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Hole Spins in Gaas Quantum Dots University of New South Wales, Sydney School of Physics Hole Spins in GaAs Quantum Dots Qingwen Wang A thesis submitted in fulfillment of the requirement for the degree of Doctor of Philosophy September 2015 2 Acknowledgements Foremost, my most sincere thanks go to my supervisor Alex Hamilton, for his con- tinuous support during the past four years, for his patience, guidance and encour- agement. Alex always has endless interesting ideas and suggestions about the exper- iments, without which I would not be able to get the exciting results in this thesis. Even though I sometimes make fun of his hairstyle and "fashion" taste, I really enjoy talking with Alex, and listening to his "grandpa" stories. Secondly I wish to thank my co-supervisor Oleh Klochan, without whom I would not be able to make any working devices or know how to run the fridge. Thanks for giving me so many useful suggestions on fabrication, listening to me complaining about everything in the lab, and keeping all the equipments working. I will let beer to express my appreciation when you come back form Ukraine. I would also like to thank everyone else now or formerly in the QED group for making life at UNSW enjoyable: Jason Chen, Andrew See, Jack Cochrane, Ashwin Srinivasan, LaReine Yeoh, Sarah Macleod, Roy Li, Karina Hudson, Scott Liles, Matt Rendell and Elizabeth Marcellina. Special thanks to people who helped me during this project: thanks to Jason Chen and Andrew See for showing me how to do fabrication; thanks to Fay Hudson who helped me with the EBL alignment; thanks to Oleg Sushkov, Dmitry Miserev, Dimitrie Culcer and Elizabeth Marcellina for useful discussions on hole systems. Finally, special thanks go to my parents and friends who are always there for me. Without you, my life would not have been so happy. 3 4 Abstract In this thesis, we report a new architecture for making lateral hole quantum dots based on shallow accumulation-mode AlGaAs/GaAs heterostructures. Utilizing a double-level-gate architecture, we demonstrate the operation of ultra-small single and double quantum dots in the few-hole regime using electrical measurements. Devices with different dimensions and layouts are tested to reach the single-hole limit. With the flexibility of the double-level-gate architecture, both single and double quantum dots can be formed within the same device with good tunability. With the ability to isolate a single heavy-hole spin, we study the Zeeman splitting of the orbital states in different field orientations via magnetospectroscopy measure- ments. The extracted value of the hole effective g-factor is found to be strongly dependent on the orbital state, and highly anisotropic with respect to the mag- netic field direction. We show that these peculiar behaviours of the heavy-hole spin can be qualitatively explained by the effects of strong spin-orbit coupling and strong Coulomb interactions in hole systems. By varying the dot size in situ, we also demonstrate the tuning of the g-factor anisotropy, and estimate the shape of electrically-defined quantum dot. With the few-hole double quantum dot, we present the first observation of Pauli spin blockade in GaAs hole quantum dots. Utilizing a vector field magnet system, we study the lifting of spin blockade due to the spin-orbit interaction. We found that the effect of spin-orbit coupling on spin blockade to be highly anisotropic in different magnetic field orientations, which agrees with previous theoretical predic- tions on systems with strong spin-orbit coupling. From the anisotropic lifting of spin blockade, we identify the orientation of the effective spin-orbit field to be along the transport direction, which is very different from experimental results from electron quantum dots and highlights the uniqueness of hole systems. 2 Contents 1 Introduction and Thesis Outline 7 1.1 Introduction . .7 1.2 Thesis Outline . .8 2 Background Chapter 10 2.1 Introduction . 10 2.2 2D systems in GaAs/AlGaAs heterostructures . 10 2.2.1 Modulation-doped heterostructures . 10 2.2.2 Undoped accumulation-mode heterostructures . 12 2.3 Holes in GaAs/AlGaAs heterostructure . 14 2.3.1 Valence band structure in GaAs . 15 2.3.2 Large hole effective mass . 17 2.3.3 Hyperfine interaction . 18 2.3.4 Spin-orbit interaction . 20 2.3.5 The Zeeman splitting in 2D hole systems . 21 2.4 Single quantum dots . 22 2.4.1 Constant-interaction model . 23 2.4.2 Coulomb blockade . 25 2.4.3 Bias spectroscopy . 26 2.4.4 Spin states in a single dot . 29 2.5 Double quantum dots . 32 2.5.1 Charge stability diagram . 32 2.5.2 Bias triangles . 36 2.5.3 Pauli spin blockade . 38 2.5.4 The lifting of spin blockade . 42 3 Device Fabrication and Measurement Setup 46 3.1 Introduction . 46 3.2 Device fabrication . 46 3 4 CONTENTS 3.2.1 Device structure and operation principles . 47 3.2.2 Dielectric material . 49 3.2.3 Shallow wafers . 52 3.2.4 Electron Beam Lithography . 53 3.3 Measurement setup . 55 4 Double-level-gate Architecture for Few-hole GaAs Quantum Dots 58 4.1 Introduction . 58 4.2 Literature Review . 59 4.3 Nanowire-inspired quantum dot on a planar GaAs heterostructure . 64 4.4 Single dot operation . 66 4.4.1 Coulomb blockade and bias spectroscopy . 66 4.4.2 Zeeman splitting and anisotropic Land´eg-factor . 67 4.5 Double dot operation . 70 4.5.1 Tunable interdot coupling . 70 4.5.2 Bias triangles and resonant tunnelling . 71 4.6 Conclusions and improvements of the design . 75 5 Single Hole GaAs Lateral Quantum Dots 79 5.1 Introduction . 79 5.2 Literature Review . 81 5.3 Single hole quantum dot - Experimental results . 87 5.3.1 Device Characterization . 87 5.3.2 Bias spectroscopy . 89 5.4 Zeeman splitting of the single hole states . 94 5.4.1 Suppression of the ground state g-factor . 95 5.4.2 Orbital dependence of the hole g-factor . 97 5.4.3 Observation of a fourfold degenerate orbital state . 99 5.5 Land´eg-factor anisotropy . 100 5.6 Conclusions and Future Work . 104 6 Anisotropic Pauli Spin Blockade in GaAs Double Hole Quantum Dots 106 6.1 Introduction . 106 6.2 Literature Review . 107 6.3 Few-hole double quantum dots - experimental results . 114 6.4 Pauli spin blockade . 116 6.5 Spin-orbit interaction lifted spin blockade . 117 6.6 Anisotropic lifting of spin blockade . 119 4 5 CONTENTS 6.7 Conclusion and Future Work . 125 7 Conclusions and Future Work 127 7.1 Summary of Results . 127 7.2 Future work . 128 7.2.1 Theoretical modelling . 128 7.2.2 Future experiments . 129 A Influence of surface states on quantum and transport lifetimes in high-quality undoped heterostructures 131 A.1 Introduction . 131 A.2 Literature Review . 132 A.3 Experimental results . 133 A.3.1 Sample and experimental setup . 133 A.3.2 Measurements of lifetimes from Shubnikov de Haas oscillations 133 A.4 Comparison with theory and discussions . 136 A.5 Predictions from theory . 138 A.6 Conclusions and Future work . 140 B Magnetospectroscopy of the two-hole states 143 C The effects of barriers on the double dot transport 144 D The (1; 1) ! (0; 2) transition 145 5 6 Chapter 1 Introduction and Thesis Outline 1.1 Introduction Spintronics, i.e. spin-based semiconductor electronics, is an emerging technology which utilizes the spin of charge carriers to store and process information. Grow- ing interests in this field have placed the study of quantum mechanical properties of semiconductors in the centre of research over the past few decades. Thanks to the development of fabrication and experimental techniques, impressive progress, in- cluding spin initialization, manipulation and readout [1, 2, 3], as well as all-electric control of a single electron spin [4, 5, 6], has been realized using electron quantum dots, which are one of the most widely used semiconductor systems in quantum information processing. However, fast decoherence of electron spins due to the un- avoidable hyperfine interaction with surrounding nuclear spins [7, 8, 6] still remains a major problem for most electron systems with a none-zero nuclear spin. As one possible replacement for electron spins, heavy-hole spins have drawn a lot of attention recently. Unlike conduction band electrons whose wavefunctions are constructed by s-orbitals, holes in the valence band have p-symmetry Bloch wavefunctions with zero density at the site of the nuclei, leading to a vanishing contact hyperfine interaction [8, 9]. Heavy-holes (Jz = ±3=2) consisting of pure p-orbitals are predicted to have negligible spin flip-flops, resulting in an Ising-type hyperfine interaction and potentially long spin coherence times on the scale of µs [10, 11]. Furthermore, holes also have strong spin-orbit coupling due to the non-zero orbital momentum, which provides the possibility of fast all-electric control of hole spins via the spin-orbit interaction [12]. GaAs hole quantum dots have always been a popular candidate for quantum information processing due to the possibility of implementing spin manipulation techniques that have already been developed in their electron counterparts [3, 2]. Up 7 8 Introduction and Thesis Outline to date, experimental work on GaAs hole quantum dots have been mainly conducted via optical measurements of self-assembled quantum dots. Various results of the spin ∗ decoherence time T2 [13, 14, 15] have been obtained and impurity-induced electrical noise in self-assembled quantum dots is considered to be the limiting factor of the ∗ short T2 time [14]. In addition, it is very difficult to incorporate self-assembled quantum dots into complex electric circuits for all-electric control of the hole states.
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