39 research outputs found
Density functional approach to the band gaps of finite and periodic two-dimensional systems
No full textWe present an approach based on density functional theory for the calculation of fundamental gaps of both finite and periodic two-dimensional (2D) electronic systems. The computational cost of our approach is comparable to that of total energy calculations performed via standard semilocal forms. We achieve this by replacing the 2D local density approximation with a more sophisticated—yet computationally simple—orbital-dependent modeling of the exchange potential within the procedure by Guandalini et al. [Phys. Rev. B 99, 125140 (2019)]. We showcase promising results for semiconductor 2D quantum dots and artificial graphene systems, where the band structure can be tuned through, e.g., Kekulé distortion
Eccitazioni cariche e neutre non lineari in sistemi a bassa dimensionalità e molecolari mediante l'utilizzo di approcci basati sui funzionali della densità
No full textLe eccitazioni elettroniche assumono un ruolo di fondamentale importanza in diverse proprietà fisiche dei materiali, ad esempio nel trasporto quantistico, trasporto termico, conducibilità e proprietà ottiche. A seconda della carica elettrica dello stato finale, possiamo distinguere tra eccitazioni cariche e neutre. Nelle eccitazioni cariche, consideriamo elettroni che vengono aggiunti o sottratti al sistema. Questi processi possono essere studiati tramite esperimenti di fotoemissione diretta o inversa. Invece, nelle eccitazioni neutre, la carica totale del sistema viene conservata durante il processo di eccitazione. Questo tipo di eccitazioni possono essere rilevate attraverso misure di assorbimento ottico, sia in regime lineare che non lineare.
La teoria del funzionale della densità (DFT) e la sua estensione dipendente dal tempo (TDDFT) sono spesso il primo quadro teorico di riferimento nella descrizione a primi principi dei processi di eccitazione. Tuttavia, è noto che la DFT e la TDDFT danno luogo ad errori e limiti di applicabilità a causa delle approssimazioni funzionali che devono essere necessariamente utilizzate in pratica. Pertanto, lo sviluppo di approssimazioni più accurate ed altre estensioni teoriche è un campo di ricerca interessante e attivo.
In questo lavoro, mi occupo dello sviluppo di nuovi metodi per il calcolo delle eccitazioni cariche e neutre.
Nella prima parte, mostro come il gap fondamentale dei punti quantici bidimensionali può essere accuratamente stimato al costo computazionale di un calcolo di stato fondamentale, seguito da uno step non autoconsistente dal costo computazionale trascurabile, il tutto eseguito all'interno dell'approssimazione della densità locale. Nonostante ciò, la procedura include formalmente la discontinuità del potenziale di scambio espressa attraverso il metodo del potenziale effettivo orbitale.
Nella seconda parte, ricavo un'approssimazione del potenziale che include esplicitamente un gap di scambio diverso da zero per sistemi bidimensionali sia finiti che periodici. Sebbene la forma funzionale utilizzata coinvolga direttamente gli orbitali a singola particella, il costo computazionale è paragonabile ai calcoli DFT standard. L'approssimazione del potenziale è applicata al grafene artificiale, in cui una distorsione di Kekulé utilizzata per aprire un gap nei punti di Dirac.
Nella terza parte di questo lavoro mi occupo di studiare le eccitazioni neutre non lineari. In particolare, derivo la sezione d'urto ottica per un sistema a più elettroni soggetto a un campo elettrico impulsivo nel regime non perturbativo, cioè per valori arbitrari dell'intensità del campo incidente, partendo dallo stato fondamentale. Successivamente mostro che la sezione d'urto include assorbimenti da stati eccitati all'aumentare dell'intensità del campo elettrico. Queste transizioni ottiche non sono possibili all'interno del regime lineare. Come esempio di applicazione, considero il caso di un sistema modello unidimensionale composto da due elettroni interagenti. L'analisi rivela che gli stati eccitati di tipo gerade, che non partecipano alle proprietà ottiche nel regime lineare, sono popolati nel regime non lineare a causa dell'assorbimento da stato eccitato. Questa analisi aiuta a interpretare le simulazioni di TDDFT in tempo reale che impiegano campi elettrici impulsivi oltre il regime lineare, come per lo studio dei processi coinvolti nei fenomeni di limitazione ottica.
I risultati ottenuti in questa tesi di dottorato contribuiscono allo sviluppo di metodi accurati e praticabili per studiare le eccitazioni elettroniche nei sistemi quantistici e, in particolare, allo sviluppo teorico nel campo degli approcci a principi primi basati sui funzionali della densità.Electronic excitations play a prominent role in a large variety of physical properties of materials, e.g., quantum transport, heat transport, conductivity, and optical properties. Depending on the electric charge of the final state, we may distinguish between charged and neutral excitations. In charged excitations, we consider electrons that are added or subtracted to the system. Direct or inverse photoemission experiments are a primary tool for the experimental observation of such processes.
Instead, in neutral excitations, the total charge of the system is conserved during the excitation process. These can be probed through optical absorption measurements, both in the linear and nonlinear regimes.
Density functional theory (DFT) and its time-dependent extension (TDDFT) are often the theoretical framework of first choice in the first-principles description of excitation processes. However, it is well known that DFT and TDDFT show failures and limitations due to the functional approximations which are necessary in practice. Thus, the development of more accurate approximations and theoretical extensions is an interesting and intense field of research.
In this work, I develop new advances in the calculation of charged and neutral excitations.
In the first part, it is shown that the fundamental gap of two-dimensional quantum dots can be accurately estimated at the effort of a standard ground-state calculation supplemented with a non-self-consistent step of negligible cost, all performed at the level of the local-density approximation. Yet, the procedure formally exploits the exchange discontinuity as expressed through the orbital-effective-potential method.
In the second part, I derive an approximate potential that can capture non-vanishing exchange gaps both infinite and periodic two-dimensional systems. Although the procedure involves single-particle orbitals directly, the computational cost is comparable to standard DFT calculations. The potential approximation is applied to the artificial graphene, Kekulé distorted to open a gap at the Dirac points.
In the third part of this work, nonlinear neutral excitations are investigated. In particular, I derive the optical cross section of a many-electron system subject to an impulsive electric field in the nonperturbative regime, i.e. for arbitrary values of the field strength, starting from the ground state. I show that the cross section includes absorptions from excited states for increasing intensities of the electric field - which are optical transitions that cannot be captured within the linear regime.
As an example, I consider the case of a 1D two-electron model system. The analysis reveals that gerade excited states, which are dark in the linear regime, are populated in the nonlinear regime due to excited-state absorption. This analysis helps to interpret real-time TDDFT simulations which employ impulsive electric fields beyond the linear regime, as for studying processes in optical limiting phenomena.
The results obtained in this Ph.D. thesis contribute to the development of accurate and feasible methods to investigate electronic excitations in quantum systems, and, more generally, to the theory development of first-principles density-functional approaches
Efficient GW calculations in two dimensional materials through a stochastic integration of the screened potential
No full textAbstract Many-body perturbation theory methods, such as the G 0 W 0 approximation, are able to accurately predict quasiparticle (QP) properties of several classes of materials. However, the calculation of the QP band structure of two-dimensional (2D) semiconductors is known to require a very dense BZ sampling, due to the sharp q-dependence of the dielectric matrix in the long-wavelength limit (q → 0). In this work, we show how the convergence of the QP corrections of 2D semiconductors with respect to the BZ sampling can be drastically improved, by combining a Monte Carlo integration with an interpolation scheme able to represent the screened potential between the calculated grid points. The method has been validated by computing the band gap of three different prototype monolayer materials: a transition metal dichalcogenide (MoS2), a wide band gap insulator (hBN) and an anisotropic semiconductor (phosphorene). The proposed scheme shows that the convergence of the gap for these three materials up to 50meV is achieved by using k-point grids comparable to those needed by DFT calculations, while keeping the grid uniform
On the estimation of the concentration curve under complex sampling designs
No full textThis paper focuses on the estimation of the concentration curve of a finite population, when data are collected according to a complex sampling design with different inclusion probabilities. The asymptotic law of the finite population version of the concentration process is first studied. Then, a resampling scheme able to approximate such a law is constructed. Finally, an application to the construction of confidence bands is considered
Fundamental gaps of quantum dots on the cheap
No full textWe show that the fundamental gaps of quantum dots can be accurately estimated at the computational effort of a standard ground-state calculation supplemented with a non-self-consistent step of negligible cost, all performed within density-functional theory at the level of the local-density approximation
On the estimation of the Lorenz curve under complex sampling designs
No full textThis paper focuses on the estimation of the concentration curve of a finite population, when data are collected according to a complex sampling design with different inclusion probabilities. A (design-based) Hájek type estimator for the Lorenz curve is proposed, and its asymptotic properties are studied. Then, a resampling scheme able to approximate the asymptotic law of the Lorenz curve estimator is constructed. Applications are given to the construction of (i) a confidence band for the Lorenz curve, (ii) confidence intervals for the Gini concentration ratio, and (iii) a test for Lorenz dominance. The merits of the proposed resampling procedure are evaluated through
a simulation study
Efficient GW calculations via interpolation of the screened interaction in momentum and frequency space. The case of graphene
No full textThe GW self-energy may become computationally challenging to evaluate because of frequency and momentum convolutions. These difficulties were recently addressed by the development of the multipole approximation (MPA) and the W-av methods: MPA accurately approximates full-frequency response functions using a small number of poles, while W-av improves the convergence with respect to the k-point sampling in 2D materials. In this work, we (i) present a theoretical scheme to combine them, and (ii) apply the newly developed approach to the paradigmatic case of graphene. Our findings show an excellent agreement of the calculated QP band structure with angle resolved photoemission spectroscopy (ARPES) data. Furthermore, the computational efficiency of MPA and W-av allows us to explore the logarithmic renormalization of the Dirac cone. To this aim, we develop an analytical model, derived from a Dirac Hamiltonian, that we parametrize using ab initio data. The comparison of the models obtained with the plasmon pole approximation (PPA) and MPA results highlights an important role of the dynamical screening in the cone renormalization
On the estimation of the Lorenz curve under complex sampling designs
No full textThis paper focuses on the estimation of the concentration curve of a finite population, when data are collected according to a complex sampling design with different inclusion probabilities. A (design-based) Hájek type estimator for the Lorenz curve is
proposed, and its asymptotic properties are studied. Then, a resampling scheme able to approximate the asymptotic law of the Lorenz curve estimator is constructed. Applications are given to the construction of (i) a confidence band for the Lorenz curve, (ii) confidence intervals for the Gini concentration ratio, and (iii) a test for Lorenz dominance. The merits of the proposed resampling procedure are evaluated through a simulation study
Nonlinear light absorption in many-electron systems excited by an instantaneous electric field. A non-perturbative approach
No full textApplications of low-cost non-perturbative approaches in real time, such as time-dependent density functional theory, for the study of nonlinear optical properties of large and complex systems are gaining increasing popularity. However, their assessment still requires the analysis and understanding of elementary dynamical processes in simple model systems. Motivated by the aim of simulating optical nonlinearities in molecules, here exemplified by the case of the quaterthiophene oligomer, we investigate light absorption in many-electron interacting systems beyond the linear regime by using a single broadband impulse of an electric field; i.e. an electrical impulse in the instantaneous limit. We determine non-pertubatively the absorption cross section from the Fourier transform of the time-dependent induced dipole moment, which can be obtained from the time evolution of the wavefunction. We discuss the dependence of the resulting cross section on the magnitude of the impulse and we highlight the advantages of this method in comparison with perturbation theory by working on a one-dimensional model system for which numerically exact solutions are accessible. Thus, we demonstrate that the considered non-pertubative approach provides us with an effective tool for investigating fluence-dependent nonlinear optical excitations
Assessment of mental stress through the analysis of physiological signals acquired from wearable devices
No full textMental stress is a physiological state that directly correlates to the quality of life of individuals. Generally speaking, but especially true for disabled or elderly subjects, the assessment of such condition represents a very strong indicator correlated to the difficulties, and, in some case, to the frustration that derives from the execution of a task that results troublesome to be accomplished. This article describes a novel procedure for the assessment of the mental stress level through the use of low invasive wireless wearable devices. The information contained in electrocardiogram, respiratory signal, blood volume pulse, and electroencephalogram was extracted to set up an estimator for the cognitive workload level. A random forest classifier was implemented to assess the level of mental stress starting from a pool of 3481 features computed from the aforementioned physiological quantities. The proposed system was applied in a scenario in which two different mental states were elicited in the subject under investigation: first, a baseline resting condition was induced by the presentation of a relaxing video; then a stressful cognitive state was provoked by the administration of a mental arithmetic task. The random forest classifier shows an accuracy of 97.5% in discerning between these two mental states
