Resonant and Inelastic Andreev Tunneling Observed on a Carbon Nanotube Quantum Dot

Edge Contacts to Atomically Precise Graphene Nanoribbons

Bottom-up-synthesized graphene nanoribbons (GNRs) are an emerging class of designer quantum materials that possess superior properties, including atomically controlled uniformity and chemically tunable electronic properties. GNR-based devices are promising candidates for next-generation electronic, spintronic, and thermoelectric applications. However, due to their extremely small size, making electrical contact with GNRs remains a major challenge. Currently, the most commonly used methods are top metallic electrodes and bottom graphene electrodes, but for both, the contact resistance is expected to scale with overlap area. Here, we develop metallic edge contacts to contact nine-atom-wide armchair GNRs (9-AGNRs) after encapsulation in hexagonal boron-nitride (h-BN), resulting in ultrashort contact lengths. We find that charge transport in our devices occurs via two different mechanisms: at low temperatures (9 K), charges flow through single GNRs, resulting in quantum dot (QD) behavior with well-defined Coulomb diamonds (CDs), with addition energies in the range of 16 to 400 meV. For temperatures above 100 K, a combination of temperature-activated hopping and polaron-assisted tunneling takes over, with charges being able to flow through a network of 9-AGNRs across distances significantly exceeding the length of individual GNRs. At room temperature, our short-channel field-effect transistor devices exhibit on/off ratios as high as 3 × 105 with on-state current up to 50 nA at 0.2 V. Moreover, we find that the contact performance of our edge-contact devices is comparable to that of top/bottom contact geometries but with a significantly reduced footprint. Overall, our work demonstrates that 9-AGNRs can be contacted at their ends in ultra-short-channel FET devices while being encapsulated in h-BN.

Determining the Number of Graphene Nanoribbons in Dual-Gate Field-Effect Transistors

Bottom-up synthesized graphene nanoribbons (GNRs) are increasingly attracting interest due to their atomically controlled structure and customizable physical properties. In recent years, a range of GNR-based field-effect transistors (FETs) has been fabricated, with several demonstrating quantum-dot (QD) behavior at cryogenic temperatures. However, understanding the relationship between the cryogenic charge-transport characteristics and the number of the GNRs in the device is challenging, as the length and location of the GNRs in the junction are not precisely controlled. Here, we present a methodology based on a dual-gate FET that allows us to identify different scenarios, such as single GNRs, double or multiple GNRs in parallel, and a single GNR interacting with charge traps. Our dual-gate FET architecture therefore offers a quantitative approach for comprehending charge transport in atomically precise GNRs.

Triplet correlations in Cooper pair splitters realized in a two-dimensional electron gas

Cooper pairs occupy the ground state of superconductors and are typically composed of maximally entangled electrons with opposite spin. In order to study the spin and entanglement properties of these electrons, one must separate them spatially via a process known as Cooper pair splitting (CPS). Here we provide the first demonstration of CPS in a semiconductor two-dimensional electron gas (2DEG). By coupling two quantum dots to a superconductor-semiconductor hybrid region we achieve efficient Cooper pair splitting, and clearly distinguish it from other local and non-local processes. When the spin degeneracy of the dots is lifted, they can be operated as spin-filters to obtain information about the spin of the electrons forming the Cooper pair. Not only do we observe a near perfect splitting of Cooper pairs into opposite-spin electrons (i.e. conventional singlet pairing), but also into equal-spin electrons, thus achieving triplet correlations between the quantum dots. Importantly, the exceptionally large spin-orbit interaction in our 2DEGs results in a strong triplet component, comparable in amplitude to the singlet pairing. The demonstration of CPS in a scalable and flexible platform provides a credible route to study on-chip entanglement and topological superconductivity in the form of artificial Kitaev chains.

Large-bias spectroscopy of Yu-Shiba-Rusinov states in a double quantum dot

We have performed tunnel transport spectroscopy on a quantum dot (QD) molecule proximitized by a superconducting contact. In such a system, the scattering between QD spins and Bogoliubov quasiparticles leads to the formation of Yu-Shiba-Rusinov (YSR) states within the superconducting gap. In this work, we investigate interactions appearing when one- and two-electron spin states in a double-QD energetically align with the superconducting gap edge. We find that the inter-dot spin-triplet state interacts considerably stronger with the superconductor than the corresponding singlet, pointing to stronger screening. By forming a ring molecule with a significant orbital contribution to the effectiveg-factor, we observe interactions of all four spin-orbital one-electron states with the superconductor under a weak magnetic field.

Zero energy states clustering in an elemental nanowire coupled to a superconductor

Nanoelectronic hybrid devices combining superconductors and a one-dimensional nanowire are promising platforms to realize topological superconductivity and its resulting exotic excitations. The bulk of experimental studies in this context are transport measurements where conductance peaks allow to perform a spectroscopy of the low lying electronic states and potentially to identify signatures of the aforementioned excitations. The complexity of the experimental landscape calls for a benchmark in an elemental situation. The present work tackles such a task using an ultra-clean carbon nanotube circuit. Specifically, we show that the combination of magnetic field, weak disorder and superconductivity can lead to states clustering at low energy, as predicted by the random matrix theory predictions. Such a phenomenology is very general and should apply to most platforms trying to realize topological superconductivity in 1D systems, thus calling for alternative probes to reveal it.

Topological superconductivity (TSC) is predicted to exist in nanowires with strong spin-orbit coupling (SOC) when they are in proximity to superconductors, with a key signature being zero-energy states in conductance measurements. Here, using weak-SOC carbon nanotubes as the nanowires, the authors show that similar looking zero-energy states can appear even in nanowires which cannot, in principle, host TSC.

Superconducting Contacts to a Monolayer Semiconductor

We demonstrate superconducting vertical interconnect access (VIA) contacts to a monolayer of molybdenum disulfide (MoS2), a layered semiconductor with highly relevant electronic 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 bandstructure 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 contacts, opening up a path to monolayer semiconductors as a platform for superconducting hybrid devices.

Thermoelectric current in a graphene Cooper pair splitter

Generation of electric voltage in a conductor by applying a temperature gradient is a fundamental phenomenon called the Seebeck effect. This effect and its inverse is widely exploited in diverse applications ranging from thermoelectric power generators to temperature sensing. Recently, a possibility of thermoelectricity arising from the interplay of the non-local Cooper pair splitting and the elastic co-tunneling in the hybrid normal metal-superconductor-normal metal structures was predicted. Here, we report the observation of the non-local Seebeck effect in a graphene-based Cooper pair splitting device comprising two quantum dots connected to an aluminum superconductor and present a theoretical description of this phenomenon. The observed non-local Seebeck effect offers an efficient tool for producing entangled electrons.

Thermoelectricity due to the interplay of the nonlocal Cooper pair splitting and the elastic co-tunneling in normal metal-superconductor-normal metal structure is predicted. Here, the authors observe the non-local Seebeck effect in a graphene-based Cooper pair splitting device.

Highly symmetric and tunable tunnel couplings in InAs/InP nanowire heterostructure quantum dots

We present a comprehensive electrical characterization of an InAs/InP nanowire (NW) heterostructure, comprising of two InP barriers forming a quantum dot (QD), two adjacent lead segments and two metallic contacts. We demonstrate how to extract valuable quantitative information of the QD. The QD shows very regular Coulomb blockade resonances over a large gate voltage range. By analyzing the resonance line shapes, we map the evolution of the tunnel couplings from the few to the many electron regime, with electrically tunable tunnel couplings from <1 μeV to >600 μeV, and a transition from the temperature to the lifetime broadened regime. The InP segments form tunnel barriers with almost fully symmetric tunnel couplings and a barrier height of ∼350 meV. All of these findings can be understood in great detail based on the deterministic material composition and geometry. Our results demonstrate that integrated InAs/InP QDs provide a promising platform for electron tunneling spectroscopy in InAs NWs, which can readily be contacted by a variety of superconducting materials to investigate subgap states in proximitized NW regions, or be used to characterize thermoelectric nanoscale devices in the quantum regime.

Current cross-correlations in double quantum dot based Cooper pair splitters with ferromagnetic leads

We investigate the current cross-correlations in a double quantum dot based Cooper pair splitter coupled to one superconducting and two ferromagnetic electrodes. The analysis is performed by assuming a weak coupling between the double dot and ferromagnetic leads, while the coupling to the superconductor is arbitrary. Employing the perturbative real-time diagrammatic technique, we study the Andreev transport properties of the device, focusing on the Andreev current cross-correlations, for various parameters of the model, both in the linear and nonlinear response regimes. Depending on parameters and transport regime, we find both positive and negative current cross-correlations. Enhancement of the former type of cross-correlations indicates transport regimes, in which the device works with high Cooper pair splitting efficiency, contrary to the latter type of correlations, which imply negative influence on the splitting. The processes and mechanisms leading to both types of current cross-correlations are thoroughly examined and discussed, giving a detailed insight into the Andreev transport properties of the considered device.

Ground-State Cooling of a Mechanical Oscillator by Interference in Andreev Reflection

We study the ground-state cooling of a mechanical oscillator linearly coupled to the charge of a quantum dot inserted between a normal metal and a superconducting contact. Such a system can be realized, e.g., by a suspended carbon nanotube quantum dot with a capacitive coupling to a gate contact. Focusing on the subgap transport regime, we analyze the inelastic Andreev reflections which drive the resonator to a nonequilibrium state. For small coupling, we obtain that vibration-assisted reflections can occur through two distinct interference paths. The interference determines the ratio between the rates of absorption and emission of vibrational energy quanta. We show that ground-state cooling of the mechanical oscillator can be achieved for many of the oscillator's modes simultaneously or for single modes selectively, depending on the experimentally tunable coupling to the superconductor.