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Bordin A, Li X, van Driel D, Wolff JC, Wang Q, Ten Haaf SLD, Wang G, van Loo N, Kouwenhoven LP, Dvir T. Crossed Andreev Reflection and Elastic Cotunneling in Three Quantum Dots Coupled by Superconductors. PHYSICAL REVIEW LETTERS 2024; 132:056602. [PMID: 38364137 DOI: 10.1103/physrevlett.132.056602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Revised: 12/03/2023] [Accepted: 01/05/2024] [Indexed: 02/18/2024]
Abstract
The formation of a topological superconducting phase in a quantum-dot-based Kitaev chain requires nearest neighbor crossed Andreev reflection and elastic cotunneling. Here, we report on a hybrid InSb nanowire in a three-site Kitaev chain geometry-the smallest system with well-defined bulk and edge-where two superconductor-semiconductor hybrids separate three quantum dots. We demonstrate pairwise crossed Andreev reflection and elastic cotunneling between both pairs of neighboring dots and show sequential tunneling processes involving all three quantum dots. These results are the next step toward the realization of topological superconductivity in long Kitaev chain devices with many coupled quantum dots.
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Affiliation(s)
- Alberto Bordin
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Xiang Li
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - David van Driel
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Jan Cornelis Wolff
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Qingzhen Wang
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Sebastiaan L D Ten Haaf
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Guanzhong Wang
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Nick van Loo
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Tom Dvir
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
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2
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van Driel D, Wang G, Bordin A, van Loo N, Zatelli F, Mazur GP, Xu D, Gazibegovic S, Badawy G, Bakkers EPAM, Kouwenhoven LP, Dvir T. Spin-filtered measurements of Andreev bound states in semiconductor-superconductor nanowire devices. Nat Commun 2023; 14:6880. [PMID: 37898657 PMCID: PMC10613242 DOI: 10.1038/s41467-023-42026-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Accepted: 09/27/2023] [Indexed: 10/30/2023] Open
Abstract
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.
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Affiliation(s)
- David van Driel
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Guanzhong Wang
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Alberto Bordin
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Nick van Loo
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Francesco Zatelli
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Di Xu
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Tom Dvir
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands.
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Levajac V, Wang JY, Sfiligoj C, Lemang M, Wolff JC, Bordin A, Badawy G, Gazibegovic S, Bakkers EPAM, Kouwenhoven LP. Subgap spectroscopy along hybrid nanowires by nm-thick tunnel barriers. Nat Commun 2023; 14:6647. [PMID: 37863952 PMCID: PMC10589238 DOI: 10.1038/s41467-023-42422-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 10/11/2023] [Indexed: 10/22/2023] Open
Abstract
Tunneling spectroscopy is widely used to examine the subgap spectra in semiconductor-superconductor nanostructures when searching for Majorana zero modes (MZMs). Typically, semiconductor sections controlled by local gates at the ends of hybrids serve as tunnel barriers. Besides detecting states only at the hybrid ends, such gate-defined tunnel probes can cause the formation of non-topological subgap states that mimic MZMs. Here, we develop an alternative type of tunnel probes to overcome these limitations. After the growth of an InSb-Al hybrid nanowire, a precisely controlled in-situ oxidation of the Al shell is performed to yield a nm-thick AlOx layer. In such thin isolating layer, tunnel probes can be arbitrarily defined at any position along the hybrid nanowire by shadow-wall angle-deposition of metallic leads. In this work, we make multiple tunnel probes along single nanowire hybrids and successfully identify Andreev bound states (ABSs) of various spatial extension residing along the hybrids.
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Affiliation(s)
- Vukan Levajac
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Ji-Yin Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands.
- Beijing Academy of Quantum Information Sciences, 100193, Beijing, China.
| | - Cristina Sfiligoj
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Mathilde Lemang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Jan Cornelis Wolff
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Alberto Bordin
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600MB, Eindhoven, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, 5600MB, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600MB, Eindhoven, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
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van Loo N, Mazur GP, Dvir T, Wang G, Dekker RC, Wang JY, Lemang M, Sfiligoj C, Bordin A, van Driel D, Badawy G, Gazibegovic S, Bakkers EPAM, Kouwenhoven LP. Electrostatic control of the proximity effect in the bulk of semiconductor-superconductor hybrids. Nat Commun 2023; 14:3325. [PMID: 37286544 DOI: 10.1038/s41467-023-39044-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Accepted: 05/17/2023] [Indexed: 06/09/2023] Open
Abstract
The proximity effect in semiconductor-superconductor nanowires is expected to generate an induced gap in the semiconductor. The magnitude of this induced gap, together with the semiconductor properties like spin-orbit coupling and g-factor, depends on the coupling between the materials. It is predicted that this coupling can be adjusted through the use of electric fields. We study this phenomenon in InSb/Al/Pt hybrids using nonlocal spectroscopy. We show that these hybrids can be tuned such that the semiconductor and superconductor are strongly coupled. In this case, the induced gap is similar to the superconducting gap in the Al/Pt shell and closes only at high magnetic fields. In contrast, the coupling can be suppressed which leads to a strong reduction of the induced gap and critical magnetic field. At the crossover between the strong-coupling and weak-coupling regimes, we observe the closing and reopening of the induced gap in the bulk of a nanowire. Contrary to expectations, it is not accompanied by the formation of zero-bias peaks in the local conductance spectra. As a result, this cannot be attributed conclusively to the anticipated topological phase transition and we discuss possible alternative explanations.
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Affiliation(s)
- Nick van Loo
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands.
| | - Tom Dvir
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Guanzhong Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Robin C Dekker
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Ji-Yin Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Mathilde Lemang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Cristina Sfiligoj
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Alberto Bordin
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - David van Driel
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands.
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Dvir T, Wang G, van Loo N, Liu CX, Mazur GP, Bordin A, Ten Haaf SLD, Wang JY, van Driel D, Zatelli F, Li X, Malinowski FK, Gazibegovic S, Badawy G, Bakkers EPAM, Wimmer M, Kouwenhoven LP. Realization of a minimal Kitaev chain in coupled quantum dots. Nature 2023; 614:445-450. [PMID: 36792741 DOI: 10.1038/s41586-022-05585-1] [Citation(s) in RCA: 22] [Impact Index Per Article: 22.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Accepted: 11/22/2022] [Indexed: 02/17/2023]
Abstract
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.
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Affiliation(s)
- Tom Dvir
- QuTech, Delft University of Technology, Delft, The Netherlands.
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.
| | - Guanzhong Wang
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Nick van Loo
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Chun-Xiao Liu
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Alberto Bordin
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Sebastiaan L D Ten Haaf
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Ji-Yin Wang
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - David van Driel
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Francesco Zatelli
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Xiang Li
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Filip K Malinowski
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Michael Wimmer
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Leo P Kouwenhoven
- QuTech, Delft University of Technology, Delft, The Netherlands.
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.
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Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires. Nature 2022; 612:448-453. [PMID: 36418399 DOI: 10.1038/s41586-022-05352-2] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 09/15/2022] [Indexed: 11/25/2022]
Abstract
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.
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