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Erik P. A. M. Bakkers

Publications and source records attributed to Erik P. A. M. Bakkers.

At least 37 records · Page 2Linked to original sources

Coherent control of a few-channel hole type gatemon qubit

Gatemon qubits are the electrically tunable cousins of superconducting transmon qubits. In this work, we demonstrate the full coherent control of a gatemon qubit based on hole carriers in a Ge/Si core/shell nanowire, with the longest coherence times in group IV material gatemons to date. The key to these results is a high-quality Josephson junction obtained in a straightforward and reproducible annealing technique. We demonstrate that the transport through the narrow junctions is dominated by only two quantum channels, with transparencies up to unity. This novel qubit platform holds great promise for quantum information applications, not only because it incorporates technologically relevant materials, but also because it provides new opportunities, like an ultrastrong spin-orbit coupling in the few-channel regime of Josephson junctions.

cond-mat.mes-hall↗

Cryogenic hyperabrupt strontium titanate varactors for sensitive reflectometry of quantum dots

Radio frequency reflectometry techniques enable high bandwidth readout of semiconductor quantum dots. Careful impedance matching of the resonant circuit is required to achieve high sensitivity, which however proves challenging at cryogenic temperatures. Gallium arsenide-based voltage-tunable capacitors, so-called varactor diodes, can be used for in-situ tuning of the circuit impedance but deteriorate and fail at temperatures below 10 K and in magnetic fields. Here, we investigate a varactor based on strontium titanate with hyperabrupt capacitance-voltage characteristic, that is, a capacitance tunability similar to the best gallium arsenide-based devices. The varactor design introduced here is compact, scalable and easy to wirebond with an accessible capacitance range from 45 pF to 3.2 pF. We tune a resonant inductor-capacitor circuit to perfect impedance matching and observe robust, temperature and field independent matching down to 11 mK and up to 2 T in-plane field. Finally, we perform gate-dispersive charge sensing on a germanium/silicon core/shell nanowire hole double quantum dot, paving the way towards gate-based single-shot spin readout. Our results bring small, magnetic field-resilient, highly tunable varactors to mK temperatures, expanding the toolbox of cryo-radio frequency applications.

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Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states

The recent realization of a two-site Kitaev chain featuring "poor man's Majorana" states demonstrates a path forward in the field of topological superconductivity. Harnessing the potential of these states for quantum information processing, however, requires increasing their robustness to external perturbations. Here, we form a two-site Kitaev chain using proximitized quantum dots hosting Yu-Shiba-Rusinov states. The strong hybridization between such states and the superconductor enables the creation of poor man's Majorana states with a gap larger than $70 \mathrm{~μeV}$. It also greatly reduces the charge dispersion compared to Kitaev chains made with non-proximitized quantum dots. The large gap and reduced sensitivity to charge fluctuations will benefit qubit manipulation and demonstration of non-abelian physics using poor man's Majorana states.

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Charge sensing the parity of an Andreev molecule

The proximity effect of superconductivity on confined states in semiconductors gives rise to various bound states such as Andreev bound states (ABSs), Andreev molecules and Majorana zero modes. While such bound states do not conserve charge, their Fermion parity is a good quantum number. One way to measure parity is to convert it to charge first, which is then sensed. In this work, we sense the charge of ABSs and Andreev molecules in an InSb-Al hybrid nanowire using an integrated quantum dot operated as a charge sensor. We show how charge sensing measurements can resolve the even and odd states of an Andreev molecule, without affecting the parity. Such an approach can be further utilized for parity measurements of Majorana zero modes in Kitaev chains based on quantum dots.

cond-mat.mes-hall↗

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 chain. Practical proposals for its realization require coupling neighboring quantum dots in a chain via both electron tunneling and crossed Andreev reflection. While both processes have been observed in semiconducting nanowires and carbon nanotubes, 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 quantum dots in an InSb nanowire strongly coupled by both elastic co-tunneling and crossed Andreev reflection. 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. While 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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Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires

In most naturally occurring superconductors, electrons with opposite spins are paired up to form Cooper pairs. This includes both conventional $s$-wave superconductors such as aluminum as well as high-$T_\text{c}$, $d$-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 progress. Instead, engineered platforms where $s$-wave superconductors are brought into contact with magnetic materials have shown convincing signatures of equal-spin pairing. 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 chain.

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Diffusive and Ballistic Transport in Ultra-thin InSb Nanowire Devices Using a Few-layer-Graphene-AlOx Gate

Quantum devices based on InSb nanowires (NWs) are a prime candidate system for realizing and exploring topologically-protected quantum states and for electrically-controlled spin-based qubits. The influence of disorder on achieving reliable topological regimes has been studied theoretically, highlighting the importance of optimizing both growth and nanofabrication. In this work we investigate both aspects. We developed InSb nanowires with ultra-thin diameters, as well as a new gating approach, involving few-layer graphene (FLG) and Atomic Layer Deposition (ALD)-grown AlOx. Low-temperature electronic transport measurements of these devices reveal conductance plateaus and Fabry-Pérot interference, evidencing phase-coherent transport in the regime of few quantum modes. The approaches developed in this work could help mitigate the role of material and fabrication-induced disorder in semiconductor-based quantum devices.

cond-mat.mes-hall↗

Subgap spectroscopy along hybrid nanowires by nm-thick tunnel barriers

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 Al oxide 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. This allows us to make multiple tunnel probes along single nanowire hybrids and to successfully identify Andreev bound states (ABSs) of various spatial extension residing along the hybrids.

cond-mat.mes-hall↗

Spin-filtered measurements of Andreev bound states

A semiconductor nanowire brought in proximity to a superconductor can form discrete, particle-hole symmetric states, known as Andreev bound states (ABSs). An ABS can be found in its ground or excited states of different spin and parity, such as a spin-zero singlet state with an even number of electrons or a spin-1/2 doublet state with an odd number of electrons. Considering the difference between spin of the even and odd states, spin-filtered measurements have the potential to reveal the underlying ground state. To directly measure the spin of single-electron excitations, we probe an ABS 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 ABS, which in some cases is fully spin-polarized, despite the presence of strong spin-orbit interaction in the InSb nanowires. In addition, decoupling the hybrid from the normal lead blocks the ABS relaxation resulting in a current blockade where the ABS is trapped 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.

cond-mat.mes-hall↗

Controlled crossed Andreev reflection and elastic co-tunneling mediated by Andreev bound states

A short superconducting segment can couple attached quantum dots via elastic co-tunneling (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.

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Impact of junction length on supercurrent resilience against magnetic field in InSb-Al nanowire Josephson junctions

Semiconducting nanowire Josephson junctions represent an attractive platform to investigate the anomalous Josephson effect and detect topological superconductivity by studying Josephson supercurrent. However, an external magnetic field generally suppresses the supercurrent through hybrid nanowire junctions and significantly limits the field range in which the supercurrent phenomena can be studied. In this work, we investigate the impact of the length of InSb-Al nanowire Josephson junctions on the supercurrent resilience against magnetic fields. We find that the critical parallel field of the supercurrent can be considerably enhanced by reducing the junction length. Particularly, in 30 nm-long junctions supercurrent can persist up to 1.3 T parallel field - approaching the critical field of the superconducting film. Furthermore, we embed such short junctions into a superconducting loop and obtain the supercurrent interference at a parallel field of 1 T. Our findings are highly relevant for multiple experiments on hybrid nanowires requiring a magnetic field-resilient supercurrent.

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Single-crystalline PbTe film growth through reorientation

Heteroepitaxy enables the engineering of novel properties, which do not exist in a single material. Two principle growth modes are identified for material combinations with large lattice mismatch, Volmer-Weber and Stranski-Krastanov. Both lead to the formation of three-dimensional islands, hampering the growth of flat defect-free thin films. This limits the number of viable material combinations. Here, we report a distinct growth mode found in molecular beam epitaxy of PbTe on InP initiated by pre-growth surface treatments. Early nucleation forms islands analogous to the Volmer-Weber growth mode, but film closure exhibits a flat surface with atomic terracing. Remarkably, despite multiple distinct crystal orientations found in the initial islands, the final film is single-crystalline. This is possible due to a reorientation process occurring during island coalescence, facilitating high quality heteroepitaxy despite the large lattice mismatch, difference in crystal structures and diverging thermal expansion coefficients of PbTe and InP. This growth mode offers a new strategy for the heteroepitaxy of dissimilar materials and expands the realm of possible material combinations.

cond-mat.mtrl-sci↗

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 non-equilibrium 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.

cond-mat.supr-con↗

Variable and orbital-dependent spin-orbit field orientations in a InSb double quantum dot characterized via dispersive gate sensing

Utilizing dispersive gate sensing (DGS), we investigate the spin-orbit field ($\textbf{B}_{SO}$) orientation in a many-electron double quantum dot (DQD) defined in an InSb nanowire. While characterizing the inter-dot tunnel couplings, the measured dispersive signal depends on the electron charge occupancy, as well as on the amplitude and orientation of the external magnetic field. The dispersive signal is mostly insensitive to the external field orientation when a DQD is occupied by a total odd number of electrons. For a DQD occupied by a total even number of electrons, the dispersive signal is reduced when the finite external magnetic field aligns with the effective $\textbf{B}_{SO}$ orientation. This fact enables the identification of $\textbf{B}_{SO}$ orientations for different DQD electron occupancies. The $\textbf{B}_{SO}$ orientation varies drastically between charge transitions, and is generally neither perpendicular to the nanowire nor in the chip plane. Moreover, $\textbf{B}_{SO}$ is similar for pairs of transitions involving the same valence orbital, and varies between such pairs. Our work demonstrates the practicality of DGS in characterizing spin-orbit interactions in quantum dot systems, without requiring any current flow through the device.

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Parametric exploration of zero-energy modes in three-terminal InSb-Al nanowire devices

We systematically study three-terminal InSb-Al nanowire devices by using radio-frequency reflectometry. Tunneling spectroscopy measurements on both ends of the hybrid nanowires are performed while systematically varying the chemical potential, magnetic field and junction transparencies. Identifying the lowest-energy state allows for the construction of lowest- and zero-energy state diagrams, which show how the states evolve as a function of the aforementioned parameters. Importantly, comparing the diagrams taken for each end of the hybrids enables the identification of states which do not coexist simultaneously, ruling out a significant amount of the parameter space as candidates for a topological phase. Furthermore, altering junction transparencies filters out zero-energy states sensitive to a local gate potential. Such a measurement strategy significantly reduces the time necessary to identify a potential topological phase and minimizes the risk of falsely recognizing trivial bound states as Majorana zero modes.

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Epitaxy of Advanced Nanowire Quantum Devices

Semiconductor nanowires provide an ideal platform for various low-dimensional quantum devices. In particular, topological phases of matter hosting non-Abelian quasi-particles can emerge when a semiconductor nanowire with strong spin-orbit coupling is brought in contact with a superconductor. To fully exploit the potential of non-Abelian anyons for topological quantum computing, they need to be exchanged in a well-controlled braiding operation. Essential hardware for braiding is a network of single-crystalline nanowires coupled to superconducting islands. Here, we demonstrate a technique for generic bottom-up synthesis of complex quantum devices with a special focus on nanowire networks having a predefined number of superconducting islands. Structural analysis confirms the high crystalline quality of the nanowire junctions, as well as an epitaxial superconductor-semiconductor interface. Quantum transport measurements of nanowire "hashtags" reveal Aharonov-Bohm and weak-antilocalization effects, indicating a phase coherent system with strong spin-orbit coupling. In addition, a proximity-induced hard superconducting gap is demonstrated in these hybrid superconductor-semiconductor nanowires, highlighting the successful materials development necessary for a first braiding experiment. Our approach opens new avenues for the realization of epitaxial 3-dimensional quantum device architectures.

cond-mat.mes-hall↗

Electronic Structure and Epitaxy of CdTe Shells on InSb Nanowires

Indium antimonide (InSb) nanowires are used as building blocks for quantum devices because of their unique properties, i.e., strong spin-orbit interaction and large Landé g-factor. Integrating InSb nanowires with other materials could potentially unfold novel devices with distinctive functionality. A prominent example is the combination of InSb nanowires with superconductors for the emerging topological particles research. Here, we combine the II-VI cadmium telluride (CdTe) with the III-V InSb in the form of core-shell (InSb-CdTe) nanowires and explore potential applications based on the electronic structure of the InSb-CdTe interface and the epitaxy of CdTe on the InSb nanowires. We determine the electronic structure of the InSb-CdTe interface using density functional theory and extract a type-I band alignment with a small conduction band offset ($\leq$ 0.3 eV). These results indicate the potential application of these shells for surface passivation or as tunnel barriers in combination with superconductors. In terms of the structural quality of these shells, we demonstrate that the lattice-matched CdTe can be grown epitaxially on the InSb nanowires without interfacial strain or defects. These epitaxial shells do not introduce disorder to the InSb nanowires as indicated by the comparable field-effect mobility we measure for both uncapped and CdTe-capped nanowires.

cond-mat.mtrl-sci↗

Growth of PbTe nanowires by Molecular Beam Epitaxy

Advances in quantum technology may come from the discovery of new materials systems that improve the performance or allow for new functionality in electronic devices. Lead telluride (PbTe) is a member of the group IV-VI materials family that has significant untapped potential for exploration. Due to its high electron mobility, strong spin-orbit coupling and ultrahigh dielectric constant it can host few-electron quantum dots and ballistic quantum wires with opportunities for control of electron spins and other quantum degrees of freedom. Here, we report the fabrication of PbTe nanowires by molecular beam epitaxy. We achieve defect-free single crystalline PbTe with large aspect ratios up to 50 suitable for quantum devices. Furthermore, by fabricating a single nanowire field effect transistor, we attain bipolar transport, extract the bandgap and observe Fabry-Perot oscillations of conductance, a signature of quasiballistic transmission.

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