Introduction

Historically low-dimensional superconductors and semiconductors have been separated into two distinctive regimes: ultra-thin superconductors have been limited by strong disorder, while low-dimensional semiconductors can be in the clean limit but not superconducting. While many experimental attempts have been performed to search for bulk superconductivity in well-known semiconductors, disorder at high density is problematic [1]. In this context, SrTiO3 (STO) is a promising candidate, displaying versatile phenomena, in particular such as high electron mobility, and low-density superconductivity. Motivated by these properties, a variety of heterostructure implementations have been intensively studied out to explore novel two-dimensional (2D) electron physics in STO [2]. This poses several challenges: 1) structural control and cleanliness of electron layers are often restricted; 2) The lack of detailed information on the normal and superconducting properties, respectively, in both the three-dimensional (3D) and 2D limits. In order to address these questions, light is shed on the electronic structure, and superconductivity of STO in this Thesis, through control of the sample fabrication and low-temperature transport measurements. By systematic variation of the sample thickness and dopant density, we reveal 3D-2D dimensional crossovers in both the superconducting and normal states. Approaching the 2D limit, novel physics such as a change of the electron-phonon coupling and intrinsic spin-orbit interactions are unraveled, opening up new possibility of novel ground states in low dimensions.

Fabrication of high-quality δdoped SrTiO3 heterostructures

The first step necessary for investigating the transport properties is to fabricate a high-quality conducting sample. We realized atomic-scale-controlled n-type STO heterostructures by applying a δdoping technique, where a thin layer of Nb doped STO is sandwiched between 100 nm-thick undoped STO buffer and capping layers on a STO (001) substrate [Fig. 1 (a)]. The doped layer thickness d varied from a few to several hundred nanometers. The sheet carrier density N(Hall) and Hall mobility μ could be varied over a range of three orders of magnitude [Fig. 1 (b,c)]. The advantage of this δdoping structure is that we can investigate the intrinsic properties of STO in a symmetrically confined potential structure, in the absence of extrinsic effects such as interface or surface scattering, lattice mismatch, and broken inversion symmetry.

Electronic structure of SrTiO3

Taking advantage of the high-mobility electrons, we determined the dimensionality of the Fermi surface of Nb doped STO heterostructures unambiguously, and discovered a 3D to 2D crossover in the normal state from Shubnikov-de Haas (SdH) oscillations at low temperatures. As the doped layer becomes thinner, a beating pattern of the quantum oscillations appeared due to the 2D confinement [Fig. 2 (a)]. From the fact that the multi-frequency components of thin samples [Fig. 2 (b)] could be scaled only with the perpendicular magnetic field, and have similar effective mass, it can be concluded that the observed electrons are the light electrons in the conduction band of STO, split by 2D subband quantization. Interestingly, the carrier density estimated from SdH oscillations is less than 20 % of N(Hall), indicating the existence of the heavy electrons that are not observed in the SdH oscillations [Fig. 2 (c,d)].

Superconductivity of SrTiO3

How does superconductivity change as d decreases? Firstly, superconducting transition was measured in a series of 1 at. % δdoped STO samples, where an upturn in the transition temperature Tc was found in the thin limit, indicating possible change of the electron-phonon coupling [Fig. 3 (a,b)]. Secondly, the magnetic response of the samples gave vital information of dimensionality of a superconductor: We observed 1) anisotropy of the upper critical field, H(c2), developing as d becomes smaller [Fig. 4 (a)], 2) the T dependence of the parallel upper critical field, Hc(//), changed from linear to square root below d = 99 nm [Fig. 4 (b)]. These findings are consistent with linearized Ginzburg-Landau (GL) theory for 2D superconductors where the GL coherence length ζ(GL) is smaller than the thickness of superconducting layer d(Tinkham) [3]. In our experiments, ζ(GL) ~ 100 nm, whereas dTinkham monotonically decreases with d, indicating that 3D-2D superconducting crossover occurs at d ~100 nm [Fig. 4 (c)].

An important point for these δdoped samples is that Hc// exceeds the Pauli paramagnetic limit [Fig. 5 (a)], suggesting considerable SO scattering in the system. We performed a qualitative measure of SO scattering, using theoretical analysis [Fig. 5 (b,c)] of H(c2) considering the effects of spin paramagnetism and SO scattering [4], and extracted the SO scattering times τ(so) and the momentum scattering times τ(tr) [Fig. 5 (d)]. Crucially, conventional SO scattering mechanisms cannot explain the scaling of the relationship between these two characteristic scattering times, indicating the novel role of intrinsic SO interactions. Notably, τ(tr) estimated here was one order of magnitude smaller than the Drude scattering time τ(drude), indicating the different densities of superconducting and normal-state electrons, which is also suggested from the discrepancy between N(Hall) and N(superfluid) estimated from scanning probe measurements [5].

Spin-orbit interaction of SrTiO3

As a confirmation of the presence of SO scattering suggested from the superconducting data, the weak antilocalization (WAL) effect was also studied, exploiting the manifestation of SO coupling in the electron dephasing process in the normal state. As T decreases, we found a dip structure in the magnetoresistance near zero field caused by WAL [Fig. 6 (a)]. Fitting the result with Hikami-Larkin-Nagaoka theory [6], the inelastic scattering time ιi and SO scattering times ι(so) were successfully extracted. From the T dependence of ιi, we revealed that the dephasing mechanism by inelastic scattering changes as the samples becomes thinner, suggesting that the electron-phonon coupling has been altered in thin samples. We also demonstrated that SO scattering times could be controlled by back gating [Fig. 6 (b,c)], indicating SO interaction changes as the confining potential structure is tuned from symmetric to asymmetric.

Conclusion & Outlooks

We investigated the physical properties of Nb doped STO heterostructures, by fabricating high-quality STO samples with wide controllability of the structure and cleanliness by the δdoping technique. We could reveal 1) the precise information on the electronic structure and superconducting properties in 3D and 2D, and the dimensional crossover between them; 2) Novel 2D physics of STO unraveled from both the normal and superconducting states such as the change of electron-phonon coupling, and intrinsic SO interaction which can be controlled by back gating. Furthermore, these results suggest several key future steps toward searching for novel electronic phases in low dimensions: the sample cleanliness achieved in this study suggests the demonstration of the quantum Hall effect in the presence of d-electron correlation effects in the low-density limit, which has been only observed in s-p hybridized systems until now. Another novel possibility is the realization of unconventional superconductivity such as multi-gap superconductivity expected from the presence of the heavy and light electrons that are sub-band split in the 2D limit. Novel pairing state can also be expected where the distinction between spin-triplet and spin-singlet Cooper pairs is removed due to the strong SO interaction.

Fig. 1 (a) A schematic diagram of Nb δ-doped SrTiO3 heterostructures. (b) Sheet carrier density N(Hall), and (c) Hall mobility μ estimated by the Hall measurement at temperature T = 2 K.

Fig. 2 (a) SdH oscillations measured at T = 100 mK in 0.2 at. % doped samples with various thickness d. (b) Fourier transformation (FT) spectra. (c,d) Schematic diagrams of the 3D and 2D Fermi surfaces based on the results.

Fig. 3 (a) Normalized resistance plotted with temperature for 1 at. % doped samples with various thicknesses. (b) Superconducting transition temperature as a function of d. The error bar of data denotes the 10-90% width of the superconducting transition in (a).

Fig. 4 (a) Normalized upper critical field H(c2) vs angle θ of the 1% samples with various thickness. Dotted lines are the fits using 2D superconductivity theory [3]. (b) Normalized parallel upper critical field H(c2)(//) vs the reduced temperature t = T/Tc. Solid lines are the theory curves. (c) Ginzburg-Landau coherence length ζ(GL), and the thickness of superconducting layer d(Tinkham) plotted with d.

Fig. 5 (a) Upper critical field in the parallel geometry H(c2)(//), in the perpendicular geometry H(c2) , and the Pauli limiting field Hcp, plotted against 1/d. (b) Simulation result using the WHH theory [4]. Σ is [(experimental data) - (theory)]2, α is the orbital depairing parameter, and λ(so) is the spin-orbit scattering rate. (c) Anisotropy and T dependence of H(c2) of d = 5.5 nm sample. Dotted lines are the theory fit. (d) Spin-orbit scattering time τ(so) and momentum scattering time τ(tr) as a function of d.

Fig. 6 (a) Magnetoresistance of a 1 at. % sample (d = 3.9 nm) at low temperatures. (b) Gate voltage (VG) dependence of weak antilocalization correction to conductivity at T = 2 K. (c) Estimated inelastic scattering time τi, SO scattering times τ(so) from the Hikami-Larkin-Nagaoka fits [6]. The Drude scattering times τ(drude) are estimated from Hall measurements.

二次元に閉じ込められた電子系は、三次元に広がった電子系とは異なる物性を示すことから、半導体人工構造や二次元結晶を中心に研究されてきた。特に薄膜を用いた二次元超伝導と高移動度半導体を用いた二次元電子ガスは、いずれも二次元電子物性の代表的な研究対象であるが、両者を同時に観測できる系は非常に限られている。この意味で、低温で高移動度を示し、極低温で超伝導転移を起こすSrTiO3を用いた二次元構造は理想的な系である。しかし、二次元超伝導と二次元電子ガスの電子状態の詳細を同時に研究するには、不純物の低減やキャリア密度の精密制御が要求され、いずれも薄膜作製技術の向上が不可欠となる。

本論文では、このような背景のもと、SrTiO3において、デルタドープ構造と呼ばれる数原子層のドープされた半導体伝導層を絶縁体層で挟んだ構造をパルスレーザー堆積法によって作製し、低温における電子輸送特性からその二次元超伝導特性と二次元電子ガスの挙動を研究した結果が記されている。デルタドープ構造では、その伝導層の厚さとドープ量を制御することで、伝導電子が閉じ込められる領域を二次元から三次元へと変化させることができる。この点が、他の二次元電子系との大きな違いである。

本論文は7章からなる。第1章には、序論として、研究の背景と目的、論文の概要、及び、論文の構成が述べられている。

第2章には、試料作製、極低温に試料を冷却する希釈冷凍機の概要、精密な電気輸送特性を行うための測定手法が述べられている。

第3章では、デルタドープ構造の品質をこれまでよりも向上させるために行った内容が記されている。ドープ量を系統的に変化させたデルタドープ構造においてキャリア密度を二桁に渡って変調することに成功し、従来の移動度を上回る最高移動度10,000 cm2/Vsを実現した。さらに、電子を閉じ込める伝導層内のポテンシャルが低ドープ領域で弱まることを明らかとした。

第4章では、高移動度を有する試料が低温で示すシュブニコフドハース振動を詳細に解析することで、二次元と三次元のSrTiO3伝導帯の電子構造を明らかにした結果が記されている。伝導層が比較的厚い三次元構造では、軽いバンド、重いバンド、スピン軌道分裂したバンドに相当する三つのバンドをシュブニコフドハース振動から抽出し、電子状態計算と比較した。伝導層を薄くして次元性を低下させたところ、シュブニコフドハース振動に明瞭なうねりを観測し、二次元構造では伝導帯が量子化されたサブバンドが形成されることを示した。

第5章では、デルタドープ構造の超伝導特性について記されている。系の次元性の低下に伴い、ギンズブルクランダウコヒーレンス長が減少することを観測した。二次元構造においては、パウリ・リミットを大きく超える臨界磁場が観測され、系に強いスピン軌道相互作用が内在している可能性を示した。さらに、走査型SQUID顕微鏡を用いた実空間観察より超伝導相が二次元平面内に均一に生成していることを確認した。測定された超伝導電子密度は常伝導電子密度から予測される値とは隔たりを示し、伝導帯の重いバンドの伝導・超伝導への寄与の違いが重要であることを明らかとした。

第6章では、デルタドープ構造におけるスピン軌道相互作用の及ぼす影響について記されている。伝導層のキャリア密度を変化させることで、低温において弱局在現象を観測した。求められたスピン軌道散乱時間は、二次元超伝導相から示唆された値とよい一致を示し、スピン軌道相互作用がSrTiO3の伝導に大きく関わっていることを見出した。

第7章では、本研究の総括が述べられている。

なお、第3章と第6章については、C. Bell(SLAC)、疋田育之(SLAC)、H. Y. Hwang(Stanford大学)各氏との共同研究、第4章については、C. Bell(SLAC)、小塚裕介(東京大学)、疋田育之(SLAC)、H. Y. Hwang(Stanford大学)各氏との共同研究、第5章については、C. Bell(SLAC)、小塚裕介(東京大学)、疋田育之(SLAC)、H. Y. Hwang(Stanford大学)、J. A. Bert(Stanford大学)、B. Kalinsky(Stanford大学)、K. Moler(Stanford大学)各氏との共同研究であるが、いずれも論文提出者が主体となって研究を遂行したもので、論文提出者の寄与が十分であると判断する。

以上から、本論文は、SrTiO3における二次元量子現象を明らかにし、酸化物薄膜量子構造の電子物性の開拓に大きく貢献するものである。したがって、博士(科学)の学位を授与できると認める。