The phase diagram of two atomic layers of hetium four (4He) adsorbed on graphite was studied using an experimental method. Heat capacity and vapor pressure have been measured as a function of temperature for a series of coverage. The system 4He on graphite comprises a pure Bose system in the presence of a periodic potential. The second layer, especially, is subjected to a weakly comrgated potential, and various phenomena are expected to arise: for example, reentrant superfluidity was observed only in the second layer [1]. However, in reality, the phase diagram of the second layer is still controversial. Although heat capacity peaks usually indicate phase transitions, peaks observed by a previous experiment were too obscure to construct a phase diagram [2]. This thesis describes improved measurements of heat capacity using high-quality graphite, ZYX, as a substrate. As ZYX. comprises much larger crystals than Grafoil used in the previous measurement, the correlation length of films on ZYX was not overly suppressed. Vapor pressure was also measured to confirm phase boundaries determined from the heat capacity.

The important features observed to determine the phase boundaries are (a) a sub-step in vapor pressure isotherms at T = 1.75 K, (b) constant chemical potential of 4He films for wide coverage region indicating gas-liquid coexistence, and (c) substrate-dependence of heat capacity peaks from comparison with previous study results employing Grafoil.

(a) Sub-step in vapor pressure isotherms

Vapor pressure of 4He bilayer films was measured in the coverage range of 19.0 nm(-2) to 20.7 nm(-2) at temperatures less than 2.9 K. In the coverage range between 19.4 nm(-2) and 19.7 nm(-2), the vapor pressure at T = 1.75 K stays constant at 2 × 10(-3) mbar. In an adsorption isotherm with axes of coverage and pressure, this behavior looks like a slight sub-step. Since the chemical potential of the vapor is equal to that of the films in thermal equilibrium, which is a function of pressure and temperature, the sub-step shows directly that the films have constant chemical potential throughout the coverage range. Therefore, distinct phases are realized at both ends of the coverage range, ρ - 19.4 nm(-2) and 19.7 nm(-2), coexisting within the sub-step. This coverage range overlaps that of the superfluidity observed in recent torsional oscillator experiments [3].

(b) Constant chemical potential indicating liquid-gas coexistence

The chemical potential of 4He films at coverages less than 22.0 nm(-2) and that of a layer of 3He on 4He at coverages less than 8.0 nm(-2) were derived from the vapor pressure. The chemical potential of bilayer 4He stays almost constant over the coverage range between 13.0 nm(-2) and 16.0 nm(-2), while that of the 3He-4He layered films gradually increases with the coverage in the corresponding coverage range. It suggests that two phases coexist in 4He films, while 3He films form a uniform phase [4]. Beyond 16.0 nm(-2), the chemical potential of 4He films starts to increase gradually with the coverage, which indicates compression of a uniform phase.

(c) Substrate-dependence of heat capacity peaks

Heat capacity of 4He films was measured at temperature in the temperature range of 0.1–1.7 K for coverages between 2.5 nm(-2) and 23.0 nm(-2). Comparing data after the system-size change is a useful tool for distinguishing ordinal transitions from a KT transition and one-particle phenomena; thus, all heat capacities obtained were compared with precision with those in the previous study using Grafoil as a substrate [2]. On the whole, various substrate-dependencies were observed.

In the coverage range between 13.0 nm(-2) and 16.0 nm(-2), heat capacity peaks were clearly enhanced by using ZYX. A sharp kink was observed throughout the coverage range, compared to a rounded kink when using Grafoil [2]. The heat capacity diverges logarithmically around the peak temperature at 15.0 nm(-2), where the maximum peak height was obtained. On the other hand, the peak temperature was independent of both substrate and coverage. Because the chemical potential stays constant over this coverage range, there is the coexistence of two phases, the gas and liquid phase.

Meanwhile, in the coverage range of 16.5 nm(-2) to 18.7 nm(-2), the heat capacity data obtained by using ZYX and those with Grafoil look alike. Both have a bump, instead of a peak, which suggests that the characteristic length of the phenomenon, the cause of the bump, is shorter than the platelet size of Grafoil, namely 10– 20 nm. Therefore, this bump does not indicate any long-range order, though it may indicate a quasi-long-range order that arises in a KT transition. In this coverage range, the chemical potential indicates a uniform phase. It is probable that the 4He films form a uniform fluid here.

In the coverage range of 19.2 nm(-2) to 20.4 nm(-2), a broad peak was observed at ≈ 1.4 K. By using ZYX, this peak was enhanced by a maximum of 15% and the peak temperature shifted by ≈ 40 mK [2], thus indicating an ordinal phase transition. The peak amplitude increases linearly with the coverage in the coverage range between 19.3 nm(-2) and 19.7 nm(-2), where the adsorption isotherm shows a sub-step. These facts are consistent with the assumption of two-phase coexistence, suggested by the sub-step. However, even though being enhanced, the peak was still broad. Though bilayer 3He behaved similarly to bilayer 4He in the relevant coverage range, no feature was observed for a layer of 3He on 4He in corresponding coverage range. The heat capacity of the 3He-4He layered films was dominated by the contribution from the mixing of the isotope atoms between layers. The energy scale for exchange of helium atoms between layers should be as large as the onset temperature of the contribution, ≈ 0.4 K, which is much less than the peak temperature of pure isotope systems. From these observations, it can be concluded that the peak indicates a phenomenon of bilayers.

Also, higher coverages were examined, and a signature of the melting of an incommensurate solid and the gas-liquid transition of the third layer were observed; though the margin of error was large, owing to a high vapor pressure.

As a reference system, the first layer of 4He films was also investigated. For the first layer, the comrgation in the substrate potential of graphite is strong enough to cause a structural order called √3×√3 registry. The registry is completed at the density of 6.366 nm(-2), below which, the ordered sotid covers a certain portion of the graphite surface. At coverages higher than 5 nm(-2), a sharp peak observed at T ≈ 3 K indicates an order-disorder transition of the structure. Since the transition had been previously investigated using ZYX [5], the peak was measured this time to confirm the quatity of our ZYX substrate. Strong enhancement of the peak height and a small peak-temperature shift by ≈ 20 mK were reproduced; furthermore, coverage-dependency of the peak was investigated in detail, and a strong anisotropy in the peak amplitude was observed: excess atoms easily destroy the peak while holes do not affect it much. As this anisotropy was not observed in the previous experiments with Grafoil [2], it suggests higher homogeneity in the ZYX surface. (The anisotropy is almost opposite to that of the second layer in the coverage range between 19.2 nm(-2) and 20.4 nm(-2). At coverages less than 6 nm(-2), an extra bump was observed at low temperatures in several experiments using different graphites [2,6], whose cause is still not explained. To study the bump, monolayer 4He films in the coverage range between 2.5 nm(-2) and 5.5 nm(-2) were examined; this bump was clearly enhanced in amplitude, but the peak temperature depends significantly on coverage and the peak was sti[[ rounded. These features are different from other anomalies observed in the second layer.

The experimental results of the phase transitions were thus collected for 4He filmrs adsorbed on ZYX graphite. In summary of these observations, a new phase diagram of the second layer of 4He on graphite is proposed, as shown in the figure below.

Figure: Proposed phase diagram of bilayer 4He adsorbed on graphite.

本論文は、4章からなる。

第1章はIntroductionである。2次元ヘリウムのこれまでの研究結果について、ヘリウムは、グラファイト基板への吸着によって実現される理想的な量子多体系を形成し、下地の周期ポテンシャルに由来する格子模型的な振る舞いと、連続的な2次元系としての振る舞いの拮抗により豊かな物理現象が発現される事を説明している。特に、グラファイトに吸着した第2層目の4Heは、特定の密度領域のみで超流動が発現するという特異な現象が観測されており、その正体についてのこれまでの議論が説明されている。これら背景として、吸着第2層目の状態相図を熱力学的に検証する事を目的とし、広い面密度および温度範囲で2次元4Heの熱容量と蒸気圧の測定を実験手段を用いて研究したことが述べられている。

第2章は、Experimentsである。試料基板の原料である剥離グラファイトの特徴を述べると共に、これまでの研究に使用されて来たGrafoil基板が、大きな比表面積が得られる一方、結晶子の大きさが小さく、測定物理量にサイズ効果が現れやすいという問題がある事を指摘した。本研究では、従来の基板に替えてZYX基板を用いた。その有効性を調べるために、吸着第1層目の整合固相における4Heの熱容量と窒素分子の蒸気圧を測定し、ZYXはGrafoilに比べて結晶子が大きく均質性も高いことを検証した。また、この章では、本研究で用いた2次元ヘリウム試料の作成方法、熱容量および蒸気圧測定の測定装置および測定方法も詳細に紹介している。

第3章は、Results and Discussionである。熱容量測定および蒸気圧測定の実験結果とそれぞれの考察を行っている。細かな間隔で面密度を詳細に測定し、特徴的な4種類の熱容量異常を観測し、それぞれの検証を行っている。また、蒸気圧から計算される化学ポテンシャルの密度依存性を比較検討する事により、吸着第2層目にヘリウム原子が入り始める総面密度を決定し、次に、基板の効果が如実に現れた気液相転移の熱容量異常から気液共存線を検証した。その結果、高密度状態では一様流体相が存在し、その熱容量異常は基板依存性を示さないことを明らかにした。また、超流動応答が観測されている密度周辺では、特異的な相の存在を示す蒸気圧等温線の特異性を発見した。理論計算では、このような相の存在は否定されているが、本研究の熱容量測定から、この相の低密度側では一様流体相、高密度側では不整合固相と共存する事を明らかにした。この事は、この相が整合固相であることを強く示唆している。この相の存在については、3Heを用いた同位体効果も検証している。

第4章は、Conclusionsである。前章までの議論を基に、ZYX基板を用いた場合の吸着第2層目4Heの状態相図を提唱し、低密度側から、気液共存領域、一様流体領域、2相共存を経て、一次転移が起きる密度領域で整合固相を形成すること、さらに整合固相が高密度側では、2相共存相を経て不整合固相の領域に至る事を明らかにした。最後に、今後の指針を述べている。

以上のように本論文で行われた研究は、熱容量および蒸気圧測定を行い、ZYX基板上の吸着第2層目4Heの詳細な状態相図を提唱し、その諸特性を明らかにしている。これらの結果は、注意深く高い精度で行われた信頼性の高い実験によりなされ、高く評価された。

なお、本論文の一部は松井幸太、松井朋裕および福山寛との共同研究であるが、論文提出者が主体となって実験および考察を行ったもので、論文提出者の寄与が十分であると判断する。

したがって、審査員全員の一致により、博士(理学)を授与できると認める。