I.Introduction

SrTiO3 is currently widely used in oxide electronics mainly as a substrate because of the availability of atomically smooth surfaces with clear steps and terraces. Recently, there have been many efforts to realize low-dimensional electronic states in electron-doped SrTiO3 in analogy to high-mobility GaAs heterostructures. Different from carriers in such conventional semiconductors, the carriers of SrTiO3 originate from three highly anisotropic t2g bands of titanium d-orbitals. Furthermore, the most outstanding feature of SrTiO3 is the low-density superconductivity, where electron mobility is still high enough to observe quantum conduction. SrTiO3 may be the best candidate to realize coexistence of such multiple novel quantum phenomena. Although there are only theoretical studies about the interplay between such states, it is a great challenge to make a foundation to investigate unexplored physics in real materials systems.

In this study, we aimed at fabricating superconducting low-dimensional electronic states using SrTiO3. While most studies rely on the conduction at the surface of SrTiO3 by forming an LaAlO3/SrTiO3 interface or using electrostatic field-effect gating, we tried to embed the conduction layer into the host insulating SrTiO3. This is because the high electron mobility in SrTiO3 is a result of effective screening from impurities or defects by the extremely large permittivity exceeding 10,000, and such screening may not be effective at the surface due to discontinuity of the crystal lattice.

II.Experimental

For the fabrication of thin films, we employed pulsed laser deposition using a vacuum chamber equipped with an infrared laser heating system. A SrTiO3 substrate was ultrasonically washed in acetone and methanol, and mounted on a substrate holder with Pt paste for thermal contact. Thin films were deposited using Nb- or La-doped SrTiO3 targets under an oxygen partial pressure as low as 10-8 Torr. For ablating the targets, a KrF excimer laser was used with an energy of 20 mJ/pulse (0.5 J/cm2) and a repetition rate of 5 Hz. After growth, samples are annealed ex-situ at 600 °C in 1 bar flowing oxygen or in-situ at 900 °C under 10-2 Torr in order to fill oxygen vacancies introduced in the substrate as well as in the thin film. By measuring transport properties, we confirmed that oxygen vacancies are sufficiently filled in either annealing condition.

The structure of the thin films was characterized by x-ray diffraction and atomic force microscopy, and the thickness was measured by a stylus profiler. For transport measurements, electrodes were made by direct ultrasonic bonding with Al wires onto the surface of the samples. Transport properties were measured in a cryogenic dewar equipped with a superconducting magnet. For ultra-low temperature measurements, we used a dilution refrigerator equipped with a rotator as well as 14 T superconducting magnet.

III.Results and discussions

1.Fabrication of high-quality electron-doped SrTiO3 thin films

In order to realize the low-dimensional structure discussed in the Introduction section, a technique to fabricate sufficiently high-quality thin films is crucial. However, the quality of SrTiO3 thin films is usually degraded compared with that of bulk single crystals, showing low electron mobility and deactivation of carriers. This is primarily because of the high density of cation defects introduced by the nonequilibrium growth process during crystallization of adatoms. This problem is solved by using high growth temperature to provide enough energy for the adatoms to migrate on the surface.

In order to investigate the growth temperature dependence of the film quality, we grew 100 nm-thick 0.1 at. % Nb-doped SrTiO3 on SrTiO3 substrates and measured x-ray diffraction and Hall effect. Figure 1 shows the growth temperature dependence of the lattice expansion from the bulk value and the low-temperature electron mobility. The lattice expansion reflects the amount of cation vacancies. The figure indicates that high temperature above ~ 1050 °C is necessary to obtain high-electron mobility by reducing cation defects. For the purpose of forming two-dimensional structures, we fabricated a thin-film heterostructure with 100-nm-thick undoped SrTiO3 layers above and below a 1 at. % Nb-doped SrTiO3 layer. Figure 2 shows the results of transport measurements at 2 K by varying the thickness of the doped layer. While the carrier density is almost consistent with the nominal value, the electron mobility is enhanced by reducing the thickness of the doped layer. This may be an effect of nontrivial broadening of the electron wavefunction beyond the confined ionized impurity region.

2.Three-dimensional to two-dimensional crossover of superconductivity

Given the fabrication technique to make high-quality SrTiO3 thin films, we investigated the dimensional crossover of superconductivity using the same samples as in Fig. 2. Figure 3(a) shows the temperature dependent resistivity for a sample with x = 5.5 nm, exhibiting clear superconducting transition around T = 0.37 K. Effects of dimensionality is reflected by the anisotropy of the upper critical magnetic field (Hc2). In two-dimensional superconductors, the temperature dependence of Hc2 at〓 = 0° and 〓= 90° is expressed as and , respectively, where 〓0 is the quantum flux,〓 is the coherence length, d is the superconducting thickness, and Tc is the superconducting transition temperature. The experimental data are well fitted by these equations near Tc, as shown in Fig. 3(b). The square root temperature dependence of Hc2|| is characteristic of two-dimensional superconductivity in particular. By using these equations, we can estimate the superconducting thickness from . This value is compared with the intended thickness during thin film growth for several samples with different thickness of the conduction layer in Fig. 3(c), showing reasonable consistency in the regime dGrowth < 〓.

3.Shubnikov-de Haas oscillations

Because of the enhancement of electron mobility by〓-doping in thin samples, 〓c〓 can exceed 1 at high magnetic fields, satisfying the condition to observe Shubnikov-de Haas oscillations at low temperatures, where 〓c = eB/m* is the cyclotron frequency and〓 is the scattering time. High-field magnetoresistance was measured for a sample with x = 5.5 nm at 100 mK as shown in Fig. 4(a). Parallel magnetoresistance showed small magnetic-field dependence, while perpendicular magnetoresistance was strongly positive with small oscillations. By subtracting the positive background of the perpendicular magnetoresistance, clear Shubnikov-de Haas oscillations were observed, as shown in Fig 4(b). By rotating the samples with respect to the magnetic field direction, we found that the oscillations are well scaled by H〓= Hsin〓 instead of the absolute value of the magnetic field, as is evident from comparing Figs. 4(b) and 4(c). This indicates a cylindrical-shaped two-dimensional Fermi surface. This is the first direct observation of a two-dimensional Fermi surface in SrTiO3. However, the carrier density estimated from these oscillations is about one order of magnitude smaller than the carrier density estimated from Hall effect. This is probably because only some of the electrons in the selected subbands contribute to the oscillations, while total number of electrons are measured by Hall effect.

IV.Conclusion

In this study, we aimed at realizing a superconducting two-dimensional electron gas in SrTiO3. As a result, we succeeded in making high-quality SrTiO3 thin films and observing a two-dimensional Fermi surface by Shubnikov-de Haas oscillations when the thickness of the conducting layer reduced. We also observed a crossover from three-dimensional to two-dimensional superconductivity. Although multiple subband occupation prevented clear observation of a quantum Hall effect, further improvements may lead to a new phase where novel phenomena based on interplay between multiple quantum effects can be observed.

Fig. 1. Growth temperature dependence of the lattice expansion (filled circles) and electron mobility at 2 K (open circles) for 0.1 at. % Nb-doped SrTiO3 grown on SrTiO3 substrate. The lattice constant of bulk SrTiO3 is 0.3905 nm.

Fig. 2. Carrier density (filled circles) and electron mobility (open circles) estimated by Hall effect at 2 K as a function of doped layer thickness for the structure shown in Fig. 1. The dopant concentration of the doped layer is 1 at. %.

Fig. 3. Superconducting properties of a Nb-doped SrTiO3 layer embedded in undoped SrTiO3 layers (a) Temperature dependence of the resistivity with Tc = 0.37 K. (b) Temperature dependence of Hc2 in the two geometries. The curves are fitting by the functional forms of Hc2〓 and Hc2|| represented in the text. The inset shows the geometry of the sample. In (a) and (b), the thickness of the conduction layer is 5.5 nm. (c) The thickness estimated using a functional form of dTinkham is compared with the intended thickness during growth.

Fig. 4. (a) High-field magnetoresistance of a sample shown in Fig. 1 with x = 5.5 nm at〓 = 0° and 〓= 90° measured at 100 mK. (b) Angular dependence of Shubnikov-de Haas oscillations with the positive background subtracted from (a). (c) Shubnikov-de Haas oscillations plotted using H〓=Hsin〓nstead of the absolute value of the magnetic field.

本論文は10章からなり、第1章はペロブスカイト型遷移金属酸化物薄膜を中心とした酸化物エレクトロニクスの発展と現状を概観したのち、それを踏まえて今回の研究の目的を述べている。第2章はこの研究において注目したチタン酸ストロンチウムのバルクについて過去の研究を概観している。特に、フォノン構造と構造相転移、電子バンド構造、超伝導、また、単結晶作製に必要な相図と欠陥構造を詳しく説明している。第3章は今回用いた主な装置である、パルスレーザー堆積用真空チャンバー、構造解析用のX折装置、低温測定用のクライオスタットと希釈冷凍機について一般的原理と今回の実験において特徴的な点を説明している。第4章から第7章は本論文の研究における実験結果について述べられており、各々の章では高品質チタン酸ストロンチウムの薄膜作製、低次元構造の作製、超伝導の次元性転移、低次元電子状態の観測にそれぞれ焦点が当てられている。第8章では実験で用いた低次元構造の電子状態について簡単なモデル計算を行った結果を示している。第9章は今回の結果を踏まえ研究の将来展望を見据えた現在の研究状況を述べている。最後に第10章において全体を総括している。

本論文は非常に多彩な物性を示す遷移金属酸化物に注目し、特にその中でも従来の半導体と同程度な高移動度電子をもち、かつ超伝導を示すチタン酸ストロンチウムにおいて高品質な低次元構造を作製し、その低次元特有の物性を測定することを主題としている。実験の第一段階として、バルク単結晶品質の薄膜が過去に作製されていないことに着目し、薄膜品質改善を単結晶の相図と欠陥生成という基本的な点に立ち返り試みている。その結果、従来のチタン酸ストロンチウム薄膜よりおよそ一桁以上移動度が高く、二桁程度電子濃度の低いバルク品質並みの高電子移動度を示す単結晶薄膜作製に成功している。

その作製手法を用い、従来の半導体で用いられてきたデルタドープという方法によって低次元系の作製を行っている。この方法はドープされていない半導体の極薄い一部分のみにキャリアをドープする手法で高移動度酸化物薄膜においては初めての試みである。結果として金属伝導を保ったままおよそ4 nmの膜厚まで伝導層を薄くすることに成功しており、さらにデルタドープの効果によって移動度はバルクのおよそ4倍程度まで増加する結果を得ている。

このような様々な伝導層厚さを持ったデルタドープの試料を用い、超伝導の次元性転移を観測している。この結果はセラミックス薄膜では初めての観測であり、高温超伝導体など層状構造を示す多くの超伝導体との類似性からも大変興味深いものである。さらに、試料の高品質さを反映して、低温において抵抗に磁気振動を観測している。特に、伝導層の薄い試料において、フェルミ面は二次元的になっていることわかり、これはペロブスカイト型酸化物では初めての観測である。このような高移動度二次元電子が超伝導を示す物質は他にはないため、今回作製されたチタン酸ストロンチウムの人工低次元構造は高移動度電子と超伝導電子という二つの量子状態の共存系を調べることが可能な唯一の系である。さらに電子の希薄でかつ移動度の高い試料を作製することで今後の展開が期待される。

チタン酸ストロンチウムは半導体の一つであるが、従来の半導体と比べ有効質量や誘電率が大きく異なり、ボーア半径やランダウレベルの準位間などが大きく異なり、定性的にも非常に異なった領域に存在する。そのため、今回作製した試料構造に対し簡単なモデルを立て、電子状態の計算を試みている。その結果として、有効質量の大きさからサブバンド間のエネルギー差が少なく、今回の試料においては電子が複数のサブバンドに存在していることを見出しており、単サブバンドのみ電子が占有する完全な二次元系の実現は、従来の半導体に比べ格段に難しいことを示している。しかしながら、最後にそのような系を実現するにあたり克服しなければならない課題とその具体的な解決法の展望が明確に述べられている。

本論文はチタン酸ストロンチウムという物質の低次元系作製という課題を試料の質の改善からその低次元物性測定まで多角的かつ総合的に行われており、酸化物エレクトロニクスにおける一つのブレイクスルーといえる。今回確立された薄膜作製手法と実現された物理系は将来この分野におけるメゾスコピック系物理の基盤になると期待される。

なお、第6章および第7章は金 民祐、ベル クリストファー、金 福基、疋田 育之、ファン ハロルドとの共同研究であるが、論文提出者が主体となって試料作製、測定、解析を行ったもので、論文提出者の寄与が十分であると判断する。

したがって、博士(科学)の学位を授与できると認める。