Using on-chip microwave measurements, we investigate multilevel π-junctions formed by proximitized quantum dot (QD) in a germanium (Ge)/silicon-germanium (SiGe) heterostructure. In the multilevel regime, where several QD orbitals contribute simultaneously to superconducting transport, the Josephson ground state is no longer determined solely by the occupation of a single orbital. By combining DC transport and microwave techniques, we identify the qualitative signatures of multilevel π-junctions in both their gate-voltage dependence and microwave response. In particular, we observe combinations phase transitions that are sharp or smooth in gate voltage and which exhibit distinct inductive and dissipative signatures. Such multilevel Josephson transport has previously been observed primarily in exceptionally clean systems such as carbon nanotubes. Our results establish proximitized Ge as a platform for investigating hybrid superconductor/semiconductor physics and demonstrate the integration of gate-defined superconducting quantum devices with high-quality on-chip microwave resonators.

Superconducting resonators integrated with germanium (Ge) quantum wells (QWs) offer a promising platform for hybrid quantum devices. Yet, in the most common heterostructure architectures, they have so far been limited by sizable photon losses. Here, we report the fabrication and characterization of microwave resonators patterned in the aluminum (Al) thin film of an in-situ grown superconductor/semiconductor hybrid heterostructure (HS). The semiconductor part of this hybrid HS is grown on a commercial Ge substrate. We consistently achieve internal quality factors Q i > 1000, surpassing previous results on Ge QW heterostructures grown using the concept of a virtual Ge substrate on silicon (Si) substrates. We reach Q i ≈ 49,000 at single-photon occupation and a plateau of Q i ≈ 20,000 at sub-one photon, an order of magnitude larger than any previously reported value of resonators on Ge QW structures at low power. We further characterize the thin Al film forming the resonator, extracting its kinetic inductance and superconducting gap, and studying its magnetic field dependence. Notably, the resonance remains well-defined up to in-plane magnetic fields of 850 mT. A hysteresis emerges in the out-of-plane magnetic field dependence, for both the resonance frequency and the quality factor, indicating an interesting interplay between vortex-and quasiparticle loss mechanisms.

We introduce a graphite-gated architecture for bilayer graphene devices in which the active device is completely isolated from the natural graphene edges. Using a single patterned graphite-gate layer, we realize a fully electrostatically defined Hall-bar. Longitudinal and Hall measurements reveal mesoscopic transport features, including Hall-effect quenching and magnetoresistance peaks associated with boundary scattering. The dependence of the mesoscopic features on the carrierdensity shows that the effective channel width increases with the Fermi level and the electrostatic confinement at the gate-defined boundaries, and indicates that the carriers scatter at the electrostatic boundary. Raman spectroscopy and Kelvin probe force microscopy suggest that this boundary is disordered due to the used fabrication methods. Comparably, the quantum mobility in a fieldeffect transistor fabricated with the same architecture is not limited by boundary scattering and the visibility of quantum oscillations down to 4 mT suggests a record value of 2.5 x 10^6 cm2/Vs.

Germanium-silicon-germanium (Ge/Si_xGe_1-x) heterostructures have emerged as a promising platform for hole-spin quantum technologies and high-mobility electronics, where strain and quantum confinement strongly reshape the Ge valence bands. However, the momentum-resolved valence-band structure of buried strained Ge quantum wells has so far been inferred only indirectly. Here we use soft X-ray angle-resolved photoemission spectroscopy (SX-ARPES) to directly probe the electronic structure of strained Ge quantum wells embedded in SiGe barriers. We resolve strain-split and size-quantized valence subbands, determine their heavy-hole, light-hole and split-off composition, and measure the valence-band offset at the Ge/SiGe heterojunction. Comparison with ab initio calculations shows that an accurate description requires explicit inclusion of the confinement potential imposed by the SiGe barrier, which plays a decisive role in determining the dispersion, ordering and mixing of the hole states. Our results provide the first direct experimental picture of how strain and confinement determine the valence-band structure of Ge quantum wells, establishing a foundation for predictive modelling of hole-spin qubits and high-mobility devices based on group-IV heterostructures.

We demonstrate a method to determine energy level degeneracies using non-equilibrium electronic transport through voltage-biased quantum dots. We establish the general validity of this approach using single and double quantum dots in bilayer graphene and GaAs. Unlike established methods based on entropy measurements or time-resolved tunneling statistics, our approach achieves comparable precision without requiring calibrated electron heating or real-time charge detection. We resolve the predicted symmetric shell structure in bilayer graphene quantum dots, including a singlet ground state at half filling and the ground state degeneracies of the first 13 carriers. Extending the method to double quantum dots, we observe degeneracy doubling associated with bonding and antibonding orbitals for a single carrier and a fourfold degeneracy for two carriers, previously inaccessible with existing techniques. These results establish a conceptually general and experimentally straightforward approach for probing energy level degeneracies in complex quantum systems.

Germanium (Ge) has been identified as a good candidate among semiconductor‐based materials for quantum applications. One of the main reasons lies in the long coherence time of spins of localized holes, its ability to host superconducting pairing correlations, and compatibility with complementary metal‐oxide‐semiconductor (CMOS) technology. Recent studies reveal how the growth of strained germanium quantum wells (QWs) embedded in silicon‐germanium (SiGe) barriers is crucial to enhance charges' mobility in this system. In this work, a study is presented of the distribution of in‐plane and out‐of‐plane strain in germanium quantum wells embedded in Si 1 − x Ge x barriers in order to engineer strain in the quantum well, thus tuning the charge mobility therein for quantum computing purposes. Therefore, experimental techniques such as Raman spectroscopy, transmission electron microscopy (TEM), and geometric phase analysis (GPA) are combined with Schrödinger–Poisson solver simulations in order to find the optimal quantum well thickness and silicon (Si) content in the Si 1 − x Ge x barriers to enhance and control electrical properties in Ge/SiGe planar heterostructures.

Germanium (Ge) has been identified as a good candidate among semiconductor-based materials for quantum applications. One of the main reasons lies in the long coherence time of spins of localized holes, its ability to host superconducting pairing correlations, and compatibility with complementary metal-oxide-semiconductor (CMOS) technology. Recent studies reveal how the growth of strained germanium quantum wells (QWs) embedded in silicon-germanium (SiGe) barriers is crucial to enhance charges' mobility in this system. In this work, a study is presented of the distribution of in-plane and out-of-plane strain in germanium quantum wells embedded in Si1 - xGex barriers in order to engineer strain in the quantum well, thus tuning the charge mobility therein for quantum computing purposes. Therefore, experimental techniques such as Raman spectroscopy, transmission electron microscopy (TEM), and geometric phase analysis (GPA) are combined with Schr & ouml;dinger-Poisson solver simulations in order to find the optimal quantum well thickness and silicon (Si) content in the Si1 - xGex barriers to enhance and control electrical properties in Ge/SiGe planar heterostructures.

Holes in planar germanium (Ge) heterostructures show promise for quantum applications, particularly in superconducting and spin qubits, due to strong spin-orbit interaction, low effective mass, and the absence of valley degeneracies. However, charge traps cause issues such as gate hysteresis and charge noise. This study examines the effect of surface treatments on the accumulation behavior and transport properties of Ge-based two-dimensional hole gases (2DHGs). Oxygen plasma treatment reduces conduction in a setting without applied top gate voltage, improves the mobility, and lowers the percolation density, while hydrofluoric acid (HF) etching provides no benefit. The results suggest that interface traps from the partially oxidized silicon (Si) cap pin the Fermi level and that oxygen plasma reduces the trap density by fully oxidizing the Si cap. Therefore, optimizing surface treatments is crucial for minimizing the charge traps and thereby enhancing the device's performance.

Hybrid systems comprising superconducting and semiconducting materials are promising architectures for quantum computing. Superconductors induce long-range interactions between the spin degrees of freedom of semiconducting quantum dots. These interactions are widely anisotropic when the semiconductor material has strong spin-orbit interactions. We show that this anisotropy is tunable and enables fast and high-fidelity two-qubit gates between singlet-triplet (ST) spin qubits. Our design is immune to leakage of the quantum information into noncomputational states and removes always-on interactions between the qubits, thus resolving key open challenges for these architectures. Our ST qubits do not require additional technologically demanding components nor fine-tuning of parameters. They operate at low magnetic fields of a few millitesla and are fully compatible with superconductors. By suppressing systematic errors in realistic devices, we estimate infidelities below $10^{-3}$, which could pave the way toward large-scale hybrid superconducting-semiconducting quantum processors.

A great deal of interest is directed nowadays towards the development of innovative technologies in the field of quantum information and quantum computing, with emphasis on obtaining reliable qubits as building blocks. The realization of highly stable, controllable and accessible hole spin qubits is strongly dependent on the quality of the materials hosting them. Ultra-clean germanium/silicon-germanium heterostructures have been predicted and proven to be promising candidates and due to their large scalability potential, they are opening the door towards the development of realistic and reliable solid state, all-electric, silicon-based quantum computers. In order to obtain ultra-clean germanium/silicon-germanium heterostructures in a reverse grading approach, the understanding and control over the growth of Ge virtual substrates and thin films is key. Here, we present a detailed study on the growth kinetics, morphology, and crystal quality of Ge thin films grown via chemical vapor deposition by investigating the effects of growth temperature, partial pressure of the precursor gas and the use of Ar or H2 atmosphere. The presence of carrier gases catalyzes the deposition rate and induces a smoothening on the surfaces of films grown at low temperatures. We investigated the surface roughness and threading dislocation density as a function of deposition temperature, partial pressure and gas mixture. Ge thin films deposited by diluting GeH4 in Ar or H2 were employed as virtual substrates for the growth of full Ge/SiGe QW heterostructures. Their defect density was analyzed and their electric transport properties were characterized via Hall measurements. Similar results were obtained for both carrier gases used.

One of the most promising platforms for the realization of spin-based quantum computing are planar germanium quantum wells embedded between silicon-germanium barriers. To achieve comparably thin stacks with little surface roughness, this type of heterostructure can be grown using the so-called reverse linear grading approach, where the growth starts with a virtual germanium substrate followed by a graded silicon-germanium alloy with an increasing silicon content. However, the compatibility of such reverse-graded heterostructures with superconducting microwave resonators has not yet been demonstrated. Here, we report on the successful realization of well-controlled double quantum dots and high-quality coplanar waveguide resonators on the same reverse-graded Ge/SiGe heterostructure.

Planar semiconductor heterostructures offer versatile device designs and are promising candidates for scalable quantum computing. Notably, heterostructures based on strained germanium have been extensively studied in recent years, with an emphasis on their strong and tunable spin-orbit interaction, low effective mass, and high hole mobility. However, planar systems are still limited by the fact that the shape of the confinement potential is directly related to the density. In this work, we present the successful implementation of a backgate for a planar germanium heterostructure. The backgate, in combination with a topgate, enables independent control over the density and the electric field, which determines important state properties such as the effective mass, the g-factor, and the quantum lifetime. This unparalleled degree of control paves the way toward engineering qubit properties and facilitates the targeted tuning of bilayer quantum wells, which promise denser qubit packing.

This study analysed diversity patterns of sedimentary, littoral and planktic diatoms in 43 mountain lakes in the northern European Alps and identified processes that contribute to these patterns. Linear regression models showed a significant increase of sedimentary α -diversity with lake area and conductivity and a negative trend with increasing elevation, whilst the littoral diatom α -diversity increased significantly with conductivity and lake water temperature. Planktic diatom α -diversity significantly decreased with lake area and depth. August water temperature, total phosphorus, conductivity and lake depth explained a significant part of the variation and were significantly correlated with pairwise β -diversities in the data sets, but spatial and shared effects of space and environment were more important for planktic and littoral diatoms. A null model approach based on assemblages’ dissimilarities revealed that the structure of littoral and planktic assemblages was predominantly stochastic. In contrast, sedimentary diatoms were formed by both deterministic and stochastic processes. Abundant and widespread species contributed a large part to the assemblage β -diversity. The results point to a stronger role of niche assembly in sedimentary than for littoral and planktic diatoms. Dispersal limitation, in turn, is likely to contribute to the spatial patterns and stochastic assembly processes observed for littoral and planktic diatoms.

The spin-orbit interaction permits to control the state of a spin qubit via electric fields. For holes it is particularly strong, allowing for fast all electrical qubit manipulation, and yet an in-depth understanding of this interaction in hole systems is missing. Here we investigate, experimentally and theoretically, the effect of the cubic Rashba spin-orbit interaction on the mixing of the spin states by studying singlet-triplet oscillations in a planar Ge hole double quantum dot. Landau-Zener sweeps at different magnetic field directions allow us to disentangle the effects of the spin-orbit induced spin-flip term from those caused by strongly site-dependent and anisotropic quantum dot g tensors. Our work, therefore, provides new insights into the hole spin-orbit interaction, necessary for optimizing future qubit experiments.

Mountain lakes are unique and often isolated freshwater habitats that harbour a rich biotic diversity. This high conservation value may be reflected by diatoms, a group of algae that is known for its reliability as a bioindicator, but which has not been studied extensively in mountain lakes of the northern European Alps. In this study, the conservation value of these lakes was assessed by characterizing the number, share, and abundance of diatom Red List (RL) taxa and their relationship with environmental variables, diatom α and β diversity (assemblage uniqueness). For this purpose, linear regression models, generalized linear models, and generalized additive models were fitted and spatial descriptors were included when relevant. Of the 560 diatom taxa identified, 64% were on the RL and half of these were assigned a threat status. As hypothesized, a decreasing share of RL species in sediment and littoral samples at higher trophic levels was reflected by higher total phosphorous content and lower Secchi depth, respectively. Species-rich lakes contained a high number of RL taxa, contrasting our hypothesis of a logarithmic relationship. In turn, RL abundance increased with uniqueness, confirming our initial hypothesis. However, some of the most unique sites were degraded by fish stocking and contained low abundances of RL species. The results demonstrate the importance of oligotrophic mountain lakes as habitats for rare freshwater biota and their vulnerability in light of human impact through cattle herding, tourism, damming, and fish stocking. Additional conservation efforts are urgently needed for mountain lakes that are still underrepresented within legal conservation frameworks. Species richness and uniqueness reflect complementary aspects of RL status and thus should be applied jointly. Uniqueness can indicate both pristine and degraded habitats, so that including information on human impacts facilitates its interpretation.

Hybrid semiconductor-superconductor devices hold great promise for realizing topological quantum computing with Majorana zero modes1-5. However, multiple claims of Majorana detection, based on either tunnelling6-10 or Coulomb blockade (CB) spectroscopy11,12, remain disputed. Here we devise an experimental protocol that allows us to perform both types of measurement on the same hybrid island by adjusting its charging energy via tunable junctions to the normal leads. This method reduces ambiguities of Majorana detections by checking the consistency between CB spectroscopy and zero-bias peaks in non-blockaded transport. Specifically, we observe junction-dependent, even-odd modulated, single-electron CB peaks in InAs/Al hybrid nanowires without concomitant low-bias peaks in tunnelling spectroscopy. We provide a theoretical interpretation of the experimental observations in terms of low-energy, longitudinally confined island states rather than overlapping Majorana modes. Our results highlight the importance of combined measurements on the same device for the identification of topological Majorana zero modes.

A semiconducting nanowire fully wrapped by a superconducting shell has been proposed as a platform for obtaining Majorana modes at small magnetic fields. In this study, we demonstrate that the appearance of subgap states in such structures is actually governed by the junction region in tunneling spectroscopy measurements and not the full-shell nanowire itself. Short tunneling regions never show subgap states, whereas longer junctions always do. This can be understood in terms of quantum dots forming in the junction and hosting Andreev levels in the Yu-Shiba-Rusinov regime. The intricate magnetic field dependence of the Andreev levels, through both the Zeeman and Little-Parks effects, may result in robust zero-bias peaks-features that could be easily misinterpreted as originating from Majorana zero modes but are unrelated to topological superconductivity.

We use Scanning Gate Microscopy to study electron transport through an open, gate-defined resonator in a Ga(Al)As heterostructure. Raster-scanning the voltage-biased metallic tip above the resonator, we observe distinct conductance modulations as a function of the tip-position and voltage. Quantum mechanical simulations reproduce these conductance modulations and reveal their relation to the partial local density of states in the resonator. Our measurements illustrate the current frontier between possibilities and limitations in imaging the local density of states in buried electron systems using scanning gate microscopy.

Spin qubits are considered to be among the most promising candidates for building a quantum processor. Group IV hole spin qubits are particularly interesting owing to their ease of operation and compatibility with Si technology. In addition, Ge offers the option for monolithic superconductor–semiconductor integration. Here, we demonstrate a hole spin qubit operating at fields below 10 mT, the critical field of Al, by exploiting the large out-of-plane hole g-factors in planar Ge and by encoding the qubit into the singlet-triplet states of a double quantum dot. We observe electrically controlled g-factor difference-driven and exchange-driven rotations with tunable frequencies exceeding 100 MHz and dephasing times of 1 μs, which we extend beyond 150 μs using echo techniques. These results demonstrate that Ge hole singlet-triplet qubits are competing with state-of-the-art GaAs and Si singlet-triplet qubits. In addition, their rotation frequencies and coherence are comparable with those of Ge single spin qubits, but singlet-triplet qubits can be operated at much lower fields, emphasizing their potential for on-chip integration with superconducting technologies. A singlet-triplet spin qubit using holes in a Ge quantum well is demonstrated, and can be operated at low magnetic fields of a few millitesla.