Molecular spin qudits for quantum algorithms.

Presently, one of the most ambitious technological goals is the development of devices working under the laws of quantum mechanics. One prominent target is the quantum computer, which would allow the processing of information at quantum level for purposes not achievable with even the most powerful computer resources. The large-scale implementation of quantum information would be a game changer for current technology, because it would allow unprecedented parallelised computation and secure encryption based on the principles of quantum superposition and entanglement. Currently, there are several physical platforms racing to achieve the level of performance required for the quantum hardware to step into the realm of practical quantum information applications. Several materials have been proposed to fulfil this task, ranging from quantum dots, Bose-Einstein condensates, spin impurities, superconducting circuits, molecules, amongst others. Magnetic molecules are among the list of promising building blocks, due to (i) their intrinsic monodispersity, (ii) discrete energy levels (iii) the possibility of chemical quantum state engineering, and (iv) their multilevel characteristics that lead to Qudits, where the dimension of the Hilbert space is d > 2. Herein we review how a molecular nuclear spin qudit, (d = 4), known as TbPc2, gathers all the necessary requirements to perform as a molecular hardware platform with a first generation of molecular devices enabling even quantum algorithm operations.

Electronic read-out of a single nuclear spin using a molecular spin transistor.

Quantum control of individual spins in condensed-matter devices is an emerging field with a wide range of applications, from nanospintronics to quantum computing. The electron, possessing spin and orbital degrees of freedom, is conventionally used as the carrier of quantum information in proposed devices. However, electrons couple strongly to the environment, and so have very short relaxation and coherence times. It is therefore extremely difficult to achieve quantum coherence and stable entanglement of electron spins. Alternative concepts propose nuclear spins as the building blocks for quantum computing, because such spins are extremely well isolated from the environment and less prone to decoherence. However, weak coupling comes at a price: it remains challenging to address and manipulate individual nuclear spins. Here we show that the nuclear spin of an individual metal atom embedded in a single-molecule magnet can be read out electronically. The observed long lifetimes (tens of seconds) and relaxation characteristics of nuclear spin at the single-atom scale open the way to a completely new world of devices in which quantum logic may be implemented.

Quantum phase transition in a single-molecule quantum dot.

Quantum criticality is the intriguing possibility offered by the laws of quantum mechanics when the wave function of a many-particle physical system is forced to evolve continuously between two distinct, competing ground states. This phenomenon, often related to a zero-temperature magnetic phase transition, is believed to govern many of the fascinating properties of strongly correlated systems such as heavy-fermion compounds or high-temperature superconductors. In contrast to bulk materials with very complex electronic structures, artificial nanoscale devices could offer a new and simpler means of understanding quantum phase transitions. Here we demonstrate this possibility in a single-molecule quantum dot, where a gate voltage induces a crossing of two different types of electron spin state (singlet and triplet) at zero magnetic field. The quantum dot is operated in the Kondo regime, where the electron spin on the quantum dot is partially screened by metallic electrodes. This strong electronic coupling between the quantum dot and the metallic contacts provides the strong electron correlations necessary to observe quantum critical behaviour. The quantum magnetic phase transition between two different Kondo regimes is achieved by tuning gate voltages and is fundamentally different from previously observed Kondo transitions in semiconductor and nanotube quantum dots. Our work may offer new directions in terms of control and tunability for molecular spintronics.

An original electrochemical method for assembling multilayers of terpyridine-based metallic complexes on a gold surface.

A new method based on the electrochemical oxidation of thiols was used to easily generate multilayer assemblies of coordination complexes on a gold surface. For this purpose, two complexes bearing two anchoring groups for surface attachment have been prepared: [Ru(tpySH)(2)](2+) (1) and [Fe(tpySH)(2)](2+) (2) (tpySH = 4'-(2-(p-phenoxy)ethanethiol)-2,2':6',2″-terpyridine). Cyclic voltammetry of 1 in CH(3)CN exhibits two successive oxidation processes. The first is irreversible and attributed to the oxidation of the thiol substituents, whereas the second is reversible and corresponds to the 1 e(-) metal-centered oxidation. In the case of 2 both processes are superimposed. Monolayers of 1 or 2 have been formed on gold electrodes by spontaneous adsorption from micromolar solutions of the complexes in CH(3)CN. SAMs (self-assembled monolayers) exhibit redox behavior similar to the complexes in solution. The high surface coverage value obtained (Γ = 6 × 10(-10) and 4 × 10(-10) mol cm(-2) for 1 and 2, respectively) is consistent with a vertical orientation for the complexes; thus, one thiol is bound to the gold electrode, with the second unreacted thiol moiety exposed to the outer surface. Successive cyclic voltammetry induced a layer-by-layer nanostructural growth at the surface of the SAMs, and this is presumably due to the electrochemical formation of disulfide bonds, where the thiol moieties play a double role of both an anchoring group and an electroactive coupling agent. The conditions of the deposition are studied in detail. Modified electrodes containing both 1 and 2 alternatively can be easily prepared following this new approach. The film proved to be stable, displaying a similar current/voltage response for more than 10 repeating cycles in oxidation up to 0.97 V vs Ag/AgNO(3) (10(-2) M).

Increasing the Hilbert space dimension using a single coupled molecular spin.

Quantum technologies are expected to introduce revolutionary changes in information processing in the near future. Nowadays, one of the main challenges is to be able to handle a large number of quantum bits (qubits), while preserving their quantum properties. Beyond the usual two-level encoding capacity of qubits, multi-level quantum systems are a promising way to extend and increase the amount of information that can be stored in the same number of quantum objects. Recent work (Kues et al. 2017), has shown the possibility to use devices based on photonic integrated circuits to entangle two qudits (with "d" being the number of available states). In the race to develop a mature quantum technology with real-world applications, many possible platforms are being investigated, including those that use photons, trapped ions, superconducting and silicon circuits and molecular magnets. In this work, we present the electronic read-out of a coupled molecular multi-level quantum systems, carried by a single Tb2Pc3 molecular magnet. Owning two magnetic centres, this molecular magnet architecture permits a 16 dimensions Hilbert space, opening the possibility of performing more complex quantum algorithms.

Observation of the underscreened Kondo effect in a molecular transistor.

We present the first quantitative experimental evidence for the underscreened Kondo effect, an incomplete compensation of a quantized magnetic moment by conduction electrons, as originally proposed by Nozières and Blandin. The device consists of an even charge spin S=1 molecular quantum dot, obtained by electromigration of C60 molecules into gold nanogaps and operated in a dilution fridge. The persistence of logarithmic singularities in the low temperature conductance is demonstrated by a comparison to the fully screened configuration obtained in odd charge spin S=1/2 Coulomb diamonds. We also discover an extreme sensitivity of the underscreened Kondo resonance to the magnetic field that we confirm on the basis of numerical renormalization group calculations.

Field-Tunable 0-π-Transitions in SnTe Topological Crystalline Insulator SQUIDs.

The manifestation of spin-orbit interactions, long known to dramatically affect the band structure of heavy-element compounds, governs the physics in the surging class of topological matter. A particular example is found in the new family of topological crystalline insulators. In this systems transport occurs at the surfaces and spin-momentum locking yields crystal-symmetry protected spin-polarized transport. We investigated the current-phase relation of SnTe thin films connected to superconducting electrodes to form SQUID devices. Our results demonstrate that an assisting in-plane magnetic field component can induce 0-π-transitions. We attribute these findings to giant g-factors and large spin-orbit coupling of SnTe topological crystalline insulator, which provides a new platform for investigation of the interplay between spin-orbit physics and topological transport.

Electrical Read-Out of a Single Spin Using an Exchange-Coupled Quantum Dot.

We present an original 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 nondestructive single spin detection. With conductance variations up to 4% and read-out fidelities greater than 99.5%, this method represents an alternative to systems for which spin-to-charge conversion cannot be implemented. Using a semiclassical approach, we present an asymmetric exchange coupling model in good agreement with our experimental results.

Electroburning of few-layer graphene flakes, epitaxial graphene, and turbostratic graphene discs in air and under vacuum.

Graphene-based electrodes are very promising for molecular electronics and spintronics. Here we report a systematic characterization of the electroburning (EB) process, leading to the formation of nanometer-spaced gaps, on different types of few-layer graphene (namely mechanically exfoliated graphene on SiO2, graphene epitaxially grown on the C-face of SiC and turbostratic graphene discs deposited on SiO2) under air and vacuum conditions. The EB process is found to depend on both the graphene type and on the ambient conditions. For the mechanically exfoliated graphene, performing EB under vacuum leads to a higher yield of nanometer-gap formation than working in air. Conversely, for graphene on SiC the EB process is not successful under vacuum. Finally, the EB is possible with turbostratic graphene discs only after the creation of a constriction in the sample using lithographic patterning.

Electrically driven nuclear spin resonance in single-molecule magnets.

Recent advances in addressing isolated nuclear spins have opened up a path toward using nuclear-spin-based quantum bits. Local magnetic fields are normally used to coherently manipulate the state of the nuclear spin; however, electrical manipulation would allow for fast switching and spatially confined spin control. Here, we propose and demonstrate coherent single nuclear spin manipulation using electric fields only. Because there is no direct coupling between the spin and the electric field, we make use of the hyperfine Stark effect as a magnetic field transducer at the atomic level. This quantum-mechanical process is present in all nuclear spin systems, such as phosphorus or bismuth atoms in silicon, and offers a general route toward the electrical control of nuclear-spin-based devices.

Universal transport signatures in two-electron molecular quantum dots: gate-tunable Hund's rule, underscreened Kondo effect and quantum phase transitions.

We review here some universal aspects of the physics of two-electron molecular transistors in the absence of strong spin-orbit effects. Several recent quantum dot experiments have shown that an electrostatic backgate could be used to control the energy dispersion of magnetic levels. We discuss how the generally asymmetric coupling of the metallic contacts to two different molecular orbitals can indeed lead to a gate-tunable Hund's rule in the presence of singlet and triplet states in the quantum dot. For gate voltages such that the singlet constitutes the (non-magnetic) ground state, one generally observes a suppression of low voltage transport, which can yet be restored in the form of enhanced cotunneling features at finite bias. More interestingly, when the gate voltage is controlled to obtain the triplet configuration, spin S = 1 Kondo anomalies appear at zero bias, with non-Fermi liquid features related to the underscreening of a spin larger than 1/2. Finally, the small bare singlet-triplet splitting in our device allows fine-tuning with the gate between these two magnetic configurations, leading to an unscreening quantum phase transition. This transition occurs between the non-magnetic singlet phase, where a two-stage Kondo effect occurs, and the triplet phase, where the partially compensated (underscreened) moment is akin to a magnetically 'ordered' state. These observations are put theoretically into a consistent global picture by using new numerical renormalization group simulations, tailored to capture sharp finite-voltage cotunneling features within the Coulomb diamonds, together with complementary out-of-equilibrium diagrammatic calculations on the two-orbital Anderson model. This work should shed further light on the complicated puzzle still raised by multi-orbital extensions of the classic Kondo problem.