This thesis proposes to provide a unified and systematic strategy to overcome the second timescale in protein folding, by exploiting qualities and drawbacks of the Bias Functional Method and proposing new theoretical approaches to overcome its limitations. The first half of the thesis is dedicated to the development of theoretical solutions to the dependence of the Bias Functional Method on an a-priori defined collective coordinate and microscopic non-reversibility of the dynamics. The second part of the manuscript is devoted to applications of the BF method on two different proteins: Canine milk lysozyme and alpha1-antitrypsin (A1AT).

The aim of this thesis is the study of electronic transport and mechanical properties of materials using computer simulations. In particular, we dealt with the charge transport in semiconduc- tor and metallic samples and with the peeling of a graphene layer from bulk graphite. The computational methods used to investigate the samples are (i) the Monte Carlo (MC) statis- tical method to simulate the transport of electrons in solids and (ii) the molecular dynamic (MD) approach to study the mechanical characteristics. A relevant part of this thesis is focused on carbon-based material, such as diamond and graphite, and the stable two-dimensional al- lotrope, graphene. The response of diamond and graphite to external electromagnetic pertur- bations, due to e.g. an impinging electron beam, was investigated by calculating reflection electron energy loss (REEL) spectra with MC simulations. By comparing the calculated spec- tra, obtained using different dielectric models, and in-house recorded experimental results, the most effective dielectric model better describing the plasma losses was identified. Moreover, an extension to these models to describe the anisotropic response of graphite to an external electromagnetic perturbation was developed and included in the MC approach. Owing to the central role of carbon for future electronic and technological applications, also its mechanical properties were investigated by means of MD simulations. In particular, the peeling process of a layer of graphene from a bulk of graphite was investigated. This process is exploitable for graphene production and for adhesive applications of this material. Moreover, the MC approach, employed for calculating REEL spectra, was tested and compared to other com- putational techniques based on the solution of the Ambartsumian-Chandrasekhar equations. This consistency test was realized by considering three metals (copper, silver and gold) as tar- get materials. Further studies were carried out on these materials by calculating secondary electron emission yields as a function of the electron beam energy. A remarkable good agreement with experimental data was obtained. The MC approach was also used to investigate the growth of particles in a W(CO)6 layer deposited on a SiO2 substrate upon irradiations by an electron beam in the context of the focused electron beam induced deposition technique. In particular, by applying the MC method, the radial distribution of emitted secondary electrons was calculated and then utilized as input data for further MD simulations. Moreover, the study of electron transport in an organic polymer (P3HT) was performed in order to understand how the molecular ordering affects the secondary electron emission. This aspect is of paramount importance to construct efficient organic electronic devices.

This thesis deals with the theoretical and computational modelling of materials by using a variety of ab-initio approaches to accurately predict the properties of realistic structures. A number of known and novel carbon-based materials are studied, exploiting the unique versatility of carbon to bind into several bonding configurations, with the aim of tailoring their electronic and mechanical characteristics. In this regard, the methods used to carry out electronic structure simulations depend on the system size: from the Dirac-Hartree-Fock approach to model molecular properties, to Density Functional Theory used for periodic solids, such as diamond and graphene-related materials composed by a few to some hundred of atoms, to Density Functional Tight Binding or plane Tight Binding to study nanowires or Beltrami pseudospheres, which are composed by some hundreds to a few millions atoms. The details of these methods are introduced in the chapters where they are used. The criterion used to present these concepts is to organize the chapters, with the exception of the last one, according to the increasing dimension of the systems. More in details, the first chapter uses the Dirac-Hartree-Fock approach to simulate atoms and molecules, such bromotrifluoromethane; the second chapter deals with periodic systems characterized by unit cells with a relatively small number of atoms, such as diamond and graphite; the third one discusses graphene and graphene-related materials with lower density; the fourth one present a new computational and experimental model of silicon carbide nanowires coated with silicon dioxide shell; the fifth chapter is focused on the study of sp2-hybridized carbon atoms, arranged on a Beltrami surface. The latter topic spans different research fields such as geometrical topology, physics and mechanical engineering. Finally, the last chapter is dedicated to an on going work which deals with the Non-Adiabatic Molecular Dynamics simulation of amorphous silica samples where we couple the nuclear dynamic of the system to the electronic structure.

In this thesis light matter interactions in the weak coupling regime are investigated in Si-based photonic devices. At first, spectroscopic investigation of energy transfer among Er ions and Si-nanoparticles for optical amplification has been reported. Successively, light propagation in dielectric resonator and waveguides has been addressed, in particular considering photon Local Density of States modifications and the possible Purcell enhancement effect.

The positron is the antiparticle of the electron. In general, for any particle there exists a corresponding antiparticle. The two are identical except for the charges, i.e. electric charge, leptonic number, muonic number, ..., which are equal in module but opposite sign. Examples are the electron and the positron, the first has negative electric charge, while the second has positive charge. Similarly for proton, which is positive charged, and the antiproton, which is negative charged. In the case of photons, they are their own antiparticle. When a particle and its antiparticle interact, they are destroyed in a process called annihilation which converts all their mass into energy following Einstein’s equation E=mc2. The inverse is also possible, a high-energy event creates a particle-antiparticle couple, this is called pair production. Needless to say, the products have total mass less than the one corresponding to initial energy from Einstein’s equation. For this reason, from an annihilation event, a cascade of particle-antiparticle pairs is generated, the mass of the created particle and antiparticle is less than the sum of the mass of the original particles. Still, in the annihilation process, the momentum and angular momentum of the initial particle-antiparticle system is conserved. The annihilation of a stationary positron-electron pair generates two photons. Due to the conservation of momentum, the two photons are emitted in opposite direction both with 511keV energy. The direction of emission is random. Due to their light mass, few MeV gamma-rays are capable of producing positron with pair production. In fact, the positrons are the most available antiparticle in the universe, the characteristic 511keV annihilation photons have been observed in active galactic nuclei [1], in the sun [2], and even in thunderstorm clouds on Earth [3]. The antiparticles are not easily available, the observable universe is mainly composed of matter, so any interaction would result in the annihilation. From here one of the main unanswered questions of modern physics: given the big bang was a high energy event, it should have generated matter and antimatter in equal quantity, however this symmetry is not observed in the universe around us. High-energy photons capable to produce positron-electron pairs can be generated in a controlled environment here on Earth with the use of LINACs [4] or nuclear reactor [5]. Moreover, positrons can be generated by radioisotope decay. The β^+ decay transforms a proton in a neutron in the atom nucleus, the process frees a positron, other than an electronic neutrino. This makes positrons the easiest available antiparticle and the first to be discovered and studied.In the 1920s, special relativity and quantum mechanics were two of the pillars of modern physics. One of the first attempts to combine the two was Dirac’s equation [6]. Dirac tried to explain the behavior of spin one-half particles like the electron when moving at relativistic speed, however the resulting equation admits free-particle solutions with positive and negative energies. Obviously, negative energies are not physically possible. An explanation proposed by Dirac involved a sea of particle [7]. The positive energy solution of the equation represents a particle excited from the sea, the hole left by this process corresponds to the negative energy solution. Then for any particle there is a correspond hole, called antiparticle. In the 1930s, Anderson was studying the behavior of cosmic rays interacting with a cloud chamber in the presence of a magnetic field [8]. Between the photographed particles, he demonstrated for the first time the existence if a particle with mass and charge equal in absolute value to the electron but positively charged. He called this particle positron, following studies confirmed the positron is the antiparticle of the electron. Nowadays, the positrons have found two main applications: in the medical field and in material studies. In medicine, β^+ radioisotopes are used as tracer for the individuation of cancer in patient with Positron Emission Tomography (PET). By detecting the two counterpropagating annihilation gamma-rays, it is possible to reconstruct the annihilation spot, and so the distribution of the absorption of the molecules with the radioisotope in the body. Cancerous cells have a different metabolism with respect normal cell, so their absorption of particular molecules is amplified. By selecting the correct molecular vector and radioisotope, the area in the patient body affected by the cancer is highlighted by the PET. In the case of material science, positrons are implanted in the material with energies up to tens of kiloelectronvolts. Interacting with the material, the positrons lose energy and diffuse in the material surrounding few tens of nanometers until they annihilate with an electron in the material, or they escape from the material surface. This makes the positrons a good probe because the information on the electrons transmitted outside the material by the annihilation gammas. How much time the positrons live in the material depends on the electron density. The presence of defects in the atomic structures creates spaces with lower electron density where the positron can live longer. This is studied with the Positron Annihilation Lifetime Spectroscopy (PALS). Because the positrons are generally consider thermalized at the annihilation, they have much less energy than the electron in the material. Then we can obtain information on the electron from any deviation in the direction and energy of the two annihilation photons form the case of stationary particles. The deviation in direction of the two photons is studied with Angular Correlation Annihilation Radiation (ACAR), the annihilation gammas energy with Doppler Broadening Spectroscopy (DBS). From the study of positron interaction with the matter, the bound state of the positron and the electron was discovered for the first time in the 1950s [9]. This bound state is called positronium (Ps) and it is the lightest bound matter-antimatter system. It is a hydrogen-like atom, with the positron substituting for the proton, this gives it particular properties [10]. The Ps is not stable, and, in its ground level, it is divided based on the total spin S in para- (S=0) and ortho- (S=1) positronium (p- and o- Ps, respectively) with different behaviors. Para-positronium is in a singlet spin state S=0 and m=0, where m is the projection of the spin on the z-axis. It tends to annihilate in two counterpropagating photons with 511keV energy and it has a vacuum lifetime of 125ps. Ortho-positronium corresponds to the triplet of spin states S=1 and m=-1, 0, +1. It annihilates mainly into three gamma-rays with a lifetime of 142ns in vacuum. This longer lifetime makes it possible to manipulate the o-Ps level with laser excitation [10], bringing it in longer lived levels for the study of its properties. In both the case of p-Ps and o-Ps, the conservation of energy and momentum in the annihilation fixes the gamma-rays direction and energy. For p-Ps like for free positrons, the two photons have a fixed energy and direction of one respect to the other, however the emission direction is random. The three photons resulting from the annihilation of o-Ps are emitted on a plane, called annihilation plane, with a wide range of energies and direction, the inclination of the annihilation plane is randomly distributed. In this discussion, we did not consider the conservation of the angular momentum in the annihilation process. This brings a constrain in the direction of polarization of the annihilation gamma-rays. For positronium in the ground level, the total angular momentum is given by the spin. For para-positronium and free positrons, the spin conservation means the two photons are entangled in the polarization state: the polarization of a gamma-ray is orthogonal to the other [11,12]. For ortho-positronium, the three gamma polarizations are genuinely multiparticle entangled, however the exact entanglement state depends on the emission direction of the three [13]. The correlation in the annihilation radiation of the two annihilation gammas was first experimentally studied in the 1940s [14–16]. Only a decade later, the experimental results demonstrated for the first time the existence of entanglement [17]. The entanglement in the case of three gammas has not yet been experimentally demonstrated. This is due to the complexity in the realization of a detector capable of measuring the polarization of three high-energy photon at the same time and of a source of positronium in a spin selected state in a free-field environment. This work thesis is centered on the design and study of an apparatus with the objective of study the entanglement of gamma-rays polarization generated by the annihilation of ortho-positronium. This apparatus is called PSICO (Positronium Inertial and Correlation Observations) apparatus, and it is under construction at the Antimatter laboratory (AML) of the University of Trento.At the center of the PSICO apparatus is the realization of a dense bunched positron beam capable of implanting the positrons in a positron/positronium converter in a field-free region with energy up to tens of kiloelectronvolt. No other positron beamline in the literature satisfies all these requirements. The creation of the PSICO positron beamline is based on four steps: the creation of a monoenergetic continuous positron beam, the trapping of the positrons in a buffer-gas trap (BGT) [18,19] and the generation of a dense bunched beam, the extraction of the bunched beam from the magnetic field of the trap, the acceleration, time-compression, and focalization of the positron bunches into a target in a free field region. To each step corresponds a part of the PSICO positron beamline. During this thesis work all fours parts have been designed, the last three parts are now under construction, the first part has been completed and commissioned. The creation of the monoenergetic continuous positron beam in the first step of the PSICO apparatus requires a radioactive source, a moderator, and a magnetic transport system. The design of this part of the apparatus is based on a commercial solution from First Point Scientific [20]. The source generates continuously positrons, which are emitted with a wide energy distribution. So, a moderator is required for the creation of a monoenergetic beam. The transport system guides the beam to the next section while eliminating the non-moderated positrons that are anyway emitted from the moderator. In the implementation, a sodium-22 source is used for its long half-life of 2.6 years. A solid noble gas moderator is used for the moderation process due to its high efficiency [21]. The design of the magnetic transport is based on raytracing simulation in order to optimize the speed-selection and transport of the positrons from the moderator with the minimal number of magnets. Once constructed, the first part of the PSICO apparatus can generate a continuous positron beam with up to 50 000 positrons per second with a total efficiency from the source to the end of the magnetic transport higher than 0.15%. Three solid noble gas moderators were tested: Neon, Argon, and Krypton. The advantages and disadvantages of the moderator realized with the three gases have been studied. The commissioning of the continuous positron beam has been completed by measuring the dimension of the beam spot, energy distribution, and polarization at the end of the magnetic transport system for the three gases. The measured beam dimensions are compatible with the transport simulation at the same position. The second part of the PSICO apparatus consists of the buffer-gas trap. The BGT is a modified Penning trap, where a 700G magnetic field confines radially the positrons which are accumulated in an electrostatic potential well along the magnet axis. When the positrons enter the trap, they are cooled by inelastic scattering with gas introduced into the chamber until they fall to the bottom of the potential well. The design of the PSICO BGT is based on a commercial design from First Point Scientific with changes in the magnet and terminal electron for the optimal release of the positron bunches from the BGT and their extraction from the trap magnetic field in the third stage of the PSICO beamline. From the simulation with the new trap design, the positron bunches are formed in a region with a field homogeneity ΔB\/B better than 0.1%, and the bunches are released from the trap with a temporal width less than 5ns [22].The extraction of magnetic field is done in the third step of the PSICO apparatus immediately after the trap. In the literature, a few configurations for the magnetic field extraction of positrons from the BGT have been proposed and implemented [23–25]. However, the present design is the first one where the positron extraction from the magnetic field is performed directly at the exit of the BGT. According to the simulations of our design, 60% of the positron can be extracted from the magnetic field of the trap [22].In order to perform the fourth step, a buncher-elevator followed by four lenses has been designed. After the extraction from the BGT, the positrons enter the buncher-elevator whose potential is shaped in 5.5 ns [26]. The final potential is given by a constant value superimposed by a parabolic potential. The parabolic potential has a height of 1kV at the start of the buncher-elevator and the vertex at its end, it is required for the time compression of the bunch. The constant potential value gives, instead, the majority of the implantation energy to the positrons and it can reach up to 21kV [22]. The positron bunch is then focused by the last four lenses onto the target in a spot smaller than 5mm in diameter and temporal width lower than 2ns. This will be the first positron beam from a BGT capable to operate at high implantation energy with a target in a field-free region. These four parts complete the dense bunched positron beam. For the study of the entanglement in the polarization of the o-Ps annihilation photons, a good positron/positronium converter is needed. In the literature, there are example of good converters [27,28], however they work in reflection geometry, i.e. they emit Ps on the same side where positrons are implanted. This presents some limitation in the manipulation and study of positronium in vacuum. Positron/positron converter capable of emitting Ps on the other side of the implantation can be found in the literature, however their efficiency is low [29]. So, a new kind of converter has been studied for the production of positronium in transmission [30]. It consists of silicon membranes of few microns of thickness where pass through nanochannels have been electrochemically etched. This kind of converters have shown a conversion efficiency of at least 16%. The last element needed for the entanglement measurement is the detector. This needs to be capable of measuring the polarization of the gamma-rays at the same time. The only way of measuring the polarization of hundreds of kiloelectronvolt photons is by applying the Compton scattering. For each annihilation gamma, the detector records the electron scattered from the Compton scattering and the scattered photons. The direction of the scattered photon depends on the polarization of the annihilation gammas. To reconstruct the three polarizations, the detector records six events, this requires a complex detection system. After an extensive study of literature, we are oriented into the use of modules of plastic scintillators originally developed for PET measurements by a group of the Jagiellonian University (Krakow, Poland) [31]. Two modules have been tested with the continuous positron beam from the first part of the apparatus. Just two modules were enough to reconstruct the beam spot with an uncertainty of few centimeters [31]. Using more modules, a higher precision can be obtained. Thanks to all the work done in the design, testing, and implementation of the different components of the PSICO apparatus it makes possible in the near future the realization of the first test of entanglement in the polarization of the three gamma-rays generated by annihilation of ortho-positronium.

Bose-Einstein condensates (BECs) of ultra-cold atoms have been subjects of a large research effort, that started a century ago as a purely theoretical subject and is now, since the invention of evaporative cooling thirty years ago, a rich research topic with many experimental apparatuses around the world. A deep knowledge of its underlying physics has been now acquired, for example on the thermodynamics of the gas, superfluidity, topological excitations and many-body physics. However, many topics are still open for investigation, thanks to the flexibility and the high degree of control of these systems. During the course of my PhD, I developed and realized a new experimental apparatus for the realization of coherently-coupled mixtures of sodium BECs. The highly stable and low-noise magnetic environment of this apparatus enables the experimental investigation of a previously inaccessible regime, where the energy of the coupling becomes comparable to the energy of spin excitations of the mixture. With this apparatus, I concluded two experimental investigations: I produced and investigated non-dispersive spin-waves in an two-component BEC and I experimentally observed the quantum spin-torque effect on a elongated bosonic Josephson junction.The research activity in multi-component BECs of alkali atoms begun shortly after the first realization of a condensate, thanks to the low energy splitting between the internal sub-states of the electronic ground state. These internal states can be coherently coupled with an external electromagnetic field and can interact via mutual mean-field interaction, generating interestinc effects such as ground states with different magnetic ordering depending on their interaction constants, density as well as spin dynamics and internal Josephson effects. The research interest on mixtures of sodium atoms sparks from the peculiar characteristic of the system: in the $ket{F = 1, m_F = pm 1}$ states, the interaction constants are such that the ground state has anti-ferromagnetic ordering and the system is perfectly symmetric for exchanges of the two species. In these peculiar system, density- and spin-excitations have very different energetic cost, with the latter being much less energetic, and can be completely decoupled. Moreover, spin-excitations, that are connected to excitations in the relative-phase between the components, change drastically in nature when a coupling of comparable energy is added between the states. The presence of the coupling effectively locks the relative-phase in the bulk and spin excitations become localized. While extensive theoretical predictions on the spin dynamics of this system has been already performed, experimental confirmation was still lacking because of the high sensitivity to external forces (due to the very low energy of the spin excitations) and the impossibility of realizing a low-energy coupling between these states in the presence of environmental magnetic noise. During my PhD, I realized an experimental apparatus where magnetic noises are suppressed by five orders of magnitude using a multi-layer magnetic shield made of an high-permeability metal alloy (μ-metal), that encases the science chamber. In this apparatus, I developed a protocol, compatible with the technical limitations of the magnetic shield, to produce BECs in a spin-insensitive optical trapping potential. I then characterized the residual magnetic noise and found it compatible with the requirements for observing spin-dynamics effects. Finally, I realized a system and a set of protocols for the manipulation of the internal state of the sample allowing arbitrary preparation of the sample while maintaining the long coherence times necessary to observe the spin dynamics, that have been used in the subsequent experimental observations. The first experimental result discussed in this thesis, is the production of magnetic solitons and the observation of their dynamic in a trapped sample. Waves in general spread during their propagation in a medium, however this tendency can be counterbalanced by a self-focusing effect if dispersion of the wave is non-linear, generating non-dispersive and long-lived wavepackets commonly named solitons. These have been found in many fields of physics, such as fluid dynamics, plasma physics, non-linear optics and cold-atoms BECs, attracting interest because of their ability to transport information or energy unaltered over long distances, as they are robust against the interaction with in-homogeneities in the medium. Of these systems, cold-atoms can be widely manipulated to generated different kinds of solitons, both in single and in multi-components systems. A new kind of them, named magnetic solitons, has been predicted in a balanced mixture of BECs of sodium in $ket{F = 1, m_F = pm 1}$, however experimental observation was still lacking. I deterministically produced magnetic solitons via phase engineering of the condensate using a spin-sensitive optical potential. I then developed a tomographic imaging technique to semi-concurrently measure the densities of both components and the discontinuities in their relative phase, allowing for the reconstruction of all the relevant quantities of the spinor wavefunction. This allowed to observe the dispersionless dynamics of the solitons as they perform multiple oscillation in the trapped sample in a timescale of the order of the second. Moreover, I engineered collisions between different kinds of magnetic solitons and observed their robustness to mutual interaction. The second experimental results presented in this thesis is the observation of the breaking of magnetic hetero-structures in BECs due to the quantum spin torque effect, an effect with strong analogies with electronic spins traveling through magnetic devices. Spins in magnetic material precess around the axis of the effective magnetic field, and their dynamics must take into account the external field as well as non-linear magnetization and the inhomogeneity of the material. These effects are commonly described by the Landau-Lifshitz equation and have been mainly studied for electronic spins in magnetic hetero-structures, where the inhomogeneity in the material at the interfaces enhances the exchange effects between spins. For homogeneous materials, this description reduces to the Josephson system, a closely related effect that is more known in cold-atoms systems. The Josephson effect arises when a macroscopic number of interacting bosonic particles are distributed in two possible states, weakly tunnel-coupled together, with the average energy of particles occupying each of the states depending on the occupation number itself. In these conditions, the dynamics of the system depends on the difference in occupation numbers, the relative phase between the states and the self-interaction to tunneling ratio, giving raise to macroscopic quantum effects such as oscillating AC and DC Josephson currents and self-trapping. While these phenomena has been historically studied in junctions between superconducting systems, they can be also realized with cold-atoms systems, allowing the study of Josephson junctions with finite dimensions and in regimes that are hard to reach for superconducting systems. In this thesis, I realized a magnetic hetero-structure in a two-component elongated BECs thanks to the simultaneous presence of self-trapped (ferromagnetic) and oscillating (paramagnetic) regions in the sample. While the dynamics at short times is correctly described by the Josephson effects, at the interface between the regions the particle nature of the gas creates a strong exchange effect, named the quantum spin torque, that produces magnetic excitations that spread trough the sample and break the local Josephson behaviour. I experimentally studied the spread and nature of these magnetic excitations, while numerical simulations confirmed the dominant role played by the quantum spin torque effect. The structure of this thesis is the following: in the first chapter is given a review of theoretical concepts and existing literature. In the second chapter is described the experimental apparatus and the protocols developed to prepare the ultra-cold atoms sample. In the third chapter is presented the experimental observation of magnetic solitons. In the fourth chapter is presented the experimental investigation of the quantum spin torque effect in magnetic heterostructures. The last chapter is devoted to conclusions and outlook of this work.

The investigation of real-time dynamics of charged and neutral quantum excitation propagating through macromolecular systems is receiving growing attention due to its potentially countless applications in nano-scale (opto-)electronics and in biophysics. Several key issues have not been fully clarified yet, including the role played by molecular thermal fluctuations and the possible correlations between the degree of quantum coherence and the efficiency of the transport process. In order to gain some insight, we developed a rigorous and systematic framework describing quantum transport, based on a field-theoretic formalism.

In this work, two types of nano-structured TiO2 layers were obtained by two different methods. First, during an exploratory study, a set of nano-columnar TiO2 films and niobium doped TiO2 films was obtained on stainless steel, by a RF reactive sputtering technique. The argon gas is ionized by a high negative voltage applied to the TiO2 target (cathode), and a plasma is created between the cathode and the substrate (anode). Positively charged ions (Ar+) are accelerated toward the TiO2 target (a co-target Nb is placed beside the TiO2 cathode for Nb doping) and their impact sputters atoms off the target. These atoms travel across the chamber and a fraction of them land on stainless steel, resulting in a film TiO2 and Nb-doped film TiO2. With adjusting the RF power applied on the co – target, different concentrations of Nb in the TiO2 film could be controlled. The results of EIS (Electrochemical Impedance Spectroscopy) mainly showed the presence of a barrier layer (junction metal/semiconductor or metal/oxide/semiconductor) between the TiO2 layer and the stainless steel in the absence and presence of niobium. The carrier density is estimated at almost 1018 cm-3. In the second part of this thesis, two types of TiO2 nano-tubular arrays with nanotubes (NT) aligned perpendicular to the titanium substrate were obtained by anodization of a titanium foil, in two different solutions containing fluoride ions. The NT obtained in a tetrabutylammonium / formamide solution (named: TiO2-NT(TB)) are rough, while the second solution, ethylene glycol , allows to synthesize smoother and denser tubes (named: TiO2-NT(EG)). All the nanotubular arrays were characterized by EIS and showed in the high frequency range a contribution related to the presence of surface states, and a contribution at low frequencies related to the capacity of the space charge layer. In the dark, in the Na2SO4 solution with neutral pH, the EIS study of TiO2-NT (TB) anatase showed that these two contributions vary with the applied potential. The capacity of surface states varied exponentially in a wide range of potential, but in addition the presence of a localized energy state in the gap could be evidenced. This localized state is the signature of the adsorption of molecular water. After UV exposure during 3h, and back to the dark, the quasi irreversible disappearance of the localized energy states is related to photo-induced adsorbed water dissociation at some sites on the surface of NT. Furthermore, the increase by a factor 112 of the capacity of the space charge layer was observed after UV exposure. This increase can be explained by the photo activation of the surface of NT, which was inactive before UV exposure. This activation is related to the dissociation of adsorbed molecular water and the insertion of hydrogen into the walls of NT. A geometric model considering the variation of the band bending taking place inside the wall of NT is proposed to replace the classical Mott-Schottky relation, which is only valid for a plate condensator. This model allows understanding the variation of the space charge layer as a function of the applied potential. With this new model, a carrier density of about 1018 cm-3 et 1020 cm-3 respectively before and after UV illumination were determined, confirming that the photo-induced activation of the wall of NT is linked to the phenomenon of doping due to hydrogen insertion. In the case of TiO2 –NT(EG), the contribution of adsorption of molecular water was not observed. The spectrum of EIS before and after UV exposure did not show a significant change and the capacities of space charge layer after illumination only increased by a factor 8. The simulation with the model shows that the carrier density is about 1020cm-3 before and after illumination. In other words, these tubes of TiO2 –NT(EG), are already activated before illumination and the photo-induced effects are less important compared to the TiO2 –NT(TB) array. For a better identification of the chemical nature of the surface state in the case of rough tubes of TiO2 –NT(TB), EIS measurements were performed in the same manner, but in acidic (pH=3.5) and basic (pH=12.5) media, in order to compare the behaviour to that observed in the neutral Na2SO4 solution. In the alkaline electrolyte, the band bending varies only slightly with the applied potential, reflecting a shift of band edge and the filling/emptying of the surface states during polarization. Moreover, the exponential distribution of capacities of surface states is more spread out (850 meV) in alkaline solution than in the neutral solution (257meV), showing clearly the particular role of the OH groups at the surface of the tubes. In the acidic electrolyte, a phenomenon of diffusion –insertion of protons should be taken into account for interpreting the spectra of EIS. H atoms play the role of electron donors able to increase the carrier density in the wall of the tubes. The comparison between the behaviours in the 3 media clearly associates the surface states to hydroxyl groups. In the last part of this thesis, experiments were performed on TiO2 –NT(TB) in a NaOH electrolyte, using Intensity Modulated Photocurrent Spectroscopy (IMPS), and the results are discussed in comparison with a thin compact film deposed on a titanium foil par PVD.

Recent technological advances in quantum simulators have proven that synthetic materials are very well suited to study and realise many condensed matter models. However, many of these synthetic systems are characterized by neutral particles that do not couple to real gauge fields. In order to simulate interesting electromagnetic phenomena, such as the topological insulators, or the Landau levels, there is the need for the implementation of artificial gauge fields. In particular, the topological insulators are very interesting both from the point of view of fundamental physics and concrete applications. They are bulk insulating materials that carry a certain number of edge states which are topologically protected against small perturbations of the system. An example of a topological insulator is the integer quantum Hall effect. While there have been many works studying topological physics with quantum artificial systems, little attention was dedicated to the interplay of topology and the purely classical world. Only in the last couple of years, pioneering efforts to encode a non-trivial topology in the dynamical matrix or into the Hamiltonian of a system have proven that the hallmarks of a topological insulator are not the prerogative of quantum mechanics, but can be also observed with a classical system governed by Newton’s equations. The first part of this thesis is therefore based on our studies dedicated to the implementation of a classical analogue of the integer quantum Hall system, by realizing the Harper-Hofstadter model for classical frequency-modulated coupled harmonic oscillators. The achievement of an artificial gauge field allows also for the deeper study of magnetic effects such as Landau levels. In graphene, an inhomogeneous strain of the lattice is equivalent to an artificial pseudo-magnetic field, and the low-energy spectrum shows the formation of relativistic pseudo-Landau levels. The second part of the thesis is therefore focussed on the photonics honeycomb lattice geometry and our theoretical proposal for a configuration based on an intrinsically driven-dissipative system in which to probe the physics of the Landau levels, and especially the spatial structure of their wavefunctions. Finally, we have also studied spin-orbit coupling in a mechanical system of masses and springs induced by pre-tensioned springs that split the longitudinal and transverse couplings in the honeycomb geometry. We have presented the experimental results of a simple mechanical benzene composed of six pendula connected with pre-tensioned springs, to verify that the eigenmodes of this system are well described by our theory in the presence of spin-orbit coupling.

This thesis work is focused on the investigation of a peculiar phenomenon observed in germanium: the formation of a regular network of columnar nanovoids induced by heavy ion and high fluence irradiation at room temperature. This phenomenon can represent a possible way to produce wide nanostructured areas on semiconductor surfaces by a well-established semiconductor technology process such as ion implantation. However, the formation mechanism of this regular network of Ge columnar nanovoids is still under debate. Therefore, the work has been focused on the investigation of the formation mechanisms and on the possible strategies to control the geometry and the composition of these structures, in order to exploit the results for possible technological applications. In particular, ion implantation was carried out using Sn+ ions with the double aim of creating Ge1-xSnx nanostructures and following the depth distribution of the impinging ions. Furthermore, ion implantation through ultra-thin (10-20 nm) films of silicon nitride (SiNx) was investigated as a possible way to impact on nanovoid formation kinetics, prevent ambient contaminations and prevent Sn out-diffusion upon thermal treatments. Firstly, low temperature Sn+ implants were carried out in order to define a recipe to prepare Ge1-xSnx alloy: Ge1-xSnx alloy films with thickness of 15-30 nm were obtained by implanting Sn+ in Ge at liquid nitrogen temperature and subsequent thermal annealing (600 °C for 10 s). High Sn substitutionality, no relevant diffusion, limited surface segregation and excellent crystallinity were achieved, a tin concentration of x=6-7 at.% was reached. Secondly, Ge nanostructures were prepared by high fluence ion implantation at room temperature and then morphologically and chemically characterized, determining that the obtained nanostructures are constituted by Sn-rich Ge. Nanovoids developed under the SiNx film, with reduced oxygen contamination. The first stages of nanovoid formation were observed for samples with and without the SiNx layer. The SiNx layer seems to induce a retarded nanovoid nucleation in terms of threshold fluence, without hindering nanovoid growth. The experimental data were interpreted on the basis of the vacancy clustering theory. SRIM simulations were performed to compare the distributions of point defects and implanted ions at different conditions in the SiNx/Ge stack. These helped to show that the depth distribution of energy deposition is the relevant parameter. Moreover, it was highlighted that both the redistribution in depth of the SiNx atoms and the implanted Sn+ contribute to a lowering of the Ge concentration causing the formation of a layer where nanovoid nucleation does not occur. Taking into account the ion mixing effect including the introduction of Sn, threshold value of the deposited energy was found. The thermal treatments investigated for the Ge1-xSnx alloy thin films were applied on nanostructured samples, causing a dramatic deformation of the nanovoids probably due to a melting temperature decreased by the presence of tin. The investigation of possible technological applications of Ge nanostructures was carried out, in particular in thermoelectric applications, in lithium ion batteries and gas sensors. Several samples were designed and ad-hoc substrates were produced.