Recent developments in nano-device fabrication of carbon nanotubes, semiconductor nanowires and self-assembled quantum dots (QDs) have enabled various kinds of hybrid devices such as superconductor/semiconductor and ferromagnet/semiconductor nanostructures. In particular superconductor/semiconductor QD junctions have offered research platforms for the study of proximity effect, Andreev reflections and more recently interplay between Kondo effect and superconductivity. Among such hybrid devices uncapped InAs self-assembled quantum dots (SAQDs) allow us to electrically tune the important parameters of the dots including confinement potential and tunnel coupling using a gating technique. These parameters can influence various spin effects of many-body correlation, interplay between Kondo effect and superconductivity and spin-orbit interaction, which are the main topics in this thesis.

Spin-orbit interaction (SOI), which is known as a relativistic effect, provides many intriguing effects of spin-related physics and also recently topological phenomena in semiconductors. Because the ability of SOI for the spin-based quantum processing has been demonstrated using QDs, it would be indispensable to elucidate the physical insight of SOI as well as Lande g-factor in QD systems with strong SOI and large g-factor to develop the novel spin-based qubits and to contribute to the quantum information processing. Because InAs has large SOI and g-factor compared with GaAs, InAs SAQDs are interesting.

QDJJs are useful tools for the study of the competition and interplay between the spin-1/2 Kondo effect and superconductivity. When the QD is occupied by an unpaired odd electron number the unpaired electron spin hinders the tunneling of Cooper pairs and suppresses the proximity effect. Under these conditions the supercurrent may still flow through a fourth order cotunnelling process which results in a reversal of the spin order of the Cooper pair and a π superconducting phase shift for the junction (resulting in a π-junction). This effect has been experimentally confirmed in measurements of QD SQUID devices. However when QD-lead coupling is strong such that Kondo temperature (TK) is high compared with the superconducting gap energy (Δ), the QDJJ theoretically becomes a 0-junction due to the Kondo screening of the unpaired spin in the QD. Under these conditions the system ground state undergoes a Quantum phase transition between a 'magnetic' doublet state (π-junction) to a singlet state (0-junction) at a critical ratio of TK to Δ. Although this 0-π phase transition has been experimentally deduced from the non-dissipative supercurrent behaviors, the phase in the Kondo regime has not been directly measured. Also superconducting transport in the two orbital states degenerate system in the QDJJs is attracting but has not been studied in detail experimentally.

For application as a spin qubit the advantages of the InAs system lies in its strong SOI, which results in efficient coupling of the spin state to local electrical gates. This allows fast spin manipulation at rates which exceed those observed in more conventional GaAs based spin qubits. For application it is of interest to control the strength of the SOI as this is also an important mechanism for spin relaxation. One method of achieving such control is the fine manipulation of the confinement potential of the QD device. Another proposal for all electrical spin manipulation requires a gate tunable Lande g-tensor which may also be achieved by controlling the confinement with local gates.

In this thesis we fabricate QDJJs utilizing the InAs SAQDs coupled with superconducting leads and gated by both global 'back' gates and local sidegates. In the first half of this thesis we discuss the superconducting transport which interplays with the Kondo effect. We focus on the odd number electron QD with the spin-1/2 Kondo regime and in regions with two orbital states degenerate to generate the spin-1 Kondo. Here we use the sidegate to tune in-situ the Kondo temperature and the state degeneracy. In the last half we discuss the control of SOI and g-tensor in the InAs QD using sidegates towards spin manipulations in QDs.

First to measure the superconducting junction phase in the Kondo regime with large TK, we fabricate QD SQUIDs (Fig. 1(a)). Devices are characterized in the normal state by applying a magnetic field B which exceeds the critical magnetic field of superconductivity of the aluminum leads. We confirm that QDs in each junction exist and in one QD (henceforth QD2) we detect Kondo effect with TK = 4.9 K > Δ/kB in an odd electron region. In our study we probed the transport in this junction using the 'probe' junction (QD1) in the other arm of the SQUID ring. In the superconducting state (B < Bc), we detect the zero-bias conductance oscillations as a function of B which indicate superconducting interference, shown in Fig. 1(b). The observed periodicity of the oscillation well matches to the value evaluated from the ring area of the SQUID. In Fig. 1(b) we compare the phase of the oscillations between an odd region and an even region in QD1, and find that the oscillation is shifted by π in the odd region indicating the QDJJ is a π-junction. On the other hand comparing with an even region and a Kondo regime in QD2, the oscillation is not shifted indicating that the QDJJ in the Kondo regime remains a 0-junction. This is the first experimental demonstration of 0-junction in the Kondo regimes.

Next, to realize the experimentally-tunable Singlet-Triplet degeneracy we use uncapped InAs SAQD JJs with a sidegate, shown in Fig. 2(a). In this device it is possible to control the orbital degeneracy by the sidegate altering the lateral confinement potential of the QD. By observing the normal state transport (B = 250 mT) we detect the zero-bias conductance anomaly in a region with an even number of electrons. The temperature dependence of the zero-bias anomaly in this regime indicates Singlet-Triplet (ST) Kondo effect. The existence of the ST Kondo effect means that two orbital states are almost in degeneracy. We could tune both the state degeneracy and Kondo effect by changing the sidegate voltage Vsg. From the magnetic field evolutions of Coulomb peaks, we identified that the ground state is triplet for the negative Vsg while it is singlet at Vsg =2.0 V. For making Vsg negative (Vsg =-1.0 V) to positive (Vsg =1.5 V), the Kondo temperature TK monotonically increases from 1.2 K to 2.0 K, and then suddenly drops and finally could not be measured in the singlet ground state at Vsg =2.0 V as shown in Fig. 3(b). This trend is well explained in terms of the ST Kondo effect. Non-dissipative supercurrent, which can be evaluated from the sharp zero-bias conductance peak shown in Fig. 3(c) in the superconducting state, is strongly affected by the ground state transition and ST Kondo effect. In the regions of singlet ground state and ST Kondo effect with large kBTK/Δ, the supercurrent could be observed whereas in the region of ST Kondo effect with small kBTK/Δ, where the triplet is a ground state, the supercurrent is strongly suppressed, inferring the π-junction. These results suggest that the 0-π phase transition is induced by the change of two states degeneracy and ST Kondo effect

In this paragraph we show the tuning of SOI without changing the electron charge state for the fast electron spin manipulation. Electrical tuning of SOI has not been demonstrated in the QD systems while it has been well studied in 1- and 2-dimensional systems. We use the same sample shown in Fig. 2 (a). To estimate the SOI energy ΔSOI we have to detect in transport the excited states of the system. Here, we propose to use the Kondo effect in high B. At the degenerate point of two orbital states with opposite spins the Kondo effect occurs and the split zero-bias Kondo conductance anomaly appears, indicating the separation of ground and excited states. From the splitting we can evaluate ΔSOI in QDs. Furthermore, as shown in Fig. 3(a) applying Vsg gives rise to a change in the splitting of the zero-bias Kondo anomaly. This suggests that ΔSOI can be tuned using the sidegate, which is the first demonstration for any kinds of QD systems. We also measure the in-plane anisotropy of the split zero-bias Kondo anomaly. To ensure that split zero-bias Kondo anomaly comes from SOI, we measure the in-plane anisotropy of the split zero-bias Kondo anomaly shown in Fig. 3(b). Overall trend shows a cosine-like anisotropy and ΔSOI almost quenches at an in-plane angle of θ = 30°. These are consistent with our previous studies for InAs QDs and also with theoretical explanation. From this result we confirm that the SOI energy ΔSOI can be measured by the splitting of Kondo zero-bias anomaly.

Finally we show the electrical tuning of the g-tensor by the sidegate in the device shown in Fig. 2(a). As initially demonstrated in parabolic quantum wells, it is possible to cause the electron spin resonance by electrically modulating g-tensor anisotropy, which is g-tensor modulation resonance (g-TMR). g -TMR has not been however realized in QD system. Figure 4(a) shows the in-plane angle dependence of the g-factor at Vsg = -2.0 V, -1.0 V and 0.9 V. This clearly shows that the g-tensor components are tuned by the sidegate. From this result we evaluate the spin precession vector Ω0, which the electron spin processes about, to see a change in the g-tensor anisotropy due to the sidegate voltage. Figure 4(b) shows that the precession vector angle Φ can be changed by the sidegate, indicating that the g-TMR is feasible in the InAs QDs. Taking the QD parameters into account the maximum Rabi frequency is expected to be 10 MHz .

Figure1 (a) The scanning electron microscope (SEM) image of a typical SQUID. (b) Zero bias conductance as the function of perpendicular magnetic field at ■(both QDs have even occupation.), ●(QDI has odd and QD2 has even occupation), ▲(QD1 has even and QD2 has odd occupation in the Kondo regime) and ▼(QD1 and QD2 have odd occupation and QD2 is in the Kondo regime.). e, o and Kondo indicate even and odd number of electrons and Kondo regime(kBTK > Δ), respectively.

Figure2 (a) The SEM image of an uncapped InAs SAQD coupled with superconducting leads (Ti/Al) with a sidegate. (b) TK and kBTK/Δ (red) as the function of Vsg. (c) The superconducting transport at Singlet (red, Vsg = 2.0 V and Vbg = 1.132 V), ST Kondo (Green, Vsg = 0.0 V and Vbg = 1.182 V) and Triplet states (Blue, Vsg = -1.0 V and Vbg = 1.198 V).

Figure3 (a) The differential conductance as the function of Vsd at the different Vsg from 1.5 V to -1.0 V in the center of the degenerate point. (b) The SOI energy as the function of in-plane B angle θ at ●(Vsg = 1.0 V) and ●(Vsg = -0.5 V).

Figure4 (a) The in-plane angle dependence of the g-factor at ●(Vsg = -2.0 V), ●(Vsg = -1.0 V) and ●(Vsg = 0.9 V). (b) Vsg dependence of the Lamer frequency Ω0/2π and the angle of the Ω0 Φ at θ = 54°.

本論文は「Sidegate control of superconducting transport and spin-orbit interaction in InAs self-assembled quantum dots(サイドゲートを用いた自己形成InAs量子ドットにおける超伝導輸送とスピン軌道相互作用の制御)」と題し,InAs量子ドットを介した超伝導効果と近藤効果の競合、およびスピン軌道相互作用の電圧制御に関して論文提出者が行った研究の成果をまとめたものである.

第1章では、量子ドットを超伝導金属電極で挟んだ量子ドットジョセフソン接合と量子ドットのスピン軌道相互作用に関する研究の歴史的背景と意義を述べた後,ゲート電圧でドットの内部状態を変調することにより超伝導効果と近藤効果の競合、スピン軌道相互作用を制御するという研究主題の着想を説明し、これを踏まえて研究の具体的な課題設定を行っている.

第2章では,本論文の背景にある理論と従来の実験を紹介している.InAsドットの性質と量子ドットの電気伝導の簡潔な説明に続いて、量子ドットジョセフソン接合、近藤効果、スピン軌道相互作用を本論文の研究内容に即して説明している.

第3章では,アルミニウム金属電極とInAs量子ドットから成る量子ドットジョセフソン接合の試料と電気伝導測定の原理について述べている.とくにサイドゲートを用いて量子ドットの閉じ込めポテンシャルが異方的に変調できることを電子波動関数の計算で示し、これを基に量子ドットの内部パラメータ(電極・ドット間のトンネル結合の大きさ、エネルギー準位、波動関数の対称性)が電圧で可変であることを予想している.

第4―7章は本論文の中心的な章で、前の2章では超伝導効果と近藤効果の競合、後の2章ではスピン軌道相互作用とg因子の研究成果を述べている.

第4章では、まず磁場下の常伝導測定で観測した単一電子トンネル伝導のピーク(クーロンピーク)の幅とサイドゲート電圧の関係から、第3章の予想通り、電荷状態を保持したままゲート電圧をパラメータとしてトンネル結合の大きさが変えられること、これを利用してスピン1/2の近藤効果の特性温度(近藤温度)が変えられることを実証している.次に零磁場で超伝導効果、具体的には超伝導閾値電流とアンドレーフ反射を測定し、近藤温度と超伝導ギャップの比の値1.1を境にして、大きい側では超伝導効果の増大、小さい側では急激な減少を観測している.この違いは、奇数個の電子を持つドットのジョセフソン接合が通常はπ接合であるが、近藤効果が強い場合には0接合に遷移することを示唆しており、本論文では、このことを別途作成した量子ドットスクイドの量子干渉測定により直接確認している.超伝導-近藤効果の競合に関しては、過去にナノチューブの実験があるが、これは異なる試料、異なる電荷状態で測定した実験データを集めたもので、信頼性が不足していた.同一の試料、電荷状態で実験を行ったのは本研究が初めてであり、超伝導効果と近藤効果という、固体電子系で代表的な二つのスピン相関の競合の物理の研究に信頼すべき実験を提供している.

第5章では、サイドゲートを使ってスピン3重項、3重項-1重項の縮退、1重項の間の状態遷移を実現し、これに伴って3重項状態から3-1重項縮退に近づくと近藤温度の増大、縮退点を超えて1重項状態になると急激な近藤効果の消失を常伝導測定で観測している.一方超伝導測定では、1重項状態では第4章と同様な0接合の超伝導効果、近藤効果が強い3-1重項縮退近傍ではそれを上回る超伝導効果、3重項状態により近づいて近藤温度が下がると超伝導効果の消失を観測している.このような1-3重項縮退から3重項状態へ向かう場合の変化は、超伝導ギャップと近藤温度の比で見れば、スピン1/2の近藤効果で見られた0からπ接合への遷移に類似しているが、境となる比の値は0.68と小さいことが新たな知見として指摘されている.なお、第4、5章の結果は電子数の奇偶性に依らず、超伝導-近藤効果の競合が普遍的な現象であることを意味している.

第6章では、まず強磁場下で起こる近藤効果を利用してスピン軌道相互作用エネルギーを定量的に求める方法を提案、実験実証したことを述べている.強磁場下での近藤効果は、軌道が異なりスピンが反平行の2つの状態が縮退することに由来するが、スピン軌道相互作用が存在すると縮退はスピン軌道相互作用のエネルギー分だけ僅かに解ける.本実験は、このエネルギーを近藤ピークの分裂として観測したものでスピン軌道相互作用エネルギーの高精度の測定法といえる.さらに、同エネルギーはサイドゲートで変調できることを観測し、これがゲート電圧による波動関数分布の変調に因ることを議論している.

第7章では、クーロンピークの磁場依存性がゼーマン分離を反映することを利用してg因子を求め、続いてこのg因子が異方的であり、サイドゲート電圧で可変であることを確認している.ここでは、g因子に対するサイドゲートの影響として、第6章と同様に波動関数分布の変化を議論している. 最後に観測したg因子の特性を利用してgテンソル変調による高性能のスピン量子ビットが実現できることを提案している.

第8章は,本研究の結論であり,結果の要約と今後の展望が述べられている.

以上述べたように,本研究は、InAs自己形成ドットの内部状態を変調する方法としてサイドゲート電極法を開発し、これにより超伝導効果と近藤効果の競合現象、スピン軌道相互作用の大きさと異方性を系統的に制御することに成功したもので、実験手法、得られた知見ともに固体物理、ナノ科学の進展に大きな寄与があったと評価できる.また,これらの研究成果は,半導体量子ドットをジョセフソン接合エレクトロニクス、量子情報を含めたスピントロニクスへ応用する技術の基礎となるものであり,物理工学としての貢献が大きい.よって,本論文は博士(工学)の学位申請論文として合格と認められる.