass state [15]. In the Bose glass state, the condensates
localize at the local minima of the random potentials, and
macroscopic phase coherence is lost by the localization of
atoms as in the case of narrowness-induced LBEC. Koba-
yashi and Tsubota have recently studied superfluidity of
4He confined in a 3D random model potential taking ac-
count of the feature of our 2.5-nm Gelsil [16]. They found
that superfluidity disappears above 4.2 MPa due to the lo-
calization of the BECs. It is in close agreement with our
observation.
3.2. Effects of phase fluctuations
In the LBEC state, phase of the superfluid order pa-
rameter in each LBEC is fluctuating. This phase fluctua-
tion can contribute to the superfluid properties below Tc .
We propose that the T -linear behavior in the super-(or
normal) fluid density observed at high pressures (Fig. 4)
is the manifestation of the phase fluctuations that are
induced thermally (classically).
The effects of phase fluctuation have been studied in
Josephson junction arrays [17] and granular metal films
[18], which show a superconductor–insulator quantum
phase transition by controlling some experimental param-
eters such as magnetic field. It has also been proposed in
the field of high-Tc cuprates that the phase fluctuations
play an important role on the properties of underdoped re-
gimes. Emery and Kivelson (EK) [19] argued that low
carrier-density superconductors such as high-Tc cuprates
are characterized by a small phase stiffness, and conse-
quently the large phase fluctuations dominate notably the
superconducting properties of underdoped regimes. The
emergence of the pseudo-gap states is caused by the local
Cooper pairing without global phase coherence through-
out the sample, and the onset of long range phase order
determines the true superconducting transition that is
detected by macroscopic means. This proposed mecha-
nism is exactly the same as the LBEC picture in the
4He-nanopore system. The LBEC state just corresponds
to the EK pseudogap state.
The superfluid systems that are controlled by phase
fluctuations possess the following characteristics
[22,23]:
1. The superfluid density �s is low, i.e., the phase stiff-
ness (helicity modulus) is small even at 0 K.
2. The local order occurs at higher temperature than
the long-range phase ordering.
3. If the phase fluctuation is thermally excited, �s is
proportional to T at low T .
4. The long-range ordering Tc is proportional to �s .
In high-Tc cuprates, the T -linear behavior was ob-
served by the measurement of penetration depth [20,21].
Although it is also attributed to the d-wave nature of the
gap function, XY models with classical phase fluctua-
tions reproduce quite well the overall temperature de-
pendence of �s [22]. The smallness of �s and the propor-
tionality between �s and Tc was also confirmed and
stressed as an important characteristic of various exotic
superconductors by Uemura et al. [24,25]. The proposed
«universal» relation between Tc and muon relaxation rate
was later reinterpreted by EK as an upper bound of Tc
given by the phase-order temperature [19].
All the abovementioned features of the phase-fluctua-
tion model are actually observed in the 4He-Gelsil system
we studied. As is shown in Figs. 2 and 4, the T -linear be-
havior in �s becomes prominent at pressures higher than
2.3 MPa. This behavior strongly suggests the existence of
classical phase fluctuations which dominates the normal
fluid component. It is also noted that the overall shape of
the �f T( ) curve bears striking resemblance to the
superfluid density of measured in cuprates and the calcu-
lated one in the 3D XY model [22].
Moreover, a plot of Tc versus �s (the so-called Uemura
plot [24,25]) in Fig. 6 clearly have tendencies that at
P � 2 3. MPa �s becomes small and approximately propor-
tional to Tc . The emergence of T -linear term in �s corre-
lates to the change in the slope of Tc s�� curve.
The accuracy of our data in the determination of T -lin-
ear coefficient and Tc s�� relation near Pc is degraded in
our current torsional oscillator measurement because of
the small �s (small signal-to-noise ratio) and the coupling
of oscillation to fourth sound. Measurements of �s by
other techniques such as fourth sound resonance method
will be essential.
The idea of LBEC gives a new perspective to a number
of experimental studies of 4He in restricted geometries.
The detailed torsional oscillator and specific heat studies
by Reppy and coworkers [26–28] show that the superfluid
transition occurs at slightly lower temperature than the
temperature of the broad specific heat peak. At superfluid
Tc , an extremely small peak is additionally observed. As
well as in the Gelsil case, the broad peak is attributed to
the formation of LBECs and the macroscopic superfluid
transition occur at Tc . The LBEC picture in the 4He-Vycor
system is also supported by the neutron and ultrasound
experiment conducted by Glyde, Mulders and coworkers,
in which the roton signals are observed above Tc deter-
354 Fizika Nizkikh Temperatur, 2008, v. 34, Nos. 4/5
Keiya Shirahama, Keiichi Yamamoto, and Yoshiyuki Shibayama
mined by ultrasound. Thus, the «separation» of BEC and
superfluid transition should be a universal characteristic
of 4He in nanoporous media.
The T -linear superfluid density was observed in 4He
filled in packed powders [30] and in 2.5-nm Gelsil [10] at
ambient pressures. In these studies the T -linear behavior
was attributed to the effect of zero-dimensional (0D)
phonons. However, the 0D phonons in the 3D connected
nanopores are hard to imagine. It is rather reasonable to
interpret as the effect of phase fluctuations. Then a ques-
tion arises: Why is the T -linear behavior much more
prominent in packed powder and MT’s Gelsil than ours?
It is conjectured that difference in pore structure influ-
ence the Boson localization and thus the phase fluctua-
tions. Further studies including detailed characterization
of porous materials are obviously intriguing.
4. Summary
In summary, we have determined the anomalous phase
diagram of 4He confined in the 2.5-nm Gelsil nanopores.
It is ultimately proven by torsional oscillator and heat ca-
pacity studies that BEC and superfluidity take place at
separate temperatures. Key physics to understand the
phase diagram and superfluid properties is localization of
Bose–Einstein condensates caused by confinement or dis-
order. Striking similarity to the superfluid behavior in
high-Tc cuprates may also be an important clue to eluci-
date the mechanism of quantum phase transition. The en-
tire phase diagram will be understood basically in terms
of the phase fluctuation model that was proposed by Em-
ery and Kivelson in the interpretation of phase diagrams
of high-Tc cuprates.
Our study shows that 4He in nanoporous media is an il-
lustrative example of strongly correlated bosons in poten-
tial, which produce intriguing quantum phenomena.
This work is supported by the Grant-in-Aid for Prior-
ity Areas “Physics of Superclean Materials”, and Grant-
in-Aid for Scientific Research (A) from MEXT, Japan.
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