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The quest to implement machine learning algorithms in hardware has focused on combining various materials, each mimicking a computational primitive, to create device functionality. Ultimately, these piecewise approaches limit functionality and efficiency, while complicating scaling and on-chip learning, necessitating new approaches linking physical phenomena to machine learning models. Here, we create an atomic spin system that emulates a Boltzmann machine directly in the orbital dynamics of one well-defined material system. Utilizing the concept of orbital memory based on individual cobalt atoms on black phosphorus, we fabricate the prerequisite tuneable multi-well energy landscape by gating patterned atomic ensembles using scanning tunnelling microscopy. Exploiting the anisotropic behaviour of black phosphorus, we realize plasticity with multi-valued and interlinking synapses that lead to tuneable probability distributions. Furthermore, we observe an autonomous reorganization of the synaptic weights in response to external electrical stimuli, which evolves at a different time scale compared to neural dynamics. This self-adaptive architecture paves the way for autonomous learning directly in atomic-scale machine learning hardware.Stochastic orbital dynamics of individually coupled Co atoms on black phosphorus enables the realization of a Boltzmann machine capable of self-adaption.

The influence of interface electronic structure is vital to control lower dimensional superconductivity and its applications to gated superconducting electronics, and superconducting layered heterostructures. Lower dimensional superconductors are typically synthesized on insulating substrates to reduce interfacial driven effects that destroy superconductivity and delocalize the confined wavefunction. Here, we demonstrate that the hybrid electronic structure formed at the interface between a lead film and a semiconducting and highly anisotropic black phosphorus substrate significantly renormalizes the superconductivity in the lead film. Using ultra-low temperature scanning tunneling microscopy and spectroscopy, we characterize the renormalization of lead’s quantum well states, its superconducting gap, and its vortex structure which show strong anisotropic characteristics. Density functional theory calculations confirm that the renormalization of superconductivity is driven by hybridization at the interface which modifies the confinement potential and imprints the anisotropic characteristics of the semiconductor substrate on selected regions of the Fermi surface of lead. Using an analytical model, we link the modulated superconductivity to an anisotropy that selectively tunes the superconducting order parameter in reciprocal space. These results illustrate that interfacial hybridization can be used to tune superconductivity in quantum technologies based on lower dimensional superconducting electronics. Lower-dimensional superconductors are typically synthesized on insulating substrates. Here, the authors find that the hybrid electronic structure formed at the interface between a lead film and a semiconducting black phosphorus substrate significantly renormalizes the superconductivity in the lead film.

The Boltzmann Machine (BM) is a neural network composed of stochastically firing neurons that can learn complex probability distributions by adapting the synaptic interactions between the neurons. BMs represent a very generic class of stochastic neural networks that can be used for data clustering, generative modelling and deep learning. A key drawback of software-based stochastic neural networks is the required Monte Carlo sampling, which scales intractably with the number of neurons. Here, we realize a physical implementation of a BM directly in the stochastic spin dynamics of a gated ensemble of coupled cobalt atoms on the surface of semiconducting black phosphorus. Implementing the concept of orbital memory utilizing scanning tunnelling microscopy, we demonstrate the bottom-up construction of atomic ensembles whose stochastic current noise is defined by a reconfigurable multi-well energy landscape. Exploiting the anisotropic behaviour of black phosphorus, we build ensembles of atoms with two well-separated intrinsic time scales that represent neurons and synapses. By characterizing the conditional steady-state distribution of the neurons for given synaptic configurations, we illustrate that an ensemble can represent many distinct probability distributions. By probing the intrinsic synaptic dynamics, we reveal an autonomous reorganization of the synapses in response to external electrical stimuli. This self-adaptive architecture paves the way for on-chip learning directly in atomic-scale machine learning hardware.

Orbital memory is defined by two stable valencies that can be electrically switched and read-out. To explore the influence of an electric field on orbital memory, we studied the distance-dependent influence of an atomic Cu donor on the state favorability of an individual Co atom on black phosphorus. Using low temperature scanning tunneling microscopy/spectroscopy, we characterized the electronic properties of individual Cu donors, corroborating this behavior with ab initio calculations based on density functional theory. We studied the influence of an individual donor on the charging energy and stochastic behavior of an individual Co atom. We found a strong impact on the state favorability in the stochastic limit. These findings provide quantitative information about the influence of local electric fields on atomic orbital memory.

Bistable valency in individual atoms presents a new approach toward single-atom memory, as well as a building block to create tunable and stochastic multi-well energy landscapes. Yet, this concept of orbital memory has thus far only been observed for cobalt atoms on the surface of black phosphorus, which are switched using tip-induced ionization. Here, we show that individual iron atoms on the surface of black phosphorus exhibit orbital memory using a combination of scanning tunneling microscopy and spectroscopy with ab initio calculations based on density functional theory. Unlike cobalt, the iron orbital memory can be switched in its non-ionized ground state. Based on calculations, we confirm that each iron valency has a distinct magnetic moment that is characterized by a distinguishable charge distribution due to the different orbital population. By studying the stochastic switching of the valency with varying tunneling conditions, we propose that the switching mechanism is based on a two-electron tunneling process.

Screening in reduced dimensions has strong consequences on the electronic properties in van der Waals semiconductors, impacting the quasiparticle band gap and exciton binding energy. Screening in these materials is typically treated isotropically, yet black phosphorus exhibits in-plane electronic anisotropy seen in its effective mass, carrier mobility, excitonic wavefunctions, and plasmonic dispersion. Here, we use the adsorption of individual potassium atoms on the surface of black phosphorus to vary the near-surface doping over a wide range, while simultaneously probing the dielectric screening via the ordering of the adsorbed atoms. Using scanning tunneling microscopy, we visualize the role of strongly anisotropic screening which leads to the formation of potassium chains with a well-defined orientation and spacing. We quantify the mean interaction potential utilizing statistical methods and find that the dimensionality and anisotropy of the screening is consistent with the presence of a band-bending induced confinement potential near the surface. We corroborate the observed behavior with coverage-dependent studies of the electronic structure with angle-resolved photoemission.

We describe the design and performance of a scanning tunneling microscope (STM) which operates at a base temperature of 30 mK in a vector magnetic field. The cryogenics is based on an ultra-high vacuum (UHV) top-loading wet dilution refrigerator that contains a vector magnet allowing for fields up to 9 T perpendicular and 4 T parallel to the sample. The STM is placed in a multi-chamber UHV system, which allows in-situ preparation and exchange of samples and tips. The entire system rests on a 150-ton concrete block suspended by pneumatic isolators, which is housed in an acoustically isolated and electromagnetically shielded laboratory optimized for extremely low noise scanning probe measurements. We demonstrate the overall performance by illustrating atomic resolution and quasiparticle interference imaging and detail the vibrational noise of both the laboratory and microscope. We also determine the electron temperature via measurement of the superconducting gap of Re(0001) and illustrate magnetic field-dependent measurements of the spin excitations of individual Fe atoms on Pt(111). Finally, we demonstrate spin resolution by imaging the magnetic structure of the Fe double layer on W(110).

Epitaxial semiconductor-superconductor heterostructures are promising as a platform for gate-tunable superconducting electronics. Thus far, the superconducting properties in such hybrid systems have been predicted based on simplified hybridization models which neglect the electronic structure that can arise at the interface. Here, we demonstrate that the hybrid electronic structure derived at the interface between semiconducting black phosphorus and atomically thin films of lead can drastically modify the superconducting properties of the thin metallic film. Using ultra-low temperature scanning tunneling microscopy and spectroscopy, we ascertain the moiré structure driven by the interface, and observe a strongly anisotropic renormalization of the superconducting gap and vortex structure of the lead film. Based on density functional theory, we attribute the renormalization of the superconductivity to weak hybridization at the interface where the anisotropic characteristics of the semiconductor band structure is imprinted on the Fermi surface of the superconductor. Based on a hybrid two-band model, we link this hybridization-driven renormalization to a weighting of the superconducting order parameter that quantitatively reproduces the measured spectra. These results illustrate the effect of interfacial hybridization at superconductor-semiconductor heterostructures, and pathways for engineering quantum technologies based on gate-tunable superconducting electronics.

Background The Quality-Adjusted Life Year (QALY) is internationally recognized as standard metric of health outcomes in cost-effectiveness analyses (CEAs) in healthcare. The ongoing debate concerning the appropriateness of its use for decision-making in palliative care has been recently mapped in a review. The aim was to report on and draw conclusions from two expert meetings that reflected on earlier mapped issues in order to reach consensus, and to advise on the QALY’s future use in palliative care. Methods A nominal group approach was used. In order to facilitate group decision making, three statements regarding the use of the QALY in palliative care were discussed in a structured way. Two groups of international policymakers, healthcare professionals and researchers participated. Data were analysed qualitatively using inductive coding. Results 1) Most experts agreed that the recommended measurement tool for the QALYs ‘Q’ component, the EuroQol-5D (EQ-5D), is inappropriate for palliative care. A more sensitive tool, which might be based on the capabilities approach, could be used or developed. 2) Valuation of time should be incorporated in the ‘Q’ part, leaving the linear clock time in the ‘LY’ component. 3) Most experts agreed that the QALY, in its current shape, is not suitable for palliative care. Conclusions 1) Although the EQ-5D does not suffice, a generic tool is needed for the QALY. As long as no suitable alternative is available, other tools can be used besides or serve as basis for the EQ-5D because of issues in conceptual overlap. 2) Future research should further investigate the valuation of time issue, and how best to integrate it in the ‘Q’ component. 3) A generic outcome measure of effectiveness is essential to justly allocate healthcare resources. However, experts emphasized, the QALY is and should be one of multiple criteria for choices in the healthcare insurance package.