We were one of the first group (if not the first) looking into QDs that are coupled to superconductors (SCs).1  Our devices were realized with carbon nanotubes CNTs and semiconducting nanowires (SNWs). In our early studies we were intrigued by the interplay between Kondo physics and superconducting proximity effect. We could demonstrate that if the Kondo temperature is larger than the superconducting pairing energy, the Kondo resonance would survive lading to an enhanced electrical conductance, signaling the transition to the Josephson effect.1,2 In the opposite limit, the gap of the SC would greatly suppress Kondo screening. These early studies have received great attention in recent years, since it is now possible to study hybrid QD devices with different coupling strength and also beyond two-terminals. We have recently demonstrated coherent two particle resonant and inelastic Andreev tunneling in a QD coupled to a superconducting and normal metal contact.3 We have also studied the temperature dependence and role of quasiparticles.4 Furthermore, we have found new intriguing correlations at higher coupling strengths to the SC in three terminal devices when Andreev-bound states are formed.

1. M. R. Buitelaar, T. Nussbaumer and CS, Phys. Rev. Lett. 89 (25), 256801 (2002).
2. A. Eichler, M. Weiss, S. Oberholzer, CS, A. L. Yeyati, J. C. Cuevas and A. Martin-Rodero, Phys. Rev. Lett. 99 (12), 126602 (2007).
3. J. Gramich, A. Baumgartner and CS, Phys. Rev. Lett. 115 (21), 216801 (2015).
4. J . Gramich, A. Baumgartner and CS, Appl. Phys. Lett. 108 (17), 172604 (2016).

Relevant papers (keyword: Supra):

##### 2022
• Spin Cross-Correlation Experiments in an Electron Entangler
A. Bordoloi, V. Zannier, L. Sorba, C. Schönenberger, and A. Baumgartner.
Nature (2022)
[arXiv:2203.07970 ] [ Open Data ] [Abstract ]

Correlations are fundamental in describing many body systems – not only in natural sciences. However, in experiments, correlations are notoriously difficult to assess on the microscopic scale, especially for electron spins. Here, we demonstrate a direct measurement of the spin cross-correlations between the currents of a Cooper pair splitter, an electronic device that emits electrons originating from Cooper pairs in a superconductor. While it is firmly established theoretically that these electron pairs form maximally spin-entangled singlet states with opposite spin projections, no spin correlation experiments have been demonstrated so far. We use ferromagnetic sidegates, compatible with superconducting electronic structures, to individually spin polarize the transmissions of two quantum dots fabricated in the two electronic paths, which act as tunable spin filters. The signals are detected in standard transport and in highly sensitive transconductance experiments. We find that the spin-cross correlation is negative, compatible with spin singlet emission, and deviates from the ideal value mostly due to a finite overlap of the Zeeman split quantum dot states. Our results demonstrate a new route to perform spin auto- and cross correlation experiments in nanometer scaled electronic devices, especially suitable for those relying on magnetic field sensitive superconducting elements, like unconventional, triplet or topologically non-trivial superconductors, or to perform Bell tests with massive particles, like electrons.

• Current-phase relation of WTe2 Josephson junctions
M. Endres, A. Kononov, M. Stiefel, M. Wyss, H. S. Arachchige, Jiaqiang Yan, D. Mandrus, K. Watanabe, T. Taniguchi, and C. Schönenberger.
submitted (2022)
[arXiv:2211.10273 ] [ Open Data ] [Abstract ]

Topological insulators host gapless boundary states that are protected by time-reversal symmetry against local perturbations. When incorporated into a Josephson junction, the system is predicted to demonstrate the fractional Josephson effect with a 4$\pi$-periodic current-phase relation. Here, we use an asymmetric SQUID device to study the current-phase relation of a Josephson junction formed by the higher-order topological insulator WTe$_2$. The measured critical current seems to demonstrate a 4$\pi$ periodic current-phase relation. A closer inspection, however, reveals that the data is strongly affected by inductance effects that give rise to a multivalued critical current. Further, we model our data by maximizing the supercurrent in the SQUID loop and find the 1.5 $\mu$m long junction is best described in the short ballistic limit. Our results highlight the complexity of inductance effects that can give rise to misleading topological signatures in transport measurements.

• Transparent Josephson Junctions in Higher-Order Topological Insulator WTe2 via Pd Diffusion
M. Endres, A. Kononov, M. Stiefel, M. Wyss, H. S. Arachchige, Jiaqiang Yan, D. Mandrus, K. Watanabe, T. Taniguchi, and C. Schönenberger.
Phys. Rev. Mat.  6, L081201 (2022)
[arXiv:2205.06542 ] [ Open Data ] [Abstract ]

Highly transparent superconducting contacts to a topological insulator (TI) remain a persistent challenge on the route to engineer topological superconductivity. Recently, the higher-order TI WTe2 was shown to turn superconducting when placed on palladium (Pd) bottom contacts, demonstrating a promising material system in perusing this goal. Here, we report the diffusion of Pd into WTe2 and the formation of superconducting PdTex as the origin of observed superconductivity. We find an atomically sharp interface between the diffusion layer and its host crystal, forming state-of-the-art superconducting contacts to a TI. The diffusion is discovered to be non-uniform along the width of the WTe2 crystal, with a greater extend along the edges compared to the bulk. The potential of this contacting method is highlighted in transport measurements on Josephson junctions by employing external superconducting leads.

• Origin of subgap states in normal-insulator-superconductor van der Waals heterostructures
P. Karnatak, Z. Mingazheva, K. Watanabe, T. Taniguchi, H. Berger, L. Forró, and C. Schönenberger.
submitted (2022)
[arXiv:2207.05741 ] [ Open Data ] [Abstract ]

Superconductivity in van der Waals materials, such as NbSe2 and TaS2, is fundamentally novel due to the effects of dimensionality, crystal symmetries, and strong spin-orbit coupling. In this work we perform tunnel spectroscopy on NbSe2 by utilizing MoS2 or hexagonal Boron Nitride (hBN) as a tunnel barrier. We observe subgap excitations and probe their origin by studying various heterostructure designs. We show that the edge of NbSe2 hosts many defect states, which strongly couple to the superconductor and form Andreev bound states. Furthermore, by isolating the NbSe2 edge we show that the subgap states are ubiquitous in MoS2 tunnel barriers, but absent in hBN tunnel barriers, suggesting defects in MoS2 as their origin. Their magnetic nature reveals a singlet or a doublet type ground state and based on nearly vanishing g-factors or avoided-crossing of subgap excitations we highlight the role of strong spin-orbit coupling.

• From Cooper pair splitting to the non-local spectroscopy of a Shiba state
Z. Scherübl, G. Fülöp, J. Gramich, A. Pályi, C. Schönenberger, J. Nygard, and S. Csonka.
Phys. Rev. Research  4, 23143 (2022)
[arXiv:2108.12155 ] [ Open Data ] [Abstract ]

Cooper pair splitting (CPS) is a way to create spatially separated, entangled electron pairs. To this day, CPS is often identified in experiments as a spatial current correlation. However, such correlations can arise even in the absence of CPS, when a quantum dot is strongly coupled to the superconductor, and a subgap Shiba state is formed. Here, we present a detailed experimental characterization of those spatial current correlations, as the tunnel barrier strength between the quantum dot and the neighboring normal electrode is tuned. The correlation of the non-local signal and the barrier strength reveals a competition between CPS and the non-local probing of the Shiba state. We describe our experiment with a simple transport model, and obtain the tunnel couplings of our device by fitting the model’s prediction to the measured conductance correlation curve. Furthermore, we use our theory to extract the contribution of CPS to the non-local signal.

• Phase-dependent microwave response of a graphene Josephson junction
R. Haller, G. Fülöp, D. Indolese, J. Ridderbos, R. Kraft, Luk Yi Cheung, J. H. Ungerer, K. Watanabe, T. Taniguchi, D. Beckmann, R. Danneau, P. Virtanen, and C. Schönenberger.
Phys. Rev. Research  4, 13198 (2022)
[arXiv:2108.00989 ] [ Open Data ] [Abstract ]

Gate-tunable Josephson junctions embedded in a microwave environment provide a promising platform to in-situ engineer and optimize novel superconducting quantum circuits. The key quantity for the circuit design is the phase-dependent complex admittance of the junction, which can be probed by sensing an rf SQUID with a tank circuit. Here, we investigate a graphene-based Josephson junction as a prototype gate-tunable element enclosed in a SQUID loop that is inductively coupled to a superconducting resonator operating at 3 GHz. With a concise circuit model that describes the dispersive and dissipative response of the coupled system, we extract the phase-dependent junction admittance corrected for self-screening of the SQUID loop. We decompose the admittance into the current-phase relation and the phase-dependent loss and as these quantities are dictated by the spectrum and population dynamics of the supercurrent-carrying Andreev bound states, we gain insight to the underlying microscopic transport mechanisms in the junction. We theoretically reproduce the experimental results by considering a short, diffusive junction model that takes into account the interaction between the Andreev spectrum and the electromagnetic environment, from which we deduce a lifetime of ~17 ps for non-equilibrium populations.

• Magnetic, thermal, and topographic imaging with a nanometer-scale SQUID-on-cantilever scanning probe
M. Wyss, K. Bagani, D. Jetter, E. Marchiori, A. Vervelaki, B. Gross, J. Ridderbos, S. Gliga, C. Schönenberger, and M. Poggio.
Phys. Rev. Appl.  17, 34002 (2022)
[arXiv:2109.06774 ] [Abstract ]

Scanning superconducting quantum interference device (SQUID) microscopy is a magnetic imaging technique combining high field sensitivity with nanometer-scale spatial resolution. State-of-the-art SQUID-on-tip probes are now playing an important role in mapping correlation phenomena, such as superconductivity and magnetism, which have recently been observed in two-dimensional van der Waals materials. Here, we demonstrate a scanning probe that combines the magnetic and thermal imaging provided by an on-tip SQUID with the tip-sample distance control and topographic contrast of a non-contact atomic force microscope (AFM).We pattern the nanometer-scale SQUID, including its weak-link Josephson junctions, via focused ion beam milling at the apex of a cantilever coated with Nb, yielding a sensor with an effective diameter of 365 nm, field sensitivity of 9.5 nT / sqrt(Hz)and thermal sensitivity of 620 nK / sqrt(Hz)operating in magnetic fields up to 1.0 T. The resulting SQUID-on-lever is a robust AFM-like scanning probe that expands the reach of sensitive nanometerscale magnetic and thermal imaging beyond what is currently possible.

##### 2021
• Intermediate states in Andreev bound state fusion
C. Jünger, S. Lehmann, K. A. Dick, C. Thelander, C. Schönenberger, and A. Baumgartner.
submitted (2021)
[arXiv:2111.00651 ] [ Open Data ] [Abstract ]

Hybridization is a very fundamental quantum mechanical phenomenon, with the text book example of binding two hydrogen atoms in a hydrogen molecule. In semiconductor physics, a quantum dot (QD) can be considered as an artificial atom, with two coupled QDs forming a molecular state, and two electrons on a single QD the equivalent of a helium atom. Here, we report tunnel spectroscopy experiments illustrating the hybridisation of another type of discrete quantum states, namely of superconducting subgap states that form in segments of a semiconducting nanowire in contact with superconducting reservoirs. We show and explain a collection of intermediate states found in the process of merging individual bound states, hybridizing with a central QD and eventually coherently linking the reservoirs. These results may serve as a guide in future Majorana fusion experiments and explain a large variety of recent bound state experiments.

• Boosting proximity spin orbit coupling in graphene/WSe2 heterostructures via hydrostatic pressure
B. Fülöp, A. Márffy, S. Zihlmann, M. Gmitra, E. Tóvári, B. Szentpéteri, M. Kedves, K. Watanabe, T. Taniguchi, J. Fabian, C. Schönenberger, P. Makk, and S. Csonka.
npj 2D Materials and Applications  5, 82 (2021)
[arXiv:2103.13325 ] [ Open Data ] [Abstract ]

Van der Waals heterostructures composed of multiple few layer crystals allow the engineering of novel materials with predefined properties. As an example, coupling graphene weakly to materials with large spin orbit coupling (SOC) allows to engineer a sizeable SOC in graphene via proximity effects. The strength of the proximity effect depends on the overlap of the atomic orbitals, therefore, changing the interlayer distance via hydrostatic pressure can be utilized to enhance the interlayer coupling between the layers. In this work, we report measurements on a graphene/WSe2 heterostructure exposed to increasing hydrostatic pressure. A clear transition from weak localization to weak anti-localization is visible as the pressure increases, demonstrating the increase of induced SOC in graphene.

• New method of transport measurements on van der Waals heterostructures under pressure
B. Fülöp, A. Márffy, E. Tóvári, M. Kedves, S. Zihlmann, D. Indolese, Z. Kovács-Krausz, K. Watanabe, T. Taniguchi, C. Schönenberger, Kézsmárki I. P. Makk, and S. Csonka.
J. Apl. Phys.  130, 64303 (2021)
[arXiv:2103.14617 ] [ Open Data ] [Abstract ]

The interlayer coupling, which has a strong influence on the properties of van der Waals heterostructures, strongly depends on the interlayer distance. Although considerable theoretical interest has been demonstrated, experiments exploiting a variable interlayer coupling on nanocircuits are scarce due to the experimental difficulties. Here, we demonstrate a novel method to tune the interlayer coupling using hydrostatic pressure by incorporating van der Waals heterostructure based nanocircuits in piston-cylinder hydrostatic pressure cells with a dedicated sample holder design. This technique opens the way to conduct transport measurements on nanodevices under pressure using up to 12 contacts without constraints on the sample at the fabrication level. Using transport measurements, we demonstrate that a hexagonal boron nitride capping layer provides a good protection of van der Waals heterostructures from the influence of the pressure medium, and we show experimental evidence of the influence of pressure on the interlayer coupling using weak localization measurements on a transitional metal dichalcogenide/graphene heterostructure.

• Superconducting contacts to a monolayer semiconductor
M. Ramezani, Correa I. Sampaio, K. Watanabe, T. Taniguchi, C. Schönenberger, and A. Baumgartner.
Nano Letters  21, 5614 (2021)
[arXiv:2102.06227 ] [ Open Data ] [Abstract ]

We demonstrate superconducting vertical interconnect access (VIA) contacts to a mono-layer of molybdenum disulfide (MoS2), a layered semiconductor with highly relevant elec-tronic and optical properties. As a contact material we use MoRe, a superconductor with a high critical magnetic field and high critical temperature. The electron transport is mostly dominated by a single superconductor/normal conductor junction with a clear superconductor gap. In addition, we find MoS2 regions that are strongly coupled to the superconductor, resulting in resonant Andreev tunneling and junction dependent gap characteristics, suggesting a superconducting proximity effect. Magnetoresistance measurements show that the band-structure and the high intrinsic carrier mobility remain intact in the bulk of the MoS2. This type of VIA contact is applicable to a large variety of layered materials and superconducting

• Superconductivity in type-II Weyl-semimetal WTe2 induced by a normal metal contact
A. Kononov, M. Endres, G. Abulizi, Kejian Qu, Jiaqiang Yan, D. Mandrus, K. Watanabe, T. Taniguchi, and C. Schönenberger.
Journal of Applied Physics  129, 113903 (2021)
[arXiv:2007.04752 ] [ Open Data ] [Abstract ]

WTe2 is a material with rich topological properties: it is a 2D topological insulator as a monolayer and a Weyl-semimetal and higher-order topological insulator in the bulk form. Inducing superconductivity in topological materials is a way to obtain topological superconductivity, which lays at the foundation for many proposals of fault tolerant quantum computing. Here, we demonstrate the emergence of superconductivity at the interface between WTe2 and the normal metal palladium. The superconductivity has a critical temperature of about 1.2 K. By studying the superconductivity in perpendicular magnetic field, we obtain the coherence length and the London penetration depth. These parameters correspond to a low Fermi velocity and a high density of states at the Fermi level. This hints to a possible origin of superconductivity due to the formation of flatbands. Furthermore, the critical in-plane magnetic field exceeds the Pauli limit, suggesting a non-trivial nature of the superconducting state.

• Operation of parallel SNSPDs at high detection rate
M. Perrenoud, M. Caloz, E. Amri, C. Autebert, C. Schönenberger, H. Zbinden, and F. Bussières.
Supercond. Sci. Technol.  34, 24002 (2021)
[Abstract ]

Recent progress in the development of superconducting nanowire single-photon detectors (SNSPD) has delivered excellent performance, and their increased adoption has had a great impact on a range of applications. One of the key characteristic of SNSPDs is their detection rate, which is typically higher than other types of free-running single-photon detectors. The maximum achievable rate is limited by the detector recovery time after a detection, which itself is linked to the superconducting material properties and to the geometry of the meandered SNSPD. Arrays of detectors biased individually can be used to solve this issue, but this approach significantly increases both the thermal load in the cryostat and the need for time processing of the many signals, and this scales unfavorably with a large number of detectors. One potential scalable approach to increase the detection rate of individual detectors further is based on parallelizing smaller meander sections. In this way, a single detection temporarily disables only one subsection of the whole active area, thereby leaving the overall detection efficiency mostly unaffected. In practice however, cross-talk between parallel nanowires typically leads to latching, which prevents high detection rates. Here we show how this problem can be avoided through a careful design of the whole SNSPD structure. We demonstrate molybdenum silicide-based superconducting nanowire single-photon detectors capable of detecting at more than 200 MHz using a single coaxial line. This significantly outperforms detection rates achievable with single meander SNSPDs and better maintains the efficiency with an increasing rate.

##### 2020
• Compact SQUID realized in a double layer graphene heterostructure
D. I. Indolese, P. Karnatak, A. Kononov, R. Delagrange, R. Haller, L. Wang, P. Makk, K. Watanabe, T. Taniguchi, and C. Schönenberger.
Nano Letters  20, 7129–7135 (2020)
[arXiv:2006.05522 ] [ Open Data ] [Abstract ]

Two-dimensional systems that host one-dimensional helical states are exciting from the perspective of scalable topological quantum computation when coupled with a superconductor. Graphene is particularly promising for its high electronic quality, versatility in van der Waals heterostructures and its electron and hole-like degenerate 0$th$ Landau level. Here, we study a compact double layer graphene SQUID (superconducting quantum interference device), where the superconducting loop is reduced to the superconducting contacts, connecting two parallel graphene Josephson junctions. Despite the small size of the SQUID, it is fully tunable by independent gate control of the Fermi energies in both layers. Furthermore, both Josephson junctions show a skewed current phase relationship, indicating the presence of superconducting modes with high transparency. In the quantum Hall regime we measure a well defined conductance plateau of 2$e^2/h$ an indicative of counter propagating edge channels in the two layers. Our work opens a way for engineering topological superconductivity by coupling helical edge states, from graphene’s electron-hole degenerate 0$th$ Landau level via superconducting contacts.

• Magnetic field independent sub-gap states in hybrid Rashba nanowires
C. Jünger, R. Delagrange, D. Chevallier, S. Lehmann, K. A. Dick, C. Thelander, J. Klinovaja, D. Loss, A. Baumgartner, and C. Schönenberger.
Phys. Rev. Lett.  125, 17701 (2020)
[arXiv:2001.07666 ] [ Open Data ] [Abstract ]

Sub-gap states in semiconducting-superconducting nanowire hybrid devices are controversially discussed as potential topologically non-trivial quantum states. One source of ambiguity is the lack of an energetically and spatially well de ned tunnel spectrometer. Here, we use quantum dots directly integrated into the nanowire during the growth process to perform tunnel spectroscopy of discrete sub-gap states in a long nanowire segment. In addition to sub-gap states with a standard magnetic eld dependence, we nd topologically trivial sub-gap states that are independent of the external magnetic eld, i.e. that are pinned to a constant energy as a function of eld. We explain this effect qualitatively and quantitatively by taking into account the strong spin-orbit interaction in the nanowire, which can lead to a decoupling of Andreev bound states from the eld due to a spatial spin texture of the con ned eigenstates. This result constitutes an important step forward in the research on superconducting sub-gap states in nanowires, such as Majorana bound states.

• Large spatial extension of the zero-energy Yu-Shiba-Rusinov state in magnetic field
Z. Scherübl, G. Fülöp, C. P. Moca, J. Gramich, A. Baumgartner, P. Makk, T. Elalaily, C. Schönenberger, J. Nygard, G. Zaránd, and S. Csonka.
Nature Communications  11, 1834 (2020)
[arXiv:1906.08531 ] [ Open Data ] [Abstract ]

Various promising qubit concepts have been put forward recently based on engineered superconductor (SC) subgap states like Andreev bound states, Majorana zero modes or the Yu-Shiba-Rusinov (Shiba) states. The coupling of these subgap states via a SC strongly depends on their spatial extension and is an essential next step for future quantum technologies. Here we investigate the spatial extension of a Shiba state in a semiconductor quantum dot coupled to a SC for the first time. With detailed transport measurements and numerical renormalization group calculations we find a remarkable more than 50 nm extension of the zero energy Shiba state, much larger than the one observed in very recent scanning tunneling microscopy (STM) measurements. Moreover, we demonstrate that its spatial extension increases substantially in magnetic field.

##### 2019
• Intrinsically-limited timing jitter in molybdenum silicide superconducting nanowire single-photon detectors
M. Caloz, B. Korzh, E. Ramirez, C. Schönenberger, R. J. Warburton, H. Zbinden, M. D. Shaw, and F. Bussières.
J. Appl. Phys  126, 164501 (2019)
[arXiv:1906.02073 ] [Abstract ]

Recent progress in the development of superconducting nanowire single-photon detectors (SNSPDs) has delivered excellent performances, and has had a great impact on a range of research fields. The timing jitter, which denotes the temporal resolution of the detection, is a crucial parameter for many applications. Despite extensive work since their apparition, the lowest jitter achievable with SNSPDs is still not clear, and the origin of the intrinsic limits is not fully understood. Understanding its intrinsic behaviour and limits is a mandatory step toward improvements. Here, we report our experimental study on the intrinsically-limited timing jitter in molybdenum silicide (MoSi) SNSPDs. We show that to reach intrinsic jitter, several detector properties such as the latching current and the kinetic inductance of the devices have to be understood. The dependence on the nanowire cross-section and the energy dependence of the intrinsic jitter are exhibited as well as their fundamental limitations. System timing jitter of 6.0 ps at 532 nm and 10.6 ps at 1550 nm photon wavelength have been obtained.

• Spectroscopy of the superconducting proximity effect in nanowires using integrated quantum dots
C. Jünger, A. Baumgartner, R. Delagrange, D. Chevallier, S. Lehmann, M. Nilsson, K. A. Dick, C. Thelander, and C. Schönenberger.
Communications Physics  2, 76 (2019)
[arXiv:1812.06850 ] [Abstract ]

The superconducting proximity effect has been the focus of significant research efforts over many YEARs and has recently attracted renewed interest as the basis of topologically non-trivial states in materials with a large spin orbit interaction, with protected boundary states useful for quantum information technologies. However, spectroscopy of these states is challenging because of the limited spatial and energetic control of conventional tunnel barriers. Here, we report electronic spectroscopy measurements of the proximity gap in a semiconducting indium arsenide (InAs) nanowire (NW) segment coupled to a superconductor (SC), using a spatially separated quantum dot (QD) formed deterministically during the crystal growth. We extract the characteristic parameters describing the proximity gap which is suppressed for lower electron densities and fully developed for larger ones. This gate-tunable transition of the proximity effect can be understood as a transition from the long to the short junction regime of subgap bound states in the NW segment. Our device architecture opens up the way to systematic, unambiguous spectroscopy studies of subgap bound states, such as Majorana bound states.

• GHz nanomechanical resonator in an ultraclean suspended graphene p-n junction
Minkyung Jung, P. Rickhaus, S. Zihlmann, A. Eichler, P. Makk, and C. Schönenberger.
Nanoscale  11, 4355 (2019)
[arXiv:1812.06412 ] [Abstract ]

We demonstrate high-frequency mechanical resonators in ballistic graphene p–n junctions. Fully suspended graphene devices with two bottom gates exhibit ballistic bipolar behavior after current annealing. We determine the graphene mass density and built-in tension for different current annealing steps by comparing the measured mechanical resonant response to a simplified membrane model. We consistently find that after the last annealing step the mass density compares well with the expected density of pure graphene. In a graphene membrane with high built-in tension, but still of macroscopic size with dimensions 3 × 1 micrometer^2, a record resonance frequency of 1.17 GHz is observed after the final current annealing step. We further compare the resonance response measured in the unipolar with the one in the bipolar regime. Remarkably, the resonant signals are strongly enhanced in the bipolar regime. This enhancement is caused in part by the Fabry-Pérot resonances that appear in the bipolar regime and possibly also by the photothermoelectric effect that can be very pronounced in graphene p–n junctions under microwave irradiation.

• Non-equilibrium properties of graphene probed by superconducting tunnel spectroscopy
S. Zihlmann, P. Makk, S. Castillas, J. Gramich, K. Thodkar, S. Caneva, R. Wang, S. Hofmann, and C. Schönenberger.
Phys. Rev. B  99, 75419 (2019)
[arXiv:1811.08746 ] [Abstract ]

We report on non-equilibrium properties of graphene probed by superconducting tunnel spectroscopy. A hexagonal boron nitride (hBN) tunnel barrier in combination with a superconducting Pb contact is used to extract the local energy distribution function of the quasiparticles in graphene samples in different transport regimes. In the cases where the energy distribution function resembles a Fermi-Dirac distribution, the local electron temperature can directly be accessed. This allows us to study the cooling mechanisms of hot electrons in graphene. In the case of long samples (device length L much larger than the electron-phonon scattering length le−ph), cooling through acoustic phonons is dominant. We find a cross-over from the dirty limit with a power law T3 at low temperature to the clean limit at higher temperatures with a power law T4 and a deformation potential of 13..3 eV. For shorter samples, where L is smaller than le−ph but larger than the electron-electron scattering length le−e, the well-known cooling through electron out-diffusion is found. Interestingly, we find strong indications of an enhanced Lorenz number in graphene. We also find evidence of a non-Fermi-Dirac distribution function, which is a result of non-interacting quasiparticles in very short samples

##### 2018
• Wideband and on-chip excitation for dynamical spin injection into graphene
D. I. Indolese, S. Zihlmann, P. Makk, C. Jünger, K. Thodkar, and C. Schönenberger.
Phys. Rev. Appl.  10, 44053 (2018)
[arXiv:1806.09356 ] [Abstract ]

Graphene is an ideal material for spin transport as very long spin relaxation times and lengths can be achieved even at room temperature. However, electrical spin injection is challenging due to the conductivity mismatch problem. Spin pumping driven by ferromagnetic resonance is a neat way to circumvent this problem as it produces a pure spin current in the absence of a charge current. Here, we show spin pumping into single layer graphene in micron scale devices. A broadband on-chip RF current line is used to bring micron scale permalloy (Ni80Fe20) pads to ferromagnetic resonance with a magnetic eld tunable resonance condition. At resonance, a spin current is emitted into graphene, which is detected by the inverse spin hall voltage in a close-by platinum electrode. Clear spin current signals are detected down to a power of a few milliwatts over a frequency range of 2 GHz to 8 GHz. This compact device scheme paves the way for more complex device structures and allows the investigation of novel materials.

• Signatures of van Hove singularities probed by the supercurrent in a graphene – hBN superlattice
D. I. Indolese, R. Delagrange, P. Makk, J. R. Wallbank, K. Wanatabe, T. Taniguchi, and C. Schönenberger.
Phys. Rev. Lett.  121, 137701 (2018)
[arXiv:1805.10184 ] [Abstract ]

The bandstructure of graphene can be strongly modified when it is aligned with its Boron Nitride substrate. A moiré superlattice forms, which manifests itself by the appearance of new Dirac points, accompanied by van Hove singularities. In this work, we present supercurrent measurements in a Josephson junction made from such a graphene superlattice in the long and diffusive transport regime, where the supercurrent depends on the Thouless energy. We can then estimate the specific density of states of the graphene superlattice from the combined measurement of the critical current and the normal state resistance. The result matches with theoretical predictions and highlights the strong increase of the density of states at the van Hove singularities. By measuring the magnetic field dependence of the supercurrent, we find the presence of edge currents at these singularities. We explain it by the reduction of the Fermi velocity associated with the flat band at the van Hove singularity, which suppresses the supercurrent in the bulk while the electrons at the edge remain less localized, resulting in an edge supercurrent. We attribute this different behavior of the edges to defects or chemical doping.

• Co-existence of classical snake states and Aharanov-Bohm oscillations along graphene p-n junctions
Peter Makk, Clevin Handschin, Endre Tovari, Kenji Watanabe, Takashi Taniguchi, Klaus Richter, Ming-Hao Liu, and Christian Schönenberger.
Phys. Rev. B  98, 35413 (2018)
[arXiv:1804.02590 ] [Abstract ]

Snake states and Aharonov-Bohm interferences are examples of magnetoconductance oscillations that can be observed in a graphene p-n junction. Even though they have already been reported in suspended and encapsulated devices including different geometries, a direct comparison remains challenging as they were observed in separate measurements. Due to the similar experimental signatures of these effects a consistent assignment is difficult, leaving us with an incomplete picture. Here we present measurements on p-n junctions in encapsulated graphene revealing several sets of magnetoconductance oscillations allowing for their direct comparison. We analysed them with respect to their charge carrier density, magnetic field, temperature and bias dependence in order to assign them to either snake states or Aharonov-Bohm oscillations. Furthermore we were able to consistently assign the various Aharonov-Bohm interferences to the corresponding area which the edge states enclose. Surprisingly, we find that snake states and Aharonov-Bohm interferences can co-exist within a limited parameter range

• Cooper-pair splitting in two parallel InAs nanowires
Shoji Baba, Christian Jünger, Sadashige Matsuo, Andreas Baumgartner, Yosuke Sato, Hiroshi Kamata, Kan Li, Sören Jeppesen, Lars Samuelson, Hongqi Xu, Christian Schönenberger, and Seigo Tarucha.
New Journal of Physics  20, 63021 (2018)
[arXiv:1802.08059 ] [Abstract ]

We report on the fabrication and electrical characterization of an InAs double – nanowire (NW) device consisting of two closely placed parallel NWs coupled to a common superconducting electrode on one side and individual normal metal leads on the other. In this new type of device we detect Cooper-pair splitting (CPS) with a sizeable efficiency of correlated currents in both NWs. In contrast to earlier experiments, where CPS was realized in a single NW, demonstrating an intrawire electron pairing mediated by the superconductor (SC), our experiment demonstrates an inter- wire interaction mediated by the common SC. The latter is the key for the realization of zero-magnetic field Majorana bound states, or Parafermions; in NWs and therefore constitutes a milestone towards topological superconductivity. In addition, we observe transport resonances that occur only in the superconducting state, which we tentatively attribute to Andreev Bound states and/or Yu-Shiba resonances that form in the proximitized section of one NW.

• High-detection efficiency and low-timing jitter with amorphous superconducting nanowire single-photon detectors
M. Caloz, M. Perrenoud, C. Autebert, B. Korzh, M. Weiss, C. Schönenberger, R. J. Warburton, H. Zbinden, and F. Bussières.
Appl. Phys. Lett.  112, 61103 (2018)
[arXiv:1710.06740 ] [Abstract ]

Recent progress in the development of superconducting nanowire single-photon detectors (SNSPDs) made of amorphous material has delivered excellent performances, and has had a great impact on a range of research fields. Despite showing the highest system detection effciency (SDE) ever reported with SNSPDs, amorphous materials typically lead to lower critical currents, which impacts on their jitter performance. Combining a very low jitter and a high SDE remains a challenge. Here, we report on highly effcient superconducting nanowire single-photon detectors based on amorphous MoSi, combining system jitters as low as 26 ps and a SDE of 80\% at 1550 nm. We also report detailed observations on the jitter behaviour, which hints at intrinsic limitations and leads to practical implications for SNSPD performance.

##### 2017
• Andreev bound states probed in three-terminal quantum dots
J. Gramich, A. Baumgartner, and C. Schönenberger.
Phys. Rev. B  96, 195418 (2017)
[arXiv:1612.01201 ] [Abstract ]

Andreev bound states (ABSs) are well-de ned many-body quantum states that emerge from the hybridization of individual quantum dot (QD) states with a superconductor and exhibit very rich and fundamental phenomena. We demonstrate several new electron transport phenomena mediated by ABSs that form on three-terminal carbon nanotube (CNT) QDs, with one superconducting (S) contact in the center and two adjacent normal metal (N) contacts. Three-terminal spectroscopy allows us to identify the coupling to the N contacts as the origin of the Andreev resonance (AR) linewidths and to determine the critical coupling strengths to S, for which a ground state (or quantum phase) transition in such S-QD systems can occur. In addition, we ascribe replicas of the lowest-energy ABS resonance to transitions between the ABS and odd-parity excited QD states, a process we call excited state ABS resonances. In the conductance between the two N contacts we find a characteristic pattern of positive and negative differential subgap conductance, which we explain by considering two nonlocal processes, the creation of Cooper pairs in S by electrons from both N terminals, and a novel transport mechanism called resonant ABS tunneling, possible only in multi-terminal QD devices. In the latter process, electrons are transferred via the ABS without effectively creating Cooper pairs in S. The three-terminal geometry also allows spectroscopy experiments with different boundary conditions, for example by leaving S floating. Surprisingly, we find that, depending on the boundary conditions and the device parameters, the experiments either show single-particle Coulomb blockade resonances, ABS characteristics, or both in the same measurements, seemingly contradicting the notion of ABSs replacing the single particle states as eigenstates of the QD. We qualitatively explain these results as originating from the nite time scale required for the coherent oscillations between the superposition states after a single electron tunneling event. These experiments demonstrate that three-terminal experiments on a single complex quantum object can also be useful to investigate charge dynamics otherwise not accessible due to the very high frequencies.

• Optically probing the detection mechanism in a molybdenum silicide superconducting nanowire single-photon detector
M. Caloz, B. Korzh, N. Timoney, M. Weiss, S. Gariglio, R. J. Warburton, C. Schönenberger, J. Renema, H. Zbinden, and F. Bussieres.
Applied Physics Letters  110(8), 83106 (2017)
[arXiv:1611.08238 ] [Abstract ]

We experimentally investigate the detection mechanism in a meandered molybdenum silicide superconducting nanowire single-photon detector by characterising the detection probability as a function of bias current in the wavelength range of 750–2050 Onm. Contrary to some previous observations on niobium nitride or tungsten silicide detectors, we find that the energy-current relation is nonlinear in this range. Furthermore, thanks to the presence of a saturated detection efficiency over the whole range of wavelengths, we precisely quantify the shape of the curves. This allows a detailed study of their features, which are indicative of both Fano fluctuations and position-dependent effects.

##### 2016
• A success story
Christel Möller and Christian Schönenberger.
Nature Nanotechnology  11, 908 (2016)
[arXiv:]

• Subgap resonant quasiparticle transport in normal-superconductor quantum dot devices
J. Gramich, A. Baumgartner, and C. Schönenberger.
Appl. Phys. Lett.  108(17), 172604 (2016)
[arXiv:1601.00672 ] [Abstract ]

We report thermally activated transport resonances for biases below the superconducting energy gap in a carbon nanotube quantum dot (QD) device with a superconducting Pb and a normal metal contact. These resonances are due to the superconductor’s finite quasi-particle population at elevated temperatures and can only be observed when the QD life-time broadening is considerably smaller than the gap. This condition is fulfilled in our QD devices with optimized Pd/Pb/In multi-layer contacts, which result in reproducibly large and “clean” superconducting transport gaps with a strong conductance suppression for subgap biases. We show that these gaps close monotonically with increasing magnetic field and temperature. The accurate description of the subgap resonances by a simple resonant tunneling model illustrates the ideal characteristics of the reported Pb contacts and gives an alternative access to the tunnel coupling strengths in a QD.

• Cooper-Paare tunneln durch einen Quantenpunkt
Andreas Baumgartner, Jörg Gramich, and Christian Schönenberger.
Physik in unserer Zeit  47(2), 62 (2016)
[arXiv:] [Abstract ]

Elektronische Bauteile aus Supraleitern und Quantenpunkten zeigen eine Vielzahl von neuen und fundamentalen physikalischen Eigenschaften und stellen neue quantentechnologische Anwendungen in Aussicht. Kuerzlich ist es gelungen, den wohl grundlegendsten Transportprozess in einer solchen Struktur in Experimenten zu identifizieren, naemlich den direkten Transport von Elektronen aus einem Supraleiter durch einen Quantenpunkt, das sogenannte Andreev-Tunneln. Das Verstaendnis dieses Prozesses liefert die Grundlage fuer zukuenftige Anwendungen, die quantenmechanische Phaenomene in elektronischen Bauteilen ausnutzen werden.

##### 2015
• Resonant and Inelastic Andreev Tunneling Observed on a Carbon Nanotube Quantum Dot
J. Gramich, A. Baumgartner, and C. Schönenberger.
Physical Review Letters  115, 216801 (2015)
[arXiv:1507.00526 ] [Abstract ]

We report the observation of two fundamental sub-gap transport processes through a quantum dot (QD) with a superconducting contact. The device consists of a carbon nanotube contacted by a Nb superconducting and a normal metal contact. First, we find a single resonance with position, shape and amplitude consistent with the theoretically predicted resonant Andreev tunneling (AT) through a single QD level. Second, we observe a series of discrete replicas of resonant AT at a separation of ∼145μeV, with a gate, bias and temperature dependence characteristic for boson-assisted, inelastic AT, in which energy is exchanged between a bosonic bath and the electrons. The magnetic field dependence of the replica’s amplitudes and energies suggest that two different bosons couple to the tunnel process.