Quantum Dots Coupled to Superconductors

The search for Majoranas bound states has witnessed heated efforts in the past decade. This field of research lies at the intersection of both scientific and commercial interests. The Majorana quasiparticle, being its own antiparticle and exhibiting non-abelian exchange statistics, is a unique member of the family of condensed-matter quasiparticles, distinct from most fermions or bosons. These properties are predicted to be instrumental in the building of a new type of qubits, having no energy splitting between qubit states and intrinsically protected from decoherence. In addition, the theory describing Majorana modes has a rich connection to the mathematical language of topology, making its study also of theoretical value. Thus, the prediction of the existence of Majorana zero modes in hybrid semiconducting-superconducting nanowires has been a strong driving force behind the recent technological progress in the making of these materials and devices.In this thesis, the most recent advance in materials, specifically the making of clean interfaces between semiconductors and superconductors, are applied to the study of the physical properties of superconducting-proximitized electronic states in semiconductors. This technology is combined with quantum dot techniques to investigate electron transport between individual quantum states in proximitized nanowires. The findings include better understanding of electron transport in these systems as well as presenting new potential applications to the field of Majoranas and beyond.Following the introductory chapters, this thesis first demonstrates a high-efficiency Cooper-pair splitter, enabled by quantum dots with narrow linewidth and a superconductor with a hard gap. The techniques behind the improved efficiency can be used to make a generator of entangled pairs of electrons. We also demonstrate the use of quantum dots as spin detectors capable of revealing the spin structure of individual Cooper pairs. Next, we report the effect of a Cooper-pair splitter's peculiar response to the tuning of electrical gates in both experiment and theory. This includes the discovery of a new interference effect in electron co-tunneling processes through a superconductor. The key to observing this response is to ensure the hybrid nanowire is also a discrete quantum state instead of a superconducting bulk. The discovery above forms the foundation of fine-tuning the types of electron couplings between two quantum dots coupled via a superconductor. The power of this tunability can been seen via the successful making of a minimal artificial Kitaev chain, opening up new possibilities in the search for Majorana zero modes. This approach is less prone to difficulties encountered in other platforms such as material disorder and the interpretability of data.Moving from studying quantum dots under the influence of a superconducting hybrid, later chapters of this thesis focus on investigating electron properties in the hybrid nanowire using quantum dots as spin-, charge- and energy-selective probes.We first use them to detect and quantify the spin polarization of Andreev bound states in the hybrid nanowire. Using quantum dots as charge and energy detectors instead, we observe how electrons traverse through the bulk of a hybrid nanowire and reveal a thermoelectric conversion process in the conductance measurements of these devices. Finally, we report on the selective-area growth of InSb, the semiconductor used throughout this thesis, that can form the basis of future developments.QRD/Kouwenhoven La

Tunable Superconducting Coupling of Quantum Dots via Andreev Bound States in Semiconductor-Superconductor Nanowires

Semiconductor quantum dots have proven to be a useful platform for quantum simulation in the solid state. However, implementing a superconducting coupling between quantum dots mediated by a Cooper pair has so far suffered from limited tunability and strong suppression. This has limited applications such as Cooper pair splitting and quantum dot simulation of topological Kitaev chains. In this Letter, we propose how to mediate tunable effective couplings via Andreev bound states in a semiconductor-superconductor nanowire connecting two quantum dots. We show that in this way it is possible to individually control both the coupling mediated by Cooper pairs and by single electrons by changing the properties of the Andreev bound states with easily accessible experimental parameters. In addition, the problem of coupling suppression is greatly mitigated. We also propose how to experimentally extract the coupling strengths from resonant current in a three-terminal junction. Our proposal will enable future experiments that have not been possible so far. QRD/Wimmer GroupQRD/Kouwenhoven LabQN/Wimmer Grou

Nonlocal measurement of quasiparticle charge and energy relaxation in proximitized semiconductor nanowires using quantum dots

The lowest-energy excitations of superconductors do not carry an electric charge, as their wave function is equally electron-like and hole-like. This fundamental property is not easy to study in electrical measurements that rely on the charge to generate an observable signal. The ability of a quantum dot to act as a charge filter enables us to solve this problem and measure the quasiparticle charge in superconducting-semiconducting hybrid nanowire heterostructures. We report measurements on a three-terminal circuit, in which an injection lead excites a nonequilibrium quasiparticle distribution in the hybrid system, and the electron or hole component of the resulting quasiparticles is detected using a quantum dot as a tunable charge and energy filter. The results verify the chargeless nature of the quasiparticles at the gap edge and reveal the complete relaxation of injected charge and energy in a proximitized nanowire, resolving open questions in previous three-terminal experiments.QRD/Kouwenhoven LabQuTec

Selectivity Map for Molecular Beam Epitaxy of Advanced III-V Quantum Nanowire Networks

Selective-area growth is a promising technique for enabling of the fabrication of the scalable III-V nanowire networks required to test proposals for Majorana-based quantum computing devices. However, the contours of the growth parameter window resulting in selective growth remain undefined. Herein, we present a set of experimental techniques that unambiguously establish the parameter space window resulting in selective III-V nanowire networks growth by molecular beam epitaxy. Selectivity maps are constructed for both GaAs and InAs compounds based on in situ characterization of growth kinetics on GaAs(001) substrates, where the difference in group III adatom desorption rates between the III-V surface and the amorphous mask area is identified as the primary mechanism governing selectivity. The broad applicability of this method is demonstrated by the successful realization of high-quality InAs and GaAs nanowire networks on GaAs, InP, and InAs substrates of both (001) and (111)B orientations as well as homoepitaxial InSb nanowire networks. Finally, phase coherence in Aharonov-Bohm ring experiments validates the potential of these crystals for nanoelectronics and quantum transport applications. This work should enable faster and better nanoscale crystal engineering over a range of compound semiconductors for improved device performance.QRD/Kouwenhoven LabQuTechSafety and SecurityBUS/Genera

Spin-filtered measurements of Andreev bound states in semiconductor-superconductor nanowire devices

Semiconductor nanowires coupled to superconductors can host Andreev bound states with distinct spin and parity, including a spin-zero state with an even number of electrons and a spin-1/2 state with odd-parity. Considering the difference in spin of the even and odd states, spin-filtered measurements can reveal the underlying ground state. To directly measure the spin of single-electron excitations, we probe an Andreev bound state using a spin-polarized quantum dot that acts as a bipolar spin filter, in combination with a non-polarized tunnel junction in a three-terminal circuit. We observe a spin-polarized excitation spectrum of the Andreev bound state, which can be fully spin-polarized, despite strong spin-orbit interaction in the InSb nanowires. Decoupling the hybrid from the normal lead causes a current blockade, by trapping the Andreev bound state in an excited state. Spin-polarized spectroscopy of hybrid nanowire devices, as demonstrated here, is proposed as an experimental tool to support the observation of topological superconductivity.QRD/Kouwenhoven LabQRD/Wimmer GroupBUS/Quantum DelftQN/Kouwenhoven La

Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires

In most naturally occurring superconductors, electrons with opposite spins form Cooper pairs. This includes both conventional s-wave superconductors such as aluminium, as well as high-transition-temperature, d-wave superconductors. Materials with intrinsic p-wave superconductivity, hosting Cooper pairs made of equal-spin electrons, have not been conclusively identified, nor synthesized, despite promising progress1–3. Instead, engineered platforms where s-wave superconductors are brought into contact with magnetic materials have shown convincing signatures of equal-spin pairing4–6. Here we directly measure equal-spin pairing between spin-polarized quantum dots. This pairing is proximity-induced from an s-wave superconductor into a semiconducting nanowire with strong spin–orbit interaction. We demonstrate such pairing by showing that breaking a Cooper pair can result in two electrons with equal spin polarization. Our results demonstrate controllable detection of singlet and triplet pairing between the quantum dots. Achieving such triplet pairing in a sequence of quantum dots will be required for realizing an artificial Kitaev chain7–9.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.QRD/Kouwenhoven LabBUS/Quantum DelftArchitecture and the Built EnvironmentQRD/Goswami LabQN/Wimmer GroupQN/Kouwenhoven La

Electric field tunable superconductor-semiconductor coupling in Majorana nanowires

We study the effect of external electric fields on superconductor-semiconductor coupling by measuring the electron transport in InSb semiconductor nanowires coupled to an epitaxially grown Al superconductor. We find that the gate voltage induced electric fields can greatly modify the coupling strength, which has consequences for the proximity induced superconducting gap, effective g-factor, and spin-orbit coupling, which all play a key role in understanding Majorana physics. We further show that level repulsion due to spin-orbit coupling in a finite size system can lead to seemingly stable zero bias conductance peaks, which mimic the behavior of Majorana zero modes. Our results improve the understanding of realistic Majorana nanowire systems.QRD/Kouwenhoven LabQuTechApplied SciencesQN/Bakkers La

Tunable Crossed Andreev Reflection and Elastic Cotunneling in Hybrid Nanowires

A short superconducting segment can couple attached quantum dots via elastic cotunneling (ECT) and crossed Andreev reflection (CAR). Such coupled quantum dots can host Majorana bound states provided that the ratio between CAR and ECT can be controlled. Metallic superconductors have so far been shown to mediate such tunneling phenomena, albeit with limited tunability. Here, we show that Andreev bound states formed in semiconductor-superconductor heterostructures can mediate CAR and ECT over mesoscopic length scales. Andreev bound states possess both an electron and a hole component, giving rise to an intricate interference phenomenon that allows us to tune the ratio between CAR and ECT deterministically. We further show that the combination of intrinsic spin-orbit coupling in InSb nanowires and an applied magnetic field provides another efficient knob to tune the ratio between ECT and CAR and optimize the amount of coupling between neighboring quantum dots.QRD/Kouwenhoven LabQRD/Wimmer GroupQRD/Goswami LabBUS/Quantum DelftQN/Wimmer GroupQN/Kouwenhoven LabQubit Research Divisio

Realization of a minimal Kitaev chain in coupled quantum dots

Majorana bound states constitute one of the simplest examples of emergent non-Abelian excitations in condensed matter physics. A toy model proposed by Kitaev shows that such states can arise at the ends of a spinless p-wave superconducting chain1. Practical proposals for its realization2,3 require coupling neighbouring quantum dots (QDs) in a chain through both electron tunnelling and crossed Andreev reflection4. Although both processes have been observed in semiconducting nanowires and carbon nanotubes5–8, crossed-Andreev interaction was neither easily tunable nor strong enough to induce coherent hybridization of dot states. Here we demonstrate the simultaneous presence of all necessary ingredients for an artificial Kitaev chain: two spin-polarized QDs in an InSb nanowire strongly coupled by both elastic co-tunnelling (ECT) and crossed Andreev reflection (CAR). We fine-tune this system to a sweet spot where a pair of poor man’s Majorana states is predicted to appear. At this sweet spot, the transport characteristics satisfy the theoretical predictions for such a system, including pairwise correlation, zero charge and stability against local perturbations. Although the simple system presented here can be scaled to simulate a full Kitaev chain with an emergent topological order, it can also be used imminently to explore relevant physics related to non-Abelian anyons.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.QRD/Kouwenhoven LabQRD/Wimmer GroupBUS/Quantum DelftCommunication QuTechQRD/Goswami LabApplied SciencesBUS/TNO STAFFQN/Wimmer GroupQN/Kouwenhoven La

Quantized Majorana conductance

Majorana zero-modes - a type of localized quasiparticle - hold great promise for topological quantum computing. Tunnelling spectroscopy in electrical transport is the primary tool for identifying the presence of Majorana zero-modes, for instance as a zero-bias peak in differential conductance. The height of the Majorana zero-bias peak is predicted to be quantized at the universal conductance value of 2e 2 /h at zero temperature (where e is the charge of an electron and h is the Planck constant), as a direct consequence of the famous Majorana symmetry in which a particle is its own antiparticle. The Majorana symmetry protects the quantization against disorder, interactions and variations in the tunnel coupling. Previous experiments, however, have mostly shown zero-bias peaks much smaller than 2e 2 /h, with a recent observation of a peak height close to 2e 2 /h. Here we report a quantized conductance plateau at 2e 2 /h in the zero-bias conductance measured in indium antimonide semiconductor nanowires covered with an aluminium superconducting shell. The height of our zero-bias peak remains constant despite changing parameters such as the magnetic field and tunnel coupling, indicating that it is a quantized conductance plateau. We distinguish this quantized Majorana peak from possible non-Majorana origins by investigating its robustness to electric and magnetic fields as well as its temperature dependence. The observation of a quantized conductance plateau strongly supports the existence of Majorana zero-modes in the system, consequently paving the way for future braiding experiments that could lead to topological quantum computing.Accepted Author Manuscript This title has a addendum: editorial expression of concern, see Relations belowQRD/Kouwenhoven LabApplied SciencesIntegral Design and ManagementQN/Bakkers La