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We present a general analytical formula and an ab initio study of quantum interference in multi-branch molecules. Ab initio calculations are used to investigate quantum interference in a benzene-1,2-dithiolate (BDT) molecule sandwiched between gold electrodes and through oligoynes of various lengths. We show that when a point charge is located in the plane of a BDT molecule and its position varied, the electrical conductance exhibits a clear interference effect, whereas when the charge approaches a BDT molecule along a line normal to the plane of the molecule and passing through the centre of the phenyl ring, interference effects are negligible. In the case of olygoynes, quantum interference leads to the appearance of a critical energy $E_c$, at which the electron transmission coefficient $T(E)$ of chains with even or odd numbers of atoms is independent of length. To illustrate the underlying physics, we derive a general analytical formula for electron transport through multi-branch structures and demonstrate the versatility of the formula by comparing it with the above ab-initio simulations. We also employ the analytical formula to investigate the current inside the molecule and demonstrate that large counter currents can occur within a ring-like molecule such as BDT, when the point charge is located in the plane of the molecule. The formula can be used to describe quantum interference and Fano resonances in structures with branches containing arbitrary elastic scattering regions connected to nodal sites.
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Magnetization measurements of a molecular clusters Mn12 with a spin ground state of S = 10 show resonance tunneling at avoided energy level crossings. The observed oscillations of the tunnel probability as a function of the magnetic field applied along the hard anisotropy axis are due to topological quantum phase interference of two tunnel paths of opposite windings. Mn12 is therefore the second molecular clusters presenting quantum phase interference.
A Mn4 single-molecule magnet displays asymmetric Berry-phase interference patterns in the transverse-field (HT) dependence of the magnetization tunneling probability when a longitudinal field (HL) is present, contrary to symmetric patterns observed for HL=0. Reversal of HL results in a reflection of the transverse-field asymmetry about HT=0, as expected on the basis of the time-reversal invariance of the spin-orbit Hamiltonian which is responsible for the tunneling oscillations. A fascinating motion of Berry-phase minima within the transverse-field magnitude-direction phase space results from a competition between noncollinear magnetoanisotropy tensors at the two distinct Mn sites.
Single-molecule junctions are found to show anomalous spikes in dI/dV spectra. The position in energy of the spikes are related to local vibration mode energies. A model of vibrationally induced two-level systems reproduces the data very well. This mechanism is expected to be quite general for single-molecule junctions. It acts as an intrinsic amplification mechanism for local vibration mode features and may be exploited as a new spectroscopic tool.
The influence of multiple vibrational modes on current fluctuations in electron transport through single-molecule junctions is investigated. Our analysis is based on a generic model of a molecular junction, which comprises a single electronic state on the molecular bridge coupled to multiple vibrational modes and fermionic leads, and employs a master equation approach. The results reveal that in molecular junctions with multiple vibrational modes already weak to moderate electronic-vibrational coupling may result in high noise levels, especially at the onset of resonant transport, in accordance with experimental findings of Secker et al..[1] The underlying mechanisms are analyzed in some detail. [1] D. Secker et al., Phys. Rev. Lett. 106, 136807 (2011).
Berry phase effects in spin systems lead to the suppression of tunneling effects when different tunneling paths interfere destructively. Such effects have been seen in several single-molecule magnets (SMMs) through measurements of magnetization dynamics, where the experimental signal may arise from the contributions of numerous energy levels. Here we present experimental measurements of Berry phase interference effects that are determined through electron-spin resonance on a four-fold symmetric SMM. Specifically, we measure transitions between tunnel-split excited states in the Ni$_4$ SMM in the presence of a transverse field in the hard plane of the crystalline sample. By using a home-built rotation apparatus, the direction of the sample can be changed textit{in situ} so that that the field direction can be swept through the entire hard plane of the sample. When the field is in certain directions in the plane, we observe a splitting of the transition, a hallmark of Berry phase interference. The experimental results are well reproduced by theoretical predictions, and fitting of the data provides information about the effects of dipolar interactions and sample misalignment.
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