Study of charge, spin, and structural orderings in quantum materials using nuclei and muons as local probes

Quantum Materials are many body systems displaying emergent phenomena caused by quantum collective behaviour, such as superconductivity, charge density wave, fractional hall effect, and exotic magnetism. Among quantum materials, two families have recently attracted attention: kagome metals and Kitaev materials. Kagome metals have a unique crystal structure made up of triangular lattice layers that are used to form the kagome layer. Due to superconductivity, magnetism, and charge ordering states such as the Charge Density Wave (CDW), unexpected physical phenomena such as the massive Anomalous Hall Effect (AHE) and possible Majorana fermions develop in these materials. Kitaev materials are a type of quantum material with a unique spin model named after Alexei Kitaev. They include fractional fluctuations of Majorana fermions and non-topological abelian anyons, both of which might be used in quantum computing. Furthermore, they provide a realistic framework for the development of quantum spin liquid (QSL), in which quantum fluctuations produce long-range entanglements between electronic states despite the lack of classical magnetic ordering. In my research, I performed several nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), and muon spin spectroscopy (µSR) experiments to explain and unravel novel phases of matter within these unusual families of materials. NMR has been found to be an excellent tool for studying these materials’ local electronic structures and magnetic properties. I could use NMR to determine, for the first time, the structure of a novel kagome superconductor, RbV3Sb5, below the CDW transition, and to highlight the role of chemical doping in the CDW phase of AV3Sb5 superconductors. µSR has been used to investigate the effect of doping on kagome material samples in order to study the presence and behaviour of an anomalous phase developing at low temperatures and possibly related to time-reversal symmetry breaking.

Shallow and deep deformation in northern Apennines region using seismological data

For its particular position and the complex geological history, the Northern Apennines has been considered as a natural laboratory to apply several kinds of investigations. By the way, it is complicated to joint all the knowledge about the Northern Apennines in a unique picture that explains the structural and geological emplacement that produced it. The main goal of this thesis is to put together all information on the deformation - in the crust and at depth - of this region and to describe a geodynamical model that takes account of it. To do so, we have analyzed the pattern of deformation in the crust and in the mantle. In both cases the deformation has been studied using always information recovered from earthquakes, although using different techniques. In particular the shallower deformation has been studied using seismic moment tensors information. For our purpose we used the methods described in Arvidsson and Ekstrom (1998) that allowing the use in the inversion of surface waves [and not only of the body waves as the Centroid Moment Tensor (Dziewonski et al., 1981) one] allow to determine seismic source parameters for earthquakes with magnitude as small as 4.0. We applied this tool in the Northern Apennines and through this activity we have built up the Italian CMT dataset (Pondrelli et al., 2006) and the pattern of seismic deformation using the Kostrov (1974) method on a regular grid of 0.25 degree cells. We obtained a map of lateral variations of the pattern of seismic deformation on different layers of depth, taking into account the fact that shallow earthquakes (within 15 km of depth) in the region occur everywhere while most of events with a deeper hypocenter (15-40 km) occur only in the outer part of the belt, on the Adriatic side. For the analysis of the deep deformation, i.e. that occurred in the mantle, we used the anisotropy information characterizing the structure below the Northern Apennines. The anisotropy is an earth properties that in the crust is due to the presence of aligned fluid filled cracks or alternating isotropic layers with different elastic properties while in the mantle the most important cause of seismic anisotropy is the lattice preferred orientation (LPO) of the mantle minerals as the olivine. This last is a highly anisotropic mineral and tends to align its fast crystallographic axes (a-axis) parallel to the astenospheric flow as a response to finite strain induced by geodynamic processes. The seismic anisotropy pattern of a region is measured utilizing the shear wave splitting phenomenon (that is the seismological analogue to optical birefringence). Here, to do so, we apply on teleseismic earthquakes recorded on stations located in the study region, the Sileny and Plomerova (1996) approach. The results are analyzed on the basis of their lateral and vertical variations to better define the earth structure beneath Northern Apennines. We find different anisotropic domains, a Tuscany and an Adria one, with a pattern of seismic anisotropy which laterally varies in a similar way respect to the seismic deformation. Moreover, beneath the Adriatic region the distribution of the splitting parameters is so complex to request an appropriate analysis. Therefore we applied on our data the code of Menke and Levin (2003) which allows to look for different models of structures with multilayer anisotropy. We obtained that the structure beneath the Po Plain is probably even more complicated than expected. On the basis of the results obtained for this thesis, added with those from previous works, we suggest that slab roll-back, which created the Apennines and opened the Tyrrhenian Sea, evolved in the north boundary of Northern Apennines in a different way from its southern part. In particular, the trench retreat developed primarily south of our study region, with an eastward roll-back. In the northern portion of the orogen, after a first stage during which the retreat was perpendicular to the trench, it became oblique with respect to the structure.

Modeling and simulations of some anisotropic soft-matter systems: from biaxial to chiral materials

We have modeled various soft-matter systems with molecular dynamics (MD) simulations. The first topic concerns liquid crystal (LC) biaxial nematic (Nb) phases, that can be possibly used in fast displays. We have investigated the phase organization of biaxial Gay-Berne (GB) mesogens, considering the effects of the orientation, strength and position of a molecular dipole. We have observed that for systems with a central dipole, nematic biaxial phases disappear when increasing dipole strength, while for systems characterized by an offset dipole, the Nb phase is stabilized at very low temperatures. In a second project, in view of their increasing importance as nanomaterials in LC phases, we are developing a DNA coarse-grained (CG) model, in which sugar and phosphate groups are represented with Lennard-Jones spheres, while bases with GB ellipsoids. We have obtained shape, position and orientation parameters for each bead, to best reproduce the atomistic structure of a B-DNA helix. Starting from atomistic simulations results, we have completed a first parametrization of the force field terms, accounting for bonded (bonds, angles and dihedrals) and non-bonded interactions (H-bond and stacking). We are currently validating the model, by investigating stability and melting temperature of various sequences. Finally, in a third project, we aim to explain the mechanism of enantiomeric discrimination due to the presence of a chiral helix of poly(gamma-benzyl L-glutamate) (PBLG), in solution of dimethylformamide (DMF), interacting with chiral or pro-chiral molecules (in our case heptyl butyrate, HEP), after tuning properly an atomistic force field (AMBER). We have observed that DMF and HEP molecules solvate uniformly the PBLG helix, but the pro-chiral solute is on average found closer to the helix with respect to the DMF. The solvent presents a faster isotropic diffusion, twice as HEP, also indicating a stronger interaction of the solute with the helix.

Fluid-structure interaction by a coupled lattice Boltzmann-finite element approach

In this thesis, a strategy to model the behavior of fluids and their interaction with deformable bodies is proposed. The fluid domain is modeled by using the lattice Boltzmann method, thus analyzing the fluid dynamics by a mesoscopic point of view. It has been proved that the solution provided by this method is equivalent to solve the Navier-Stokes equations for an incompressible flow with a second-order accuracy. Slender elastic structures idealized through beam finite elements are used. Large displacements are accounted for by using the corotational formulation. Structural dynamics is computed by using the Time Discontinuous Galerkin method. Therefore, two different solution procedures are used, one for the fluid domain and the other for the structural part, respectively. These two solvers need to communicate and to transfer each other several information, i.e. stresses, velocities, displacements. In order to guarantee a continuous, effective, and mutual exchange of information, a coupling strategy, consisting of three different algorithms, has been developed and numerically tested. In particular, the effectiveness of the three algorithms is shown in terms of interface energy artificially produced by the approximate fulfilling of compatibility and equilibrium conditions at the fluid-structure interface. The proposed coupled approach is used in order to solve different fluid-structure interaction problems, i.e. cantilever beams immersed in a viscous fluid, the impact of the hull of the ship on the marine free-surface, blood flow in a deformable vessels, and even flapping wings simulating the take-off of a butterfly. The good results achieved in each application highlight the effectiveness of the proposed methodology and of the C++ developed software to successfully approach several two-dimensional fluid-structure interaction problems.

Permutation classes, sorting algorithms, and lattice paths

A permutation is said to avoid a pattern if it does not contain any subsequence which is order-isomorphic to it. Donald Knuth, in the first volume of his celebrated book "The art of Computer Programming", observed that the permutations that can be computed (or, equivalently, sorted) by some particular data structures can be characterized in terms of pattern avoidance. In more recent years, the topic was reopened several times, while often in terms of sortable permutations rather than computable ones. The idea to sort permutations by using one of Knuth’s devices suggests to look for a deterministic procedure that decides, in linear time, if there exists a sequence of operations which is able to convert a given permutation into the identical one. In this thesis we show that, for the stack and the restricted deques, there exists an unique way to implement such a procedure. Moreover, we use these sorting procedures to create new sorting algorithms, and we prove some unexpected commutation properties between these procedures and the base step of bubblesort. We also show that the permutations that can be sorted by a combination of the base steps of bubblesort and its dual can be expressed, once again, in terms of pattern avoidance. In the final chapter we give an alternative proof of some enumerative results, in particular for the classes of permutations that can be sorted by the two restricted deques. It is well-known that the permutations that can be sorted through a restricted deque are counted by the Schrӧder numbers. In the thesis, we show how the deterministic sorting procedures yield a bijection between sortable permutations and Schrӧder paths.

Finite group lattice gauge theories for quantum simulation

The present manuscript focuses on Lattice Gauge Theories based on finite groups. For the purpose of Quantum Simulation, the Hamiltonian approach is considered, while the finite group serves as a discretization scheme for the degrees of freedom of the gauge fields. Several aspects of these models are studied. First, we investigate dualities in Abelian models with a restricted geometry, using a systematic approach. This leads to a rich phase diagram dependent on the super-selection sectors. Second, we construct a family of lattice Hamiltonians for gauge theories with a finite group, either Abelian or non-Abelian. We show that is possible to express the electric term as a natural graph Laplacian, and that the physical Hilbert space can be explicitly built using spin network states. In both cases we perform numerical simulations in order to establish the correctness of the theoretical results and further investigate the models.