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Publication# Spin-orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3

Abstract

When viewed as an elementary particle, the electron has spin and charge. When binding to the atomic nucleus, it also acquires an angular momentum quantum number corresponding to the quantized atomic orbital it occupies. Even if electrons in solids form bands and delocalize from the nuclei, in Mott insulators they retain their three fundamental quantum numbers: spin, charge and orbital(1). The hallmark of one-dimensional physics is a breaking up of the elementary electron into its separate degrees of freedom(2). The separation of the electron into independent quasi-particles that carry either spin (spinons) or charge (holons) was first observed fifteen years ago(3). Here we report observation of the separation of the orbital degree of freedom (orbiton) using resonant inelastic X-ray scattering on the one-dimensional Mott insulator Sr2CuO3. We resolve an orbiton separating itself from spinons and propagating through the lattice as a distinct quasi-particle with a substantial dispersion in energy over momentum, of about 0.2 electronvolts, over nearly one Brillouin zone.

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When exposed to ionising radiation, living tissue can potentially suffer somatic and genetic damage - effects depending mainly on the radiation dose or energy absorbed, the type of radiation, and the type and mass of cells affected. It is well known that large doses of radiation lead to high damage of the cell nucleus and additional cell structures, which results in harmful somatic effects, and even rapid death of the individual exposed, while at low doses, cancer is by far the most important possible consequence. Understanding the mechanisms by which low doses of radiation cause cell damage is thus of great significance, not only from this viewpoint but also from that of practical medical physics applications such as radiotherapy treatment planning. Ionising radiation, such as electrons and positrons, begins to cause damage to the genome of a living cell by direct ionisation of atoms, thus depositing energy in the DNA double helix itself. The energy threshold for inducing strand-breaks by electrons, however, is around 7 eV, well below the energy levels required for direct ionization. The low-energy electrons that are set in motion around the tracks of energetic charged particles, for example, are responsible for a multitude of low-energy events (energy transfer of the order of 10 eV), which play a significant role in inducing molecular damage. Assessing the spatial configuration of energy transfer events and the deposited energy spectra, in regions of cellular and sub-cellular dimensions, can be aimed at via the application of appropriate Monte Carlo simulation tools. Such calculations depend primarily on an accurate knowledge of the production and subsequent slowing down of secondary electrons that form the basic structure of the charged particle track. In the above context, an important requirement is the provision of detailed quantitative information concerning the interaction cross sections of electrons over an energy range extending down to low energies, i.e. including the sub-excitation domain. In addition, developing fast particle-transport simulation algorithms to cover the entire slowing down process efficiently is a key aspect. Thus, the present doctoral research has, as global goal, the development and validation of new Monte Carlo calculational tools for electron and positron transport in biological materials, both at high and low energies. More specifically, it aims at providing (i) a comprehensive and accurate set of appropriate cross section data, and (ii) a fast and reliable algorithm for the simulation of charged particle transport. Thus, the first part of the thesis concerns the assessment, further development and validation of standard theoretical models for generating electron and positron cross sections to cover the main interactions of these particles with matter, in particular with the basic atomic components of biomaterials (water, bio-polymers, etc.). This has been done for bremsstrahlung, and both elastic and inelastic scattering, considering a wide range of atomic numbers and high up to thermal incident particle energies. In particular, the excitation cross sections for medium and low energies (down to 1 eV) have been derived by using a new formalism based on many-body field theory. The accuracy of the presently obtained data sets are assessed against other theoretical models, as also a large experimental database for each type of interaction, so that both a comprehensive coverage and adequate accuracies have been ensured for the cross section data sets generated. In the second part of the thesis, an extension of the Monte Carlo code system PENELOPE is first undertaken such that use can be made of elastic scattering differential cross sections which have been made available in numerical form. Thereby, new computational routines (incorporated into the new code PENELAST) prepare the cross sections, needed for a given energy and scattering angle, by applying a fast and accurate sampling technique to a provided data set. The present development will allow various electron and positron cross section data libraries, appropriately formatted, to be used with PENELOPE for benchmarking purposes. The development of a high calculation-speed (Class I) Monte Carlo tool for charged particle transport in biological materials has then been addressed. Thereby, a numerical algorithm for calculating the multiple-scattering angular distributions of high energy electrons and positrons is developed, based on the multiple-scattering theory of Lewis which accounts for energy losses within the continuous slowing down approximation. Partial-wave elastic scattering differential cross sections made available in numerical form, as indicated above, are used for the calculations, the inelastic scattering differential cross sections being obtained from the Sternheimer-Liljequist generalized oscillator strength model implemented in PENELOPE. The new code LEWIS has been used to calculate multiple-scattering angular distributions for given path lengths and can be readily adopted for Class I Monte Carlo simulations. The simultaneous generation of a large number of Legendre expansion coefficients is rendered possible, both rapidly and accurately. Results from LEWIS have been found to be in satisfactory agreement, both with detailed simulations carried out using PENELAST and with various sets of experimental data for high to medium energy electrons. In brief, the present research represents a significant improvement in the quality of Monte Carlo modelling of charged particle slowing down processes, thus contributing to understanding the. role of low-energy secondary electrons in radiation protection studies. It will also allow the further development of a complete Class I Monte Carlo code, which can then be reliably used in practical applications such as radiation treatment planning.

Symmetry and topology are fundamental properties of nature. Mathematics provides us with a general framework to understand these concepts. On one side, symmetry describes the invariance properties of an object for specific transformations. On the other side, topology classifies objects under continuous deformations. Two objects with different topologies cannot be deformed one into each other without creating or annihilating a singularity, sometimes referred to as 'node'.
These concepts gradually found applications in physics, namely in the description of the electronic properties of solids, which is the focus of this thesis. Symmetry and topology protect special nodes in the band structure of a crystal, where several states are degenerate in energy. Close to a node, the electron wave function obeys the Dirac or Weyl Hamiltonians, which were formally introduced to describe fermions in high-energy particle physics. These exotic fermions exhibit unique optical and transport properties, fully manifesting their quantum nature. Symmetry guides us in the search for which classes of materials may host topological nodes. Recently the attention of the scientific community has been attracted by crystals with non-symmorphic symmetries (screw axes and glide planes), as promising candidates for topological phases.
This thesis focuses on two families of non-symmorphic crystals, whose topological properties have been investigated by combining conventional angle-resolved photoelectron spectroscopy (ARPES) with state-of-the-art spin-resolved (spARPES) and time-resolved ARPES (trARPES). The experimental results are supported by calculations carried out in collaboration with theory groups.
ZrSiTe and ZrSiSe belong to the same class of non-trivial semimetals. They host Dirac electrons with large mobility. The results of my spARPES experiments clarify that spin-orbit interaction (SOI) not only removes the topological nodes in ZrSiTe, but also induces a 'hidden' spin polarization of its bulk electronic states, otherwise forbidden by the inversion symmetry of the lattice. Moreover, trARPES data provide evidence that the electron-electron interaction is only partially screened in the metallic state of ZrSiSe. As a consequence, the band velocity is enhanced, at odds with general expectations. More importantly, I show that this band renormalization can be controlled at the ultrafast time scale (namely fs scale, with 1 fs=10^{-15} s) via intense optical excitation, paving the way for engineering the band structure of Dirac semimetals.
Tellurium is a chiral semiconductor, with a small and direct band gap. The low-symmetry of its lattice and the simple chemical composition make it the ideal case to study the interplay between symmetry and topology. With ARPES I determine several Weyl nodes in its electronic structure. By means of spARPES, I demonstrate that in their surrounding the spin exhibits a hedgehog configuration. This observation is new and it highlights the connection between spin-dependent and topology-related properties in Te. Finally, I illustrate promising preliminary results based on trARPES that explore the appealing possibility of optically controlling the topology of the electronic structure of Te upon excitation of coherent phonons.

Though the high superconducting transition temperature (Tc) is the most interesting technological aspect of high temperature superconductors, the complex way in which the spin, lattice and electronic degrees of freedom interplay, makes them of the highest scientific interest. This is illustrated by their rich phase diagram characterized by a variety of exotic groundstate including; Mott insulating, pseudogap and high temperature superconductivity. One of the most serious barriers that has prevented our understanding of the mechanism of high temperature superconductors thus far is the lack of information on how low energy Landau quasiparticles result from an organization of real particles. This organization, often colloquially referred to as "dressing", is a fundamental general concept in physics that explains a variety of physical phenomena, such as exotic particle formations and phase transitions. The role of the lattice in this dressing is particularly controversial. Phonons are quanta of lattice vibration energy, and play a crucial role in conventional superconductivity. They provide an attractive interaction allowing the electrons to condensate in superconducting Cooper pairs. However, high temperature superconductivity in the cuprates in achieved through hole doping in an antiferromagnetic Mott insulator. In this case, the antiferromagnetic background, the strong coulomb repulsion and the anisotropic superconducting gap all suggest a marginal role of the phonons. In order to assess experimentally the exact role of the phonon, angle resolved photoemission spectroscopy (ARPES) is the weapon of choice given its unique ability to probe the electronic structure of solids in an energy- and momentum-resolved manner. In this thesis, I will use ARPES to characterize the various form of dressing of the quasiparticles in the high temperature superconductor from the Fermi level all the way to the valence band complex. I'll show that when combined with isotope substitution and inelastic x-rays scattering, the strong electron-phonon interaction can be probed in vivid details. This thesis presents three fundamental results. 1) Using the isotope effect, the important and unusual role of the phonon is demonstrated, as well as the strong interplay between the magnetic and phonic degrees of freedom. 2) Using inelastic scattering, the intriguing interplay between the Fermi surface and the bond stretching phonon is exposed. And 3) By exploring the ARPES data up to high energy, two new energy scales at high binding energy as well as the spectral waterfalls phenomenon are revealed. When all these new elements are considered together, they clearly show the need to consider simultaneously the spin, lattice, Fermi surface topology and electronic degrees of freedom. The spectacular progress in ARPES techniques over the past two decades was critical for these results, and I will present in this thesis our current effort in pushing the techniques even further. In particular I'll present my efforts in building a laser based ARPES setup with a hemispherical analyzer and a spin resolved time of flight analyzer.