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Publication# An on/off Berry phase switch in circular graphene resonators

Résumé

The phase of a quantum state may not return to its original value after the system's parameters cycle around a closed path; instead, the wave function may acquire a measurable phase difference called the Berry phase. Berry phases typically have been accessed through interference experiments. Here, we demonstrate an unusual Berry phase-induced spectroscopic feature: a sudden and large increase in the energy of angular-momentum states in circular graphene p-n junction resonators when a relatively small critical magnetic field is reached. This behavior results from turning on a p Berry phase associated with the topological properties of Dirac fermions in graphene. The Berry phase can be switched on and off with small magnetic field changes on the order of 10 millitesla, potentially enabling a variety of optoelectronic graphene device applications.

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Graphène

Le graphène est un matériau bidimensionnel cristallin, forme allotropique du carbone dont l'empilement constitue le graphite.
Cette définition théorique est donnée par le physicien en 1947. Par la

État quantique

L'état d'un système physique décrit tous les aspects de ce système, dans le but de prévoir les résultats des expériences que l'on peut réaliser. Le fait que la mécanique quantique soit non déterminist

Fonction d'onde

thumb|300px|right|Illustration de la notion de fonction d'onde dans le cas d'un oscillateur harmonique. Le comportement en mécanique classique est représenté sur les images A et B et celui en mécaniqu

The interplay of superconductivity and magnetism is investigated for systems with dimensions ranging from the mesoscopic to the atomic scale by scanning tunneling microscopy (STM) at millikelvin temperatures and by numerical calculations. Based on geometrically confined superconductors in magnetic fields, a novel STM approach is introduced to quantitatively probe the spin polarization of tunneling electrons. In the first part of this work, the effects of magnetic fields and geometrical confinement are probed for superconducting vanadium STM tips. Due to the unique confinement ranging from the atomic to the mesoscopic scale, the superconducting properties of the STM tips vary considerably from their bulk counterparts. To analyze the experimentally determined magnetic field dependence of several V tips, the superconductivity is numerically calculated for modeled cone geometries with various opening angles. The numerical approach based on a one-dimensional Usadel equation leads to a direct correlation between the opening angle ¿ and the order of the superconducting phase transition. First order phase transitions occur when the opening angle is smaller than a critical value (¿ < ¿c), whilst larger opening angles (¿ > ¿c) result in second order phase transitions. The comparison of experimental findings and numerical results reveals the existence of first and second order quantum phase transitions in the V STM tips. In addition, the numerical calculations also explain experimentally observed broadening effects of the superconducting spectra by the specific tip geometry. In the second part, the superconducting V tips are employed in a novel approach to quantitatively probe the spin polarization of tunneling electrons on the nanoscale. For this purpose, the Meservey-Tedrow-Fulde technique is transferred to STM in order to combine their virtues, such as the quantitative probing capability of the spin polarization, the precise control at the atomic scale and the well-defined vacuum tunnel barrier. To demonstrate the capabilities of the new technique, the local spin structure is resolved for a magnetic Co nanoisland, where spin polarizations ranging from -56% up to 65% were found, depending on the local position. Furthermore, the spin polarization P strongly varies with the tip-to-sample distance z (dP/dz ¿ 10%/Å), which is described by the different decays of the spin-up and spin-down wave functions into the vacuum tunnel barrier. The final part describes the local interaction between isolated magnetic moments and the superconducting ground state. Copper phthalocyanine molecules on the superconducting V(100) surface induce bound states within the superconducting gap due to the magnetic coupling and the Coulomb potentials. Spatially resolved measurements reveal the non-isotropic structure of the spectral weights that is explained by the adsorption site on the 5x1 reconstruction of the V(100) surface. The quasi-particle excitations are not only observed on the magnetic molecule but also occur in its close vicinity. With increasing distance from the molecular structure, the intensities of the bound states decay within the distance x ¿ ±30Å and show periodic oscillations at the same time. Comparing the experimental findings to a one-dimensional model suggests the presence of a complicated scattering potential, which can be simplified by assuming two point scatterers within the molecular structure.

Two objects are entangled when their quantum mechanical wavefunctions cannot be written in a separable product form. Entangling dissimilar quantum objects, or hybridization, has been suggested as a promising route to efficient quantum information processors, but mostly realized on a limited scale. Hybrid nuclear-electronic many-body systems remain a largely unexplored challenge to both experiments and theories. The prototypical transverse-field Ising ferromagnet LiHoF4 is an ideal platform to address this issue. The Ising model is considered as an archetype both for the investigation of quantum criticality and for the evaluation of quantum simulators. The hyperfine coupling strength of a Ho ion is exceptionally large, promoting a strong hybridization or entanglement between the nuclear and electronic moments. The magnetic coupling between the Ho ions that leads to ferromagnetic ordering is predominantly through long-range dipole interactions, while nearest-neighbor exchange interaction is negligibly weak. Applying a transverse field induces a zero temperature quantum phase transition driven by quantum fluctuations. Altogether LiHoF4 represents a unique nuclear-electronic quantum magnet, whose wavefunctions can be readily obtained by diagonalizing the Hamiltonian using the mean-field approximation. In this thesis we develop an experimental setup to probe the entangled nuclear-electronic states in a model transverse-field Ising system LiHoF4. Using magnetic resonance the field and temperature evolution of the nuclear-electronic states are successfully traced across the whole phase diagram. We develop a theoretical framework based on mean-field calculations which provides close agreement with the experimental observations. Having established experimentally that the mean-field wavefunctions are an excellent approximation of the actual wavefunction, we used them to calculate the ground-state entanglement entropy between the electronic and nuclear magnetic moments. We find that the entanglement entropy between the nuclear and electronic moments exhibits a peak at the quantum phase transition. This suggests that the electronic entanglement is encoded onto each nuclear-electronic state. Our results pave the way for new theoretical and experimental investigations of quantum entanglement.