Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system, the superposition of single-particle quantum states is sufficient for Grover's algorithm. Recently, the latter has been successfully implemented using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses molecular magnets, which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theoretically that molecular magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 105, with access times as short as 10-10 seconds. We show that our proposal should be feasible using the molecular magnets Fe8 and Mn12.

By creating defects via oxygen plasma treatment, we demonstrate optical properties variation of single-layer MoS 2 . We found that, with increasing plasma exposure time, the photoluminescence (PL) evolves from very high intensity to complete quenching, accompanied by gradual reduction and broadening of MoS 2 Raman modes, indicative of distortion of the MoS 2 lattice after oxygen bombardment. X-ray photoelectron spectroscopy study shows the appearance of Mo 6+ peak, suggesting the creation of MoO 3 disordered regions in the MoS 2 flake. Finally, using band structure calculations, we demonstrate that the creation of MoO 3 disordered domains upon exposure to oxygen plasma leads to a direct to indirect bandgap transition in single-layer MoS 2 , which explains the observed PL quenching. KEYWORDS 2D materials, defect engineering, optical properties, bandgap tuning, molybdenum trioxide INTRODUCTIONThe ability to controllably tailor the properties of a material is a key factor in the development of many novel applications. In the case of bulk semiconductors, creating and manipulating defects constitutes an essential element in controlling the electrical, magnetic, and optical properties of the host material. 1 Although the role of defects is well understood in bulk semiconductors, it has received little attention in emerging two-dimensional (2D) layered semiconductors, preventing their full exploitation for tailored 2D nanoelectronic and photonic devices. Graphene and graphene oxide are examples of the impact that defects can have on 2D materials. Pristine graphene, which contains no intrinsic defect, is well known for its extraordinary high mobility, and is of great importance for high frequency device applications. 2, 3 However, its inherent lack of bandgap and low absorption of solar photons greatly limit its use in electronic and photonic devices. On the other hand, its solution processed counterparts, graphene oxide and reduced graphene oxide, have a large amount of defects, which lead to formation of a bandgap and open the way to many other applications in photodetectors, sensors, catalysis, and solar cell. [4][5][6][7][8] Recently, layered transition metal dichalcogenides (TMDs) have emerged as important materials for 2D device engineering. 9-11 Molybdenum disulfide (MoS 2 ), composed of weak van der Waals bonded S-Mo-S units, offers a large intrinsic bandgap that is strongly dependent on the number of layers, with an indirect bandgap (1.2 eV) in bulk MoS 2 transitioning to a direct

We present a comprehensive theory of the magnetization relaxation in a Mn12-acetate crystal in the high-temperature regime (T 1 K), which is based on phonon-assisted spin tunneling induced by quartic magnetic anisotropy and weak transverse magnetic fields. The overall relaxation rate as function of the longitudinal magnetic field is calculated and shown to agree well with experimental data including all resonance peaks measured so far. The Lorentzian shape of the resonances, which we obtain via a generalized master equation that includes spin tunneling, is also in good agreement with recent data. We derive a general formula for the tunnel splitting energy of these resonances. We show that fourth-order diagonal terms in the Hamiltonian lead to satellite peaks. A derivation of the effective linewidth of a resonance peak is given and shown to agree well with experimental data. In addition, previously unknown spin-phonon coupling constants are calculated explicitly. The values obtained for these constants and for the sound velocity are also in good agreement with recent data. We show that the spin relaxation in Mn12-acetate takes place via several transition paths of comparable weight. These transition paths are expressed in terms of intermediate relaxation times, which are calculated and which can be tested experimentally.

(received ; accepted ) PACS. 75.45.+j -Macroscopic quantum phenomena in magnetic systems. PACS. 75.50.Tt -Fine-particle systems. PACS. 75.30.Pd -Surface magnetism.Abstract. -We present a comprehensive theory of the magnetization relaxation in a Mn12-acetate crystal based on thermally assisted spin tunneling induced by quartic anisotropy and weak transverse magnetic fields. The overall relaxation rate as function of the magnetic field is calculated and shown to agree well with data including all resonance peaks. The Lorentzian shape of the resonances is also in good agreement with recent data. A generalized master equation including resonances is derived and solved exactly. It is shown that many transition paths with comparable weight exist that contribute to the relaxation process. Previously unknown spin-phonon coupling constants are calculated explicitly.The molecular magnet Mn 12 -acetate-a spin 10 system with large easy-axis anisotropyhas attracted much recent interest [1,2,3] since several experiments on the magnetization relaxation have revealed pronounced peaks [4,5,6] in response to a varying magnetic field H z applied along the easy axis of the crystal. These peaks occur at field values where spin states become pairwise degenerate. Following earlier suggestions [7,8], this phenomenon has been interpreted as a manifestation of resonant tunneling of the magnetization. However, in a critical comparison between model calculations [9,10,11,12,13,14] and experimental data [4,5,15] Friedman et al. [15] point out that a consistent explanation of the relaxation is still missing. One of the main challenges for theory is to explain the overall shape of the relaxation curve as well as the Lorentzian shape of the measured resonance peaks [15].In this work we shall present a model calculation of the magnetization relaxation which is based on thermally assisted tunneling. We find for the first time reasonably good agreement both with the overall relaxation rate (including the resonances) measured by Thomas et al.[5] (see fig.1) and with the Lorentzian shape of the first resonance peaks (see figs.2,3) measured by Friedman et al. [15] for four different temperatures.The model introduced below contains five independent parameters: three anisotropy constants A ≫ B ≫ B 4 , a misalignment angle θ (angle between field direction and easy axis), and sound velocity c. Previously unknown spin-phonon coupling constants are determined for the first time; we find that, quite remarkably, they can be expressed in terms of A only.Typeset using EURO-T E X

We show that it is possible to topologically induce or quench the Kondo resonance in the conductance of a single-molecule magnet (S > 1/2) strongly coupled to metallic leads. This can be achieved by applying a magnetic field perpendicular to the molecule easy axis and works for both full-and half-integer spin cases. The effect is caused by the Berry-phase interference between two quantum tunneling paths of the molecule's spin. We have calculated the renormalized Berry-phase oscillations of the Kondo peaks as a function of the transverse magnetic field as well as the conductance of the molecule by means of the poor man's scaling method. We propose to use a new variety of the single-molecule magnet Ni4 for the experimental observation of this phenomenon.PACS numbers: 72.10. Fk, 03.65.Vf, 75.45.+j, 75.50.Xx The quantum tunneling of the spin of single-molecule magnets (SMMs), such as Mn 12 [1,2] and Fe 8 [3,4], has attracted a great deal of interest. These molecules have a large total spin, strong uniaxial anisotropy, and interact very weakly when forming a crystal. They have already been proposed for high-density magnetic storage as well as quantum computing applications [5]. Yet, there is much to explore in their fundamental properties. For instance, recent measurements of the magnetization in bulk Fe 8 samples (see Ref.[6]) have observed oscillations in the tunnel splitting ∆E m,m ′ between states S z = m and m ′ as a function of a transverse magnetic field at temperatures between 0.05 K and = 0.7 K. Using a coherent spin-state path integral approach, it has been shown that this effect results from the interference between Berry phases carried by spin tunneling paths of opposite windings [7,8,9], a concept also applicable to transitions involving excited states of SMMs [10].A new approach to the study of SMMs opened up recently with the first observations of quantized electronic transport through an isolated Mn 12 molecule [11]. One expects a rich interplay between quantum tunneling, phase coherence, and electronic correlations in the transport properties of SMMs. It has been argued that the Kondo effect would only be observable for SMMs with half-integer spin [13] and therefore absent for SMMs such as Mn 12 , Fe 8 , and Ni 4 , where the spin is integer. Here we show that this prediction is only valid in the absence of an external magnetic field. Remarkably, even a moderate transverse magnetic field topologically quenches the two lowest levels of a full-integer spin SMM, making them degenerate. The same Berry-phase interference also affects transport for SMMs with half-integer spin: In that case, sweeping the magnetic field will lead not to one but a series of Kondo resonances.It is interesting to contrast the Kondo effect in a SMM with that observable in a lateral quantum dot with a single excess electron [14,15], in a single spin-1/2 atom [16], or in a single spin-1/2 molecule [17]. In those cases, at zero bias the Kondo effect is damped by an external a magnetic field because the degeneracy of the two spin ...