We introduce a new method for analysing the Bose-Hubbard model for an array of bosons with nearest neighbor interactions. It is based on a number-theoretic implementation of the creation and annihilation operators that constitute the model. One of th
e advantages of this approach is that it facilitates computation with arbitrary accuracy, enabling nearly perfect numerical experimentation. In particular, we provide a rigorous computer assisted proof of quantum phase transitions in finite systems of this type. Furthermore, we investigate properties of the infinite array via harmonic analysis on the multiplicative group of positive rationals. This furnishes an isomorphism that recasts the underlying Fock space as an infinite tensor product of Hecke spaces, i.e., spaces of square-integrable periodic functions that are a superposition of non-negative frequency harmonics. Under this isomorphism, the number-theoretic creation and annihilation operators are mapped into the Kastrup model of the harmonic oscillator on the circle. It also enables us to highlight a kinship of the model at hand with an array of spin moments with a local anisotropy field. This identifies an interesting physical system that can be mapped into the model at hand.
Chiral induced spin selectivity is a phenomenon that has been attributed to chirality, spin-orbit interactions, and non-equilibrium conditions, while the role of electron exchange and correlations have been investigated only marginally until very rec
ently. However, as recent experiments show that chiral molecules acquire a finite spin-polarization merely by being in contact with a metallic surface, these results suggest that electron correlations play a more crucial role for the emergence of the phenomenon than previously thought. Here, it is demonstrated that molecular vibrations give rise to molecular charge redistribution and accompanied spin-polarization when coupling a chiral molecule to a non-magnetic metal. It is, moreover, shown that enantiomer separation, due to spin-polarization intimately related to the chirality, can be understood in terms of the proposed model.
Electron exchange and correlations emerging from the coupling between ionic vibrations and electrons are addressed. Spin-dependent electron-phonon coupling originates from the spin-orbit interaction, and it is shown that such electron-phonon coupling
introduces exchange splitting between the spin channels in the structure. By application of these results to a model for a chiral molecular structure mounted between metallic leads, the chirality induced spin selectivity is found to become several tens of percents using experimentally feasible parameters.
Chirality induced spin selectivity, discovered about two decades ago in helical molecules, is a non-equilibrium effect that emerges from the interplay between geometrical helicity and spin-orbit interactions. Several model Hamiltonians building on th
is interplay have been proposed and while these can yield spin-polarized transport properties that agrees with experimental observations, they simultaneously depend on unrealistic values of the spin-orbit interaction parameters. It is likely, however, that a common deficit originates from the fact that all these models are uncorrelated, or, single-electron theories. Therefore, chirality induced spin selectivity is, here, addressed using a many-body approach, which allows for non-equilibrium conditions and a systematic treatment of the correlated state. The intrinsic molecular spin-polarization increases by two orders of magnitudes, or more, compared to the corresponding result in the uncorrelated model. In addition, the electronic structure responds to varying external magnetic conditions which, therefore, enables comparisons of the currents provided for different spin-polarizations in one of the (or both) leads between which the molecule is mounted. Using experimentally feasible parameters and room temperature, the obtained normalized difference between such currents may be as large as 5 - 10 % for short molecular chains, clearly suggesting the vital importance of including electron correlations when searching for explanations of the phenomenon.
We address the electronically induced anisotropy field acting on a spin moment comprised in a vibrating magnetic molecule located in the junction between ferromagnetic metals. Under weak coupling between the electrons and molecular vibrations, the na
ture of the anisotropy can be changed from favoring a high spin (easy axis) magnetic moment to a low spin (easy plane) by applying a temperature difference or a voltage bias across the junction. For unequal spin-polarizations in the ferromagnetic metals it is shown that the character of the anisotropy is essentially determined by the properties of the weaker ferromagnet. By increasing the temperature in this metal, or introducing a voltage bias, its influence can be suppressed such that the dominant contribution to the anisotropy is interchanged to the stronger ferromagnet. With increasing coupling strength between the molecular vibrations and the electrons, the nature of the anisotropy is locked into favoring easy plane magnetism.
We address the shot noise in the tunneling current through a localized spin, pertaining to recent experiments on magnetic adatoms and single molecular magnets. We show that both uncorrelated and spin-correlated scattering processes contribute vitally
to the noise spectrum. The spin-correlated scattering processes provide an additional contribution to the Landauer-Buttiker shot noise expression, accounting for correlations between the tunneling electrons and the localized spin moment. By calculating the Fano factor, we show that both super- and sub-Poissonian shot noise can be described within our approach. Our theory provides transparent insights to noise spectroscopy, consistent with recent experiments using local probing techniques on magnetic atoms.
In this theoretical study, we explore the manner in which the quantum correction due to weak localization is suppressed in weakly-disordered graphene, when it is subjected to the application of a non-zero voltage. Using a nonequilibrium Green functio
n approach, we address the scattering generated by the disorder up to the level of the maximally crossed diagrams, hereby capturing the interference among different, impurity-defined, Feynman paths. Our calculations of the charge current, and of the resulting differential conductance, reveal the logarithmic divergence typical of weak localization in linear transport. The main finding of our work is that the applied voltage suppresses the weak localization contribution in graphene, by introducing a dephasing time that decreases inversely with increasing voltage.
We consider charge and thermal transport properties of magnetically active paramagnetic molecular dimer. Generic properties for both transport quantities are reduced currents in the ferro- and anti-ferromagnetic regimes compared to the paramagnetic a
nd efficient current blockade in the anti-ferromagnetic regime. In contrast, while the charge current is about an order of magnitude larger in the ferromagnetic regime, compared to the anti-ferromagnetic, the thermal current is efficiently blockaded there as well. This disparate behavior of the thermal current is attributed to current resonances in the ferromagnetic regime which counteract the thermal flow. The temperature difference strongly reduces the exchange interaction and tends to destroy the magnetic control of the transport properties. The weakened exchange interaction opens up a possibility to tune the system into thermal rectification, for both the charge and thermal currents.
A coupled atomistic spin and lattice dynamics approach is developed which merges the dynamics of these two degrees of freedom into a single set of coupled equations of motion. The underlying microscopic model comprises local exchange interactions bet
ween the electron spin and magnetic moment and the local couplings between the electronic charge and lattice displacements. An effective action for the spin and lattice variables is constructed in which the interactions among the spin and lattice components are determined by the underlying electronic structure. In this way, expressions are obtained for the electronically mediated couplings between the spin and lattice degrees of freedom, besides the well known inter-atomic force constants and spin-spin interactions. These former susceptibilities provide an atomistic ab initio description for the coupled spin and lattice dynamics. It is important to notice that this theory is strictly bilinear in the spin and lattice variables and provides a minimal model for the coupled dynamics of these subsystems and that the two subsystems are treated on the same footing. Questions concerning time-reversal and inversion symmetry are rigorously addressed and it is shown how these aspects are absorbed in the tensor structure of the interaction fields. By means of these results regarding the spin-lattice coupling, simple explanations of ionic dimerization in double anti-ferromagnetic materials, as well as, charge density waves induced by a non-uniform spin structure are given. In the final parts, a set of coupled equations of motion for the combined spin and lattice dynamics are constructed, which subsequently can be reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations for spin dynamics and damped driven mechanical oscillator for the ...
Through a combination of experiment and theory we establish the possibility of achieving strong tuning of Fano resonances (FRs), by allowing their usual two-path geometry to interfere with an additional, intruder, continuum. As the coupling strength
to this intruder is varied, we predict strong modulations of the resonance line shape that, in principle at least, may exceed the amplitude of the original FR itself. For a proof-of-concept demonstration of this phenomenon, we construct a nanoscale interferometer from nonlocally coupled quantum point contacts and utilize the unique features of their density of states to realize the intruder. External control of the intruder coupling is enabled by means of an applied magnetic field, in the presence of which we demonstrate the predicted distortions of the FR. This general scheme for resonant control should be broadly applicable to a variety of wave-based systems, opening up the possibility of new applications in areas such as chemical and biological sensing and secure communications.
