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Graphyne (GY) and graphdiyne (GDY)-based materials represent an intriguing class of two-dimensional (2D) carbon-rich networks with tunable structures and properties surpassing those of graphene. However, the challenge of fabricating atomically well-defined crystalline GY/GDY-based systems largely hinders detailed electronic structure characterizations. Here, we report the emergence of an unconventional band structure in mesoscopically regular (~1 {\mu}m) metallated GDY sheets featuring a honeycomb lattice on Ag(111) substrates. Employing complementary scanning tunnelling and angle-resolved photoemission spectroscopies, electronic band formation with a gap of 2.5 eV is rigorously determined in agreement with real-space electronic characteristics. Extensive density functional theory calculations corroborate our observations as well as recent theoretical predictions that doubly degenerate frontier molecular orbitals on a honeycomb lattice give rise to flat, Dirac and Kagome bands close to Fermi level. These results illustrate the tremendous potential of engineering novel band structures via molecular orbital and lattice symmetries in atomically precise 2D carbon scaffolds.

As an extension of two-level quantum bits (qubits), multilevel systems, so-called qudits, where d represents the Hilbert space dimension, have been predicted to reduce the number of iterations in quantum computation algorithms. This has been tested in the well-known [TbPc2]0 SMM, which allowed the implementation of the Grover algorithm in a single molecular unit. In the quest for molecular systems possessing an increased number of accessible nuclear spin states, we explore herein a dimeric Tb2-SMM via single crystal {\mu}-SQUID measurements at sub-Kelvin temperatures. We observe ferromagnetic interactions between the Tb(III) ions and cooperative quantum tunneling of the electronic spins with spin ground state \textit{J} = {\pm}6. The strong hyperfine coupling with the Tb(III) nuclear spins leads to a multitude of spin reversal paths leading to seven strong hyperfine driven tunneling steps in the hysteresis loops. Our results show the possibility to read-out the Tb(III) nuclear spin states via the cooperative tunneling of the electronic spins, making the dimeric Tb2-SMM an excellent nuclear spin qudit candidate with d =16., Comment: Manuscript contains 17 pages, 4 figures, and SI contains 10 pages and 8 figures

Qudits, with their state space of dimension d > 2, open fascinating experimental prospects. The quantum properties of their states provide new potentialities for quantum information, quantum contextuality, expressions of geometric phases, facets of quantum entanglement and many other foundational aspects of the quantum world, which are unapproachable with qubits. We here experimentally investigate the quantum dynamics of a qudit (d = 4) that consists of a single 3/2 nuclear spin embedded in a molecular magnet transistor geometry, coherently driven by a microwave electric field. We propose and implement three protocols based on a generalization of the Ramsey interferometry to a multilevel system. First, the standard Ramsey interference is used to measure the accumulation of geometric phases. Then, two distinct transitions of the nuclear spin are addressed to measure the phase of an iSWAP quantum gate. Finally, through a succession of two Hadamard gates, the coherence time of a 3-state superposition is measured., Comment: 20 pages, 5 figures

Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation, simulation and solving large systems of linear equations. Here, we implement Grover's quantum algorithm, proposed to find an element in an unsorted list, using a single nuclear 3/2-spin carried by a Single Molecular Magnet (SMM) transistor. The coherent manipulation of this multi-level qudit is achieved by means of electric fields only. Grover's search algorithm was implemented by constructing a quantum database via a multi-level Hadamard gate. The Grover sequence then allows us to select each state. The presented method is of universal character and can be implemented in any multi-level quantum system with non-equal spaced energy levels, opening the way to novel quantum search algorithms., Comment: 5 pages, 4 figures

We present a new way of continuously reading-out the state of a single electronic spin. Our detection scheme is based on an exchange interaction between the electronic spin and a nearby read-out quantum dot. The coupling between the two systems results in a spin-dependent conductance through the read-out dot and establishes an all electrical and non-destructive single spin detection. With conductance variations up to 4% and read-out fidelities greater than 99.5%, this method represents an alternative to systems where spin to charge conversion cannot be implemented. Using a semi-classical approach, we present an asymetric exchange coupling model in good agreement with our experimental results.

We present fabrication and optical characterization of micro-cavities made of multilayer graphene (MLG) cantilevers clamped by metallic electrodes and suspended over Si/Si02 substrate. Graphene cantilevers act as a semi-transparent mirrors closing an air-wedge optical cavity. This simple geometry implements a standing-wave optical resonator along with a mechanical one. Equal thickness interference fringes are observed in both Raman and Rayleigh backscattered signals with interfringe given by their specific wavelength.Chromatic dispersion within the cavity makes possible spatial modulation of graphene Raman lines and selective rejection of the silicon background signals. Electrostatic actuation of the multilayer graphene cantilever by gate voltage tunes the cavity length and induces space and time modulation of backscattered light including Raman lines. We demonstrate the potential of those systems for high sensitivity Raman measurements of generic molecular species grafted on multilayer graphene surface. The Raman signal of the molecular layer can be modulated both in time and in space in a similar fashion and show enhancement with respect to a collapsed membrane., Comment: 12 pages, 10 figures, submitted to Journal of Optics

A multi-terminal device based on a carbon nanotube quantum dot was used at very low tem- perature to probe a single electronic and nuclear spin embedded in a bis-phthalocyanine Terbium (III) complex (TbPc2). A spin-valve signature with large conductance jumps was found when two molecules were strongly coupled to the nanotube. The application of a transverse field separated the magnetic signal of both molecules and enabled single-shot read-out of the Terbium nuclear spin. The Landau-Zener (LZ) quantum tunneling probability was studied as a function of field sweep rate, establishing a good agreement with the LZ equation and yielding the tunnel splitting \Delta. It was found that ? increased linearly as a function of the transverse field. These studies are an essential prerequisite for the coherent manipulation of a single nuclear spin in TbPc2., Comment: 7 pages, 6 figures, to appear in PRB

Magnetic molecules possess a high potential as building blocks for the design of spintronic devices. Moreover, the use of molecular materials opens the way for the controlled use of bottom-up, e.g. supramolecular, processing techniques combining massively parallel self-fabrication with conventional top-down nanostructuring techniques. The development of solid state spintronic devices based on the giant magnetoresistance (GMR), tunnel magnetoresistance (TMR), and spin valve effects has revolutionized the field of magnetic memory applications. Recently, organic semiconductors were inserted into nanometer sized tunnel junctions allowing enhancement of spin reversal, giant magneto-resistance behaviour was observed in single non-magnetic molecules coupled to magnetic electrodes, and the use of the quantum tunnelling properties of single-molecule magnets (SMMs) in hybrid devices was proposed. Herein, we present an original device in which a non-magnetic molecular quantum dot, made of a single-wall carbon nanotube (SWCNT) contacted with non-magnetic electrodes, is laterally coupled via supramolecular interactions to a TbPc2-SMM (Pc = phthalocyanine), which provides a localized magnetic moment. The conductance through the SWCNT is modulated by sweeping the magnetic field, exhibiting magnetoresistance ratios up to 300% between fully polarized and non-polarized SMMs below 1 K. We thus demonstrate the functionality of a supramolecular spin valve without magnetic leads. Our results open up prospects of circuit-integration and implementation of new device capabilities., Comment: 12 pages, 3 figures