Superconducting Niobium Calorimeter for Studies of Adsorbed Helium Monolayers
NNoname manuscript No. (will be inserted by the editor)
Superconducting Niobium Calorimeter for Studies ofAdsorbed Helium Monolayers
Jun Usami · Koki Tokeshi · TomohiroMatsui · Hiroshi Fukuyama , October 30, 2020
Abstract
We developed a calorimeter with a vacuum container made of super-conducting niobium (Nb) to study monolayers of helium adsorbed on graphitewhich are prototypical two-dimensional quantum matters below 1 K. Nb was cho-sen because of its small specific heat in the superconducting state. It is cruciallyimportant to reduce the addendum heat capacity ( C ad ) when the specific surfacearea of substrate is small. Here we show details of design, construction and resultsof C ad measurements of the Nb calorimeter down to 40 mK. The measured C ad wassufficiently small so that we can use it for heat capacity measurements on heliummonolayers in a wide temperature range below 1 K. We found a relatively largeexcess heat capacity in C ad , which was successfully attributed to atomic tunnelingof hydrogen (H) and deuterium (D) between trap centers near oxygen or nitrogenimpurities in Nb. The tunnel frequencies of H and D deduced by fitting the datato the tunneling model are consistent with the previous experiments on Nb dopedwith H or D. Keywords calorimeter, heat capacity, helium monolayer, gas-liquid transition,hydrogen tunneling
Atomically thin He and He films physisorbed on flat surfaces at low temperaturesprovide experimental opportunities for us to study bosonic and fermionic quantumphenomena, respectively, in two-dimensions (2D). Among them, a few layers of He and He adsorbed on graphite are of particular importance because of their
J. UsamiE-mail: [email protected]. FukuyamaE-mail: [email protected] Department of Physics, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033,Japan Cryogenic Research Center, The University of Tokyo, 2-11-16, Yayoi, Bunkyo-ku, Tokyo113-0032, Japan a r X i v : . [ c ond - m a t . o t h e r] O c t Jun Usami et al. rich quantum phase diagrams [1, 2, 3, 4, 5]. Heat capacity measurements are oneof the most sensitive experimental techniques to explore the phase diagrams inthese systems. One important unsolved problem in this field is the possible self-binding of He, i.e., 2D liquefaction of He, which was claimed by Sato et al [6, 7].They found that the uniform fluid state of areal densities lower than 0.6-0.9 nm − is unstable against phase separation into gas and liquid phases below 80 mK, thegas-liquid (G-L) coexistence. This theoretically unexpected finding stimulated newtheoretical studies [8, 9, 10, 11], and some of them [9, 11] can partially explainthe experimental results of Sato et al . but not sufficiently. Similar experimentalindications of the self-binding are also reported in 2D He on different substratesfrom graphite [12, 13].In general, for studies of adsorbed 2D systems, comparison of heat capacitydata obtained on substates with different surface coherence lengths ( ξ ) is cruciallyimportant for determining the true nature of detected phase transitions [14]. Inthe case of exfoliated graphite, the comparison can be done using Grafoil and ZYXsubstrates, where ZYX has a ten times longer ξ ( ≈
200 nm) than Grafoil whichis used in the most previous studies including the measurements by Sato et al .Thus, a new heat capacity measurement with ZYX is highly desirable to test iftheir results vary quantitatively or even qualitatively due to the finite size effects.In addition, it is important to observe the G-L critical point which may exist attemperatures above
80 mK, the high temperature limit of the previous surveys [6,7]. Besides the 2D liquefaction of He, there are many other interesting physics tobe explored by heat capacity measurements in 2D He systems [15, 16, 17, 18].The heat capacity contribution from the empty calorimeter (addendum) withZYX should be minimized to keep reasonably good experimental accuracies, be-cause the specific surface area of ZYX (= 2 m /g) is ten times smaller than that ofGrafoil. Previously, Nakamura et al . constructed a calorimeter with a ZYX sub-strate in a container (sample cell) made of Nylon [19]. Nylon is an easily machinablepolymer with a sufficiently small specific heat below 1 K [20]. It worked well duringthe first several thermal cycles, but then started to leak because of many microc-racks created by water absorbed inside the cell walls due to the high hygroscopyof Nylon. In order to overcome this technical problem, we have constructed a newcalorimeter with a vacuum container made of niobium (Nb), containing the sameZYX substrate as that used in the previous Nylon calorimeter. Nb is a super-conductor with the superconducting transition temperature ( T sc ) of 9.25 K. Thespecific heat of superconductors is known to fall off exponentially with decreas-ing temperature below T sc and in proportion to T below about 0 . T sc due todecreasing numbers of normal state electrons and thermal phonons, respectively.Thus the addendum of Nb calorimeter is expected to be very small below 1 K.In this article, we report design details and measurement results of the ad-dendum heat capacity of the Nb calorimeter. It turned out that the measuredaddendum is as low as that of the previous Nylon calorimeter but is at least twice as large as the estimation based on the amounts of all construction materials of thecell and their known specific heats. By comparing with a theoretical estimationfor heat capacities due to atomic tunneling of hydrogen and deuterium impuritiestrapped by oxygen or nitrogen impurities in Nb, we concluded that the measuredexcess heat capacity comes from these contributions. uperconducting Niobium Calorimeter for Studies of Adsorbed Helium Monolayers 3 There are three basic concepts in our calorimeter design. The first is to minimizethe addendum heat capacity, of course. The second is to increase thermal conduc-tances among essential parts, such as the ZYX substrate, a thermometer and aheater, as high as possible to realize a short internal thermal relaxation time overthe whole measurement temperature range. The third is to achieve a tunability ofthe thermal conductance between the calorimeter and the base temperature plateof a refrigerator so that the same calorimeter can be used in a wide temperature( T ) range from 1 K to even below 1 mK depending on the experiment.To meet these requirements, we carefully chose the other construction mate-rials, besides superconducting Nb, as well as the thermal contact and isolationmethods. For example, no stainless steel or BeCu parts such as bolts and nuts totighten demountable thermal contacts were used in order to reduce the addendumheat capacity. Instead, a specially manufactured alloy, Si . Ag . (Tokuriki Hon-ten Co., Ltd.), was used for this purpose. Most of the thermal links are made ofhigh purity silver (Ag) (Tokuriki Honten Co., Ltd.; 99.999%) rather than copper(Cu), since higher residual resistivity ratios (RRRs) of up to 3000 can more easilybe obtained for Ag than Cu by a simple heat treatment at 630 ◦ C for 2 h in anoxygen pressure of 0.1 Pa unless the size effect limits RRR. The mechanism be-hind this heat treatment is the “internal oxidation and segregation” of magneticimpurities in noble metals [21]. Due to the higher RRR value, we could reduce theamount of Ag used.To our knowledge, Nb has never been used as a main construction material inpreviously developed vacuum chambers for low- T experiments. This is presumablybecause it does not seem easy to make a leak-proof seal for Nb which cannot besoldered. Note that Nb has a very small thermal contraction [22] compared totypical epoxy sealants for cryogenic applications such as Stycast 1266 or 2850FT.It was also unknown for us if commercially available Nb materials are helium leak-proof or not. Therefore, we first confirmed the leak-proofness of a prototypical Nbcell sealed with Stycast 1266 at T = 77 K, and then constructed the actual samplecell.Fig. 1 shows a schematic drawing and a photograph of the calorimeter con-structed in this work. The sample cell consists of three Nb parts: the (a)circulartop and (b)bottom covers of 45 mm in outer diameter and the (c)main cell bodywith a rectangular inner cross section of 22 ×
33 mm . They are machined from asingle Nb rod (Changsha South Tantalum Niobium Co., Ltd.). Typical impurityconcentrations in the Nb rod ( > . µ m thick Ag foil toassist thermalization of the substrate. Details of the original substrate preparationare reported elsewhere [19]. The ZYX substrate was taken out of the previous Nylon cell and was baked at 110 ◦ C for 10 h in vacuum. Then, it was enclosedin the new Nb cell and sealed with Stycast 1266 in a glove box with a nitrogen(N ) atmosphere. The (e)thin Ag foils are tightly connected to (f)three thick Agfoils (0.2 mm thickness) with the (g)SiAg bolt and nuts inside the cell. The thickAg foils and (h)two CuNi capillaries (0.6 mm inner diameter) are fed through Jun Usami et al.
20 mm ( e ) Thin Ag foils ( k ) Chip resistor heater ( n ) Cu weak thermal link ( j ) RuO2 thermometer ( a ) Nb top cover( d ) ZYX substrate ( f ) Ag foil thermal links ( g ) SiAg bot and nut ( h ) CuNi capillaries ( i ) Stycast 1266 cap for feedthroughs ( m ) Vespel SP22 thermal isolation rods( l ) Vespel SP22 thermal isolation pillars( o ) Mixing chamber ( b ) Nb bottom cover( c ) Nb cell body Fig. 1
Schematic drawing ( left ) and photograph ( right ) of the Nb calorimeter constructed inthis work. a (i)small Stycast 1266 cap on the top Nb cover which are sealed with Stycast1266. One of the CuNi capillaries is for sample filling, and the other is to connectthe cell to a low- T strain pressure gauge (not shown in the figure) to measuresample gas pressure in situ . After curing the bond, the calorimeter was takenout from the glove box and assembled underneath the mixing chamber plate of adilution refrigerator as described below. No He leak was detected from the Nb cell( < × − ccSTP/s) when He gas of 1 . × Pa was introduced to the cell at T = 40 K.Two of the three thick Ag foils thermally connect the (j)RuO thermometer andthe (k)heater to the ZYX substrate directly. The last one connects the substratewith the mixing chamber through a weak thermal link. The thermometer, whichmonitors the substrate temperature, is a RuO chip register (Alps Electric Co.,Ltd., 470 Ω) wrapped in a silver foil of 50 µ m thickness. This foil serves not only asa thermal link but also as a radiation shield for the register. As the heater elementfor heat capacity measurements, we used a metal thin film resistor (Susumu Co.,Ltd., 100 Ω). The thermometer and the heater are supported from the Nb top coverwith (l)thermal isolation pillars made of Vespel SP22 (E. I. du Pont de Nemoursand Company).The Nb cell is supported from the mixing chamber plate with (m)three VespelSP22 rods. The (n)weak thermal link, which consists of two copper wires of 0.1 mmin diameter and 10 cm in length (RRR = 133), connects between the ZYX substrateand the (o)mixing chamber with a moderate thermal conductance so that we canemploy the quasi-adiabatic heat pulse method [23] for heat capacity measurements in the temperature range of 40 mK ≤ T ≤ uperconducting Niobium Calorimeter for Studies of Adsorbed Helium Monolayers 5 Table 1
Construction materials and their weights, which are used in the present Nb calorime-ter. The symbols correspond to those in Fig. 2(b).symbol material weight (g)A niobium 200B silver 20C copper 4.3D ZYX exfoliated graphite 19E Stycast 1266 2 is 40 mK, while the base temperature of the mixing temperature is 18 mK. Wedidn’t employ a superconducting heat switch nor a mechanical heat switch notonly to simplify the cell design but also to avoid large heat generation when theyopen at the lowest temperature. In Table 1, we list amounts of all materials usedin the present calorimeter.
Figure 2(a) shows the measured addendum heat capacity ( C ad ) of the presentNb cell ( C Nbad : (yellow) dots). It has a steep temperature dependence at T (cid:28) T c as is expected for superconductors. Thus, C Nbad is much smaller than C ad of thesample cell made of silver, a normal metal, ( C Agad : (blue) dashed dotted line [7]),where the specific heat of conduction electrons falls slowly in proportion to thetemperature at T ≤ T = 0 . C ) anomaly associated with the G-Ltransition in the second layer of He adsorbed on Grafoil [3] (areal density ρ =14 nm − ) whose magnitude is normalized to be consistent with the surface areaof our substrate. Our Nb calorimeter would be able to detect this anomaly, sincethe peak height is larger than C Nbad by a factor of two at the same temperature.The kink at T = 0 .
12 K drawn by the (pink) line (anomaly-2) in the figure isthe C anomaly associated possibly with the G-L transition in He submonolayer(0.092 layers) floating on a 1.23 nm-thick superfluid He film adsorbed on Nucle-pore substrate [12]. C Nbad is about seven times smaller than this anomaly at thesame temperature, which indicates that its detection would be much easier thanthe 0.7 K anomaly. As mentioned in Introduction, the possible G-L critical temper-ature ( T c ) in monolayers of He, which we are seeking for, is expected to emergeat T ≥
80 mK. The upper bound should be T c = 740 mK in the second layer of He on Grafoil [24]. Note that T c in He systems should be lower than in Hesystems due to larger zero-point energies. Although the phase transition natureis unknown, the magnitude of the expected C anomaly would not be so differentfrom those of the two above-mentioned anomalies that were found previously indifferent 2D He systems. Therefore, we expect to detect the possible finite- T G-Ltransition of He in 2D with this Nb calorimeter which is immune from moisture brittleness unlike the Nylon cell.As can be seen in Fig. 2(a), C Nbad is substantially larger than the calculatedaddendum heat capacity ( C Nbcal ; (black) thick solid line) in the whole temperaturerange we studied. We denote the excess heat capacity as C Nbex = C Nbad − C Nbcal . Here, C Nbcal is evaluated from the known properties of all construction materials used in
Jun Usami et al. -5 -4 -3 measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) (a) (b) anomaly-2 anomaly-1 adNb C calNb C C [19] calNylon [19] CC [7] BA: Nb [25]B: Ag [26]C: Cu [26]D: graphite [27]E: Stycast1266 [28] A CDE adNylon adAg calNb C measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) -5 -4 -3 measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) -5 -4 -3 measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) -5 -4 -3 measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) -5 -4 -3 measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) -5 -4 -3 measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) -5 -4 -3 measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) -5 -4 -3 measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) -5 -4 -3 measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) -5 -4 -3 measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) -5 -4 -3 measure data ZYX Nb stycast Cu Ag ZYX+Nb+stycast Temperature (K) H ea t c apa c i t y ( J / K ) Fig. 2 (a) Measured addendum heat capacities of the present Nb cell ((yellow) dots), the Agcell ((blue) dashed dotted line [7]), and the Nylon cell ((green) dashed double-dotted line [19])are compared. The heat capacity anomaly peaked at T = 0 . He on Grafoil [3] (anomaly-1: (purple) line). The anomalyat T = 0 .
12 K observed in He submonolayer on a He superfluid thin film on Nuclepore issupposed to be related to the G-L transition [12] (anomaly-2: (pink) line). The (black) thickand (green) thin solid lines are addenda calculated from known properties of their constructionmaterials in the Nb and Nylon cells, respectively. (b) Calculated heat capacity contributionsfrom all construction materials shown in Table 1 to the total one ((black) thick line) in the Nbcell. Here we used the published specific heat data for (A) Nb [25], (B) Ag [26], (C) Cu [26],(D) graphite [27], and (E) Stycast 1266 [28]. the cell (see Table 1). The contribution from the Nb cell walls to C Nbcal is dominantat T ≥ . C Nylonad − C Nyloncal ) than C Nbex . In Fig. 2(a), the measured addendumheat capacity C Nylonad and the calculated one C Nyloncal are also shown by the (green)dashed double-dotted line and the (green) thin line, respectively [19].The observed large C Nbex can be explained by atomic tunneling of hydrogen (H)or deuterium (D) impurities trapped by trap centers such as oxygen (O) or nitrogen(N) in Nb [29]. Figure 3(a) shows the excess specific heat of our Nb cell c ex , i.e., C Nbex divided by the molar amount of Nb used in the calorimeter, ((blue) dots). The dataseem to consist of two components. One component, which dominates c ex at hightemperatures, rapidly falls down with decreasing. The other one dominates below0.2 K. Also shown in Fig. 3(a) are excess specific heats obtained by the previousworkers for Nb samples with H of 0.08at% ((green) dashed dotted line [29]), Dof 0.0137at% ((orange) dashed line [25]) and 1.4at% ((orange) dotted line [29])introduced after high-vacuum annealing. Here the concentrations of H and D inthe data of Ref. [29] are those determined by the authors themselves, and those of Ref. [25] are obtained by fitting their data by ourselves with functional formsdescribed below. Note that the measured specific heat of the Nb sample afterthe high-vacuum annealing at 2250 ◦ C in Ref. [25] follows almost exactly C ∝ T expected from the Debye model (lattice vibrations). All the data shown in Fig. 3are plotted after subtracting the T contribution. As can be seen in the figure, the uperconducting Niobium Calorimeter for Studies of Adsorbed Helium Monolayers 7 (a) (b) This workH: 0.08% [29]D: 1.4% [29]D: 0.0137% [25] This workFitted to Eq. 6H: 0.06%D: 0.0016%
Fig. 3 (a) Excess specific heat data ( c ex : dots) of the present Nb cell are plotted with the c ex data of Nb doped with hydrogen (H) at 0.08% ((green) dashed line [29]) and with deuterium(D) at 0.0137% ((orange) dotted line [25]) and 1.4% ((orange) dashed dotted line [29]) measuredby the previous workers. (b) Fitting of the c ex data (dots) to Eq. 6 (solid line). The fittingparameters are given in Table 2. The dashed and dotted lines are contributions from the H-and D-tunneling terms in Eq. 6, respectively. high- T component of our data is likely due to the H tunneling and the low- T onedue to the D tunneling.Based on the above-mentioned scenario, we analyzed our data, c ex ( T ), quanti-tatively following the method described in Ref. [29] as follows. The energy splitting E of the ground state for a particle in an asymmetric double well potential is givenby E = (cid:0) J + (cid:15) (cid:1) , (1)where J is the tunnel frequency, and (cid:15) is the potential energy difference between thetwo minima caused by a random arrangement of neighboring O(N)-H or O(N)-Dcomplexes. Such (cid:15) has a distribution approximated by the Lorentzian distributionfunction Z ( (cid:15) ) [30]: Z ( (cid:15) ) = (cid:15) π ( (cid:15) + (cid:15) ) . (2)Here the width (cid:15) is the typical energy difference of the double well. The specificheat of this tunneling system per one O(N)-H(D) complex, c TS , can be written as c TS = k B (cid:90) ∞ J dEZ ( E ) c ( E, T ) , (3) where Z ( E ) = 2 E(cid:15) π ( E − J ) / ( (cid:15) + E − J ) , (4) c ( E, T ) = (cid:18) Ek B T (cid:19) exp ( − E/k B T )[1 + exp ( − E/k B T )] (5) Jun Usami et al. Table 2
Physical parameters obtained by fitting the c ex data of our Nb calorimeter to Eq. 6.Also shown are parameters obtained from the c ex data by other workers [25, 29]. The param-eters of Ref. [25] are the results we obtained by fitting their c ex data in the same manner asfor our data, whereas those of Ref. [29] are results of their own analyses where n H and n D arefixed at those estimated from the measured RRR values. J H [K] n H [%] (cid:15) , H [K] J D [K] n D [%] (cid:15) , D [K] Ref.1.85(9) 0.06(2) 12(5) 0.11(9) 0.0016(5) 0.9(5) This work1.5(1) 0.017(3) 5(1) — — — [25]— — — 0.2(1) 0.0137(4) 2.9(3) [25]1.8(6) 0.08 21(4) — — — [29]2.0(2) 0.24 58(2) — — — [29]— — — 0.21(4) 0.05 10(10) [29]— — — 0.2(1) 0.26 33(1) [29]— — — 0.2(3) 1.4 88(7) [29] and k B is the Boltzmann constant. Finally, we fit our c ex data to the followingexpression: c TS = (cid:88) i =H , D n i N A k B (cid:90) ∞ J i dEZ i ( E ) c i ( E, T ) , (6)where N A is Avogadro’s number, and n H and n D are the concentrations of O-Hand O-D complexes in Nb, respectively. Here, i stands for H or D.The fitting result is shown as the (blue) solid line in Fig. 3(b), and the fittingparameters are summarized in Table 2. In the whole temperature range, the fittingquality is satisfactory. The deduced J values, J H = 1 . ± .
09 K and J D = 0 . ± .
09 K, are in reasonable agreement with the previous workers’ results: J H = 2 . ± . J D = 0 . ± .
02 K obtained by heat capacity measurements by Wipf andNeumaier (WN) [29] and neutron spectroscopy measurement [31]. The larger errorbar in our J D estimation is due to the much lower deuterium concentration n D in our as-received Nb sample compared to those in the previous workers’ samplesinto which the D impurities were intentionally doped after cleaning by the high-vacuum annealing. It is known that J i is independent of n i , whereas (cid:15) increasesrapidly with increasing n i [29]. Our data are consistent with these trends. Overall,it is strongly suggested that the measured excess heat capacity in the addendumof our calorimeter is due to atomic tunneling of hydrogen isotopes embedded inthe Nb parts. We developed the calorimeter that is mainly made of Nb for the study of lowtemperature properties of He monolayers adsorbed on a ZYX graphite substrate.
The use of Nb is because of its small contribution to the addendum heat capac-ity, C ad , in the superconducting state. The measured moderate thermal relaxationtime, lowest attainable temperature (40 mK) and the small C ad meet the require-ments to detect subtle heat capacity anomalies associated with phase transitionsin adsorbed He systems in the temperature range between 40 mK and 1 K. One uperconducting Niobium Calorimeter for Studies of Adsorbed Helium Monolayers 9 promising application is the possible finite- T gas-liquid transitions in He mono-layers expected to be observable at temperatures between 80 and 740 mK.We also found the additional heat capacity ( C ex ), an excess over the expectedaddendum heat capacity that is calculated from the known specific heats of con-struction materials. C ex can be explained by atomic tunneling of hydrogen (H) anddeuterium (D) impurities in Nb. The tunneling frequencies of H and D obtainedby fitting the C ex data to this model are consistent with those obtained in the pre-vious studies. If one can anneal Nb parts in a high vacuum at T = 2200 ◦ C beforeassembling the cell, C ad would be further reduced by a factor of three providing afurther improvement in the resolution of heat capacity measurement. Acknowledgements
We are grateful to Sachiko Nakamura for helpful discussions and shar-ing her technical experiences on the construction of the previous Nylon calorimeter with us.The authors appreciate Megumi A. Yoshitomi for her contributions to the early stage of thiswork. We also thank Ryo Toda and Satoshi Murakawa for their valuable discussions and themachine shop of the School of Science, the University of Tokyo for machining the Nb calorime-ter. This work was financially supported by JSPS KAKENHI Grant Number JP18H01170.J.U. was supported by Japan Society for the Promotion of Science (JSPS) through Programfor Leading Graduate Schools (MERIT) and Grant-in-Aid for JSPS Fellows JP20J12304.
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