The first and main part of this thesis concerns the quantization of the transverse transport in diverse periodic quantum systems. From a theoretical point of view, the Hall conductivity's quantization may be understood at the single-particle level in terms of topological invariants. In periodic media such as crystals, the single-particle energy spectrum depicts a specific band structure. A modern approach, based on topology and differential geometry, consists in assigning an abstract mathematical object, a fibre bundle, to each energy band. The fibre bundle's topology is measured by a topological invariant, called the Chern number, which only takes integral values. Surprisingly, the transverse conductivity can be expressed as a sum of Chern numbers. In this work, one provides a rigorous derivation of this fact and one presents several methods which allow the numerical and analytical computation of the Chern numbers for diverse systems. <p><p>The first original study concerns the physics of ultracold atoms trapped in optical lattices. These very popular experimental setups, which are currently designed in several laboratories worldwide, allow for the exploration of fundamental problems encountered in modern physics. In particular atoms trapped in optical lattices reproduce with a very high accuracy the physics of the Hubbard-type models which describe a huge variety of condensed <p>matter phenomena, such as high-Tc superconductivity and the Mott quantum phase transition. Particularly interesting is the possibility to create artificial magnetic fields in optical lattices. Generated by complex laser configurations or by rotation of the trap, these artificial fields allow the simulation of electronic systems subjected to intense magnetic fields. In this thesis, one explores the possibility of a quantum Hall-like effect for neutral particles in such arrangements. In particular one focuses on the exotic situation in which non-Abelian gauge potentials are generated in the system. In these interesting arrangements, the atomic hoppings are assisted by external lasers and are described by non-commutating translation operators. The non-Abelian fields which are generated in these systems are well known in high-energy physics, where they play a key role in modern theories of fundamental interactions. <p>Thereafter, our study of the IQHE in periodic systems concerns quantum graphs. These models which describe the propagation of a quantum wave within an arbitrary complex object are extremely versatile and hence allow the study of various interesting quantum phenomena. Quantum graphs appear in diverse fields such as solid state physics, quantum chemistry, quantum chaology and wave physics. On the other hand, in the context of quantum chaology, graphs have been the vehicle to confirm important conjectures about chaos signatures. In this thesis, one studies the spectral and chaological properties of infinite rectangular quantum graphs in the presence of a magnetic field. One then establishes the quantization of the Hall transverse conductivity for these systems.<p><p>The second part of the thesis is devoted to the physics of interacting atoms trapped in optical lattices and subjected to artificial gauge potentials. One explores the Mott quantum phase transition in both bosonic and fermionic optical lattices subjected to such fields. The optical lattices are described through the Hubbard model in which the dynamics is ruled by two competing parameters: the interaction strength U and the tunneling amplitude t. The Mott phase is characterized by a commensurate filling of the lattice and is reached by increasing the ration U/t, which can be easily achieved experimentally by varying the depth of the optical potential. In this thesis one studies how this quantum phase transition is modified when the optical lattice is subjected to diverse artificial gauge potentials. <p><p>Moreover, one shows that vortices are created in bosonic optical lattices in the vicinity of the Mott regime. The vortices are topological defects in the macroscopic wave function that describes the superfluid. One comments on the vortex patterns that are observed for several configurations of the gauge potential. <p><p>%%%%%%%%%%%%%%%%%%%%%<p>%%%%%%%%%%%%%%%%%%%%%<p>%%%%%%%%%%%%%%%%%%%%%<p><p><p>La physique statistique quantique prédit l’émergence de propriétés remarquables lorsque la matière est soumise à des conditions extrêmes de basses températures. Aujourd’hui ces nouvelles phases de la matière jouent un rôle fondamental pour les technologies actuelles et ainsi méritent d’être étudiées sur le plan théorique. <p><p>Dans le cadre de ma thèse, j’ai étudié l’effet Hall quantique qui se manifeste dans des systèmes bidimensionnels ultra froids et soumis à des champs magnétiques intenses. Cet effet remarquable se manifeste par la quantification parfaite d’un coefficient de transport appelé conductivité de Hall. Cette grandeur physique évolue alors sur divers plateaux qui correspondent à des valeurs entières d’une constante fondamentale de la nature. D’un point de vue théorique, cette quantification peut être approchée par la théorie des espaces fibrés qui permet d’exprimer la conductivité de Hall en termes d’invariants topologiques. <p><p>Nous explorons l'effet Hall quantique pour différents systèmes en nous appuyant sur l’interprétation topologique de la quantification de la conductivité de Hall. Nous démontrons ainsi que l’effet Hall quantique se manifeste aussi bien dans les métaux que dans les graphes quantiques et les réseaux optiques. Les graphes quantiques sont des modèles permettant l’étude du transport dans des circuits fins, alors que les réseaux optiques sont des dispositifs actuellement réalisés en laboratoire qui piègent des atomes froids de façon périodique. Considérant différents champs magnétiques externes et variant la géométrie des systèmes, nous montrons que cet effet subit des modifications remarquables. Notamment, l’effet Hall quantique est représenté par des diagrammes des phases impressionnants :les multiples phases correspondant à la valeur entière de la conductivité de Hall se répartissent alors dans des structures fractales. De plus, ces diagrammes des phases se révèlent caractéristiques des différents systèmes étudiés. <p><p>D’autre part, nous étudions la transition quantique de Mott dans les réseaux optiques. En augmentant l’interaction entre les particules, le système devient isolant et se caractérise par le remplissage homogène du réseau. Nous étudions également l’apparition de tourbillons quantiques lorsque le système est soumis à un champ magnétique au voisinage de la phase isolante. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Ce document présente notre travail sur la modélisation en formalisme des fonctions de Green (abrégé formalisme de Green) du transport quantique et de l’intéraction éléctron-photon dans une cellule photovoltaïque composée d’une boîte quantique connectée à deux nanofils semi-infinis, La simulation numérique a été réalisée sur le cluster de calculs MERLIN (IM2NP). Nous présentons le formalisme de Green en général puis appliqué à cellule. Le fonctionnement général de la cellule est déduit de son diagramme de bande qui comporte des contacts sélectifs. Ensuite, nous présentons les résultats obtenus dans l’approximation de bande plate, qui simplifie le contact aux nanofils. Ceux-ci mettent en lumière des effets intriqués du couplage tunnel (couplage entre la boîte et les nanofils) et du couplage optique (couplage avec la lumière). Nous présentons ensuite un calcul analytique effectué dans le régime de fort couplage tunnel et qui explique le fonctionnement contre-intuitif du couplage tunnel dans ce régime. Nous observons également une transition dans le processus de production du courant entre le régime de fort couplage tunnel et le régime de fort couplage optique. Ensuite, nous sortons de l’approximation de bande plate et découvrons que les effets contre-intuitifs sont toujours valides, même si le modèle analytique lui ne l’est plus. Nous présentons le nouvel effet induit par la nouvelle forme du couplage aux réservoirs hors de l’approximation de bande plate: la courbe courant-tension présente une conductance de shunt négative. Cela n’a jamais été observé dans une cellule photovoltaïque auparavant. Enfin, nous présentons une réalisation possible de notre cellule. / This document present our work on the modeling of quantum transport coupled to electron-photon interaction in a solar cell composed of one quantum dot connected to two semi-infinite quantum wires. The proposed cell based on a dot in a wire, is a concept imagined in order to investigate quantum effects inside 1D structures in contact with 0D ones. The numerical simulation powered on the Merlin cluster (IM2NP) relies on Green’s function formalism. The philosophy of Green’s function formalism is introduced and then applied to the photovoltaic cell. An overview of the functioning of the cell is given. Results on the cell are presented in the wide band limit (approximation that simplifies the contact to wires). We observe an interlinked impact of the tunneling coupling (dot-wires coupling) and the optical coupling (to light) on the current. In the strong tunneling regime, an increase of the tunneling coupling decreases the current and similarly in the strong optical coupling regime, an increase of the optical coupling decreases the current. We investigate the counter-intuitive impact of the tunneling coupling in the strong tunneling regime through analytical calculations, considering only the first loop of the numerical code instead of the whole self-consistent process. We observe a transition in the current creation process while switching from the strong tunneling regime to the strong optical coupling regime. Results on the cell beyond the wide band limit approximation are presented in which the system exhibits another atypical response to illumination: I-V curve exhibits a negative shunt conductance! Finally, a realization proposal for the concept cell is described.

Cette thèse présente des mesures de transport électronique dans des systèmes bi-dimensionels et uni-dimensionels à base de graphène sous champ magnétique pulsé (60T). L'objectif de ces travaux consiste à sonder la dynamique des porteurs de charge en modifiant la densité d'états du système par l'application d'un champ magnétique. Une première partie est consacrée à l'étude de l'influence des îlots électrons-trous sur les propriétés de transport du graphène au voisinage du point de neutralité de charge. Nous avons constaté l'apparition de fluctuations de la magnéto-résistance liée à la transition progressive des îlots de taille finie dans le régime quantique lorsque le champ magnétique augmente. Nous avons aussi montré que la variation de l'énergie de Fermi, liée à l'augmentation de la dégénérescence orbitale des niveaux de Landau, est directement responsable d'une modification du ratio entre électrons et trous. Dans une deuxième partie consacrée à l'étude des nanorubans de graphène, nous avons exploré deux gammes de largeur différentes. Dans les rubans larges (W>60nm), la quantification de la résistance a été observée révélant ainsi une signature évidente de la quantification du spectre énergétique en niveaux de Landau. Le confinement magnétique des porteurs de charge sur les bords des nanorubans a permis de mettre en évidence, pour la première fois, la levée de dégénérescence de vallée liée à la configuration armchair du ruban. Pour des rubans plus étroits (W<30nm), en présence de défauts de bord et d'impuretés chargées, la formation progressive des états de bords chiraux donne lieu à une magnéto-conductance positive quelque soit la densité de porteurs. Enfin, la dernière partie traite du magnéto-transport dans le graphene multi-feuillet. En particulier, nous avons observé l'effet Hall quantique dans les systèmes tri-couche de graphène. Une étude comparative des résultats expérimentaux avec des simulations numériques a permis de déterminer l'empilement rhombohedral des trois couches de graphene constituant l'échantillon / This thesis presents transport measurements on two-dimensional and one-dimensional graphene-based systems under pulsed magnetic field (60T). The objective of this work is to probe the dynamics of charge carriers by changing the density of states of the system by applying a strong magnetic field. The first part is devoted to the study of the influence of electron-hole pockets on the transport properties of graphene near the charge neutrality point. We found the appearance of fluctuations in the magneto-resistance due to the progressive transition of the electron/hole puddles of finite size in the quantum regime as the magnetic field increases. We have also shown that the variation of the Fermi energy, due to the increase of orbital Landau level degeneracy, is directly responsible of a change in the electron and hole ratio. The second part is devoted to the study of graphene nano-ribbons, we explored two different ranges of width. In the broad nano-ribbons of width W larger than 60 nm, the quantification of the resistance is observed, revealing a clear signature of the quantization of the energy spectrum into Landau levels. We show for the first time the effect of valley degeneracy lifting induced by the magnetic confinement of charge carriers at the edges of the armchair nano-ribbons. For narrower nano-ribbons (W <30 nm) in presence of edge defects and charged impurities, the progressive formation of chiral edge states leads to a positive magneto-conductance whatever the carrier density. Finally, the last part of this thesis deals with magneto-transport fingerprints in multi-layer graphene as we observed the quantum Hall effect in tri-layer graphene. A comparative study of the experimental results with numerical simulations was used to determine the rhombohedral stacking of three layers of graphene in the sample

<div>The work involves two new method implementation and application in the Quantum transport community for nano-scale electronic devices. </div><div><br></div><div>First method: Ab-initio Tight-Binding(TB)</div><div> </div><div>As the surfacing of novel 2D materials, layers can be stacked freely on top of each other bound by Van der Waals force with atomic precision. New devices created with unique characteristics will need the theoretical guidance. The empirical tight-binding method is known to have difficulty accurately representing Hamiltonian of the 2D materials. Maximally localized Wannier function(MLWF) constructed directly from ab-initio calculation is an efficient and accurate method for basis construction. Together with NEGF, device calculation can be conducted. The implementation of MLWF in NEMO5 and the application on 2D MOS structure to demystify interlayer coupling are addressed. </div><div> </div><div>Second method: Büttiker-probe Recombination/Generation(RG) method:</div><div><br></div><div>The non-equilibrium Green function (NEGF) method is capable of nanodevice performance predictions including coherent and incoherent effects. To treat incoherent scattering, carrier generation and recombination is computationally very expensive. In this work, the numerically efficient Büttiker-probe model is expanded to cover recombination and generation effects in addition to various incoherent scattering processes. The capability of the new method to predict nanodevices is exemplified with quantum well III-N light-emitting diodes and photo-detector. Comparison is made with the state of art drift-diffusion method. Agreements are found to justify the method and disagreements are identified attributing to quantum effects. </div><div><br></div><div>The two menthod are individually developed and utilized together to study BP/MoS2 interface. In this vertical 2D device, anti-ambipolar(AAP) IV curve has been identified experimentally with different explanation in the current literature. An atomistic simulation is performed with basis generated from density functional theory. Recombination process is included and is able to explain the experiment findings and to provide insights into 2D interface devices.</div><div><br></div><div> </div>

Carbon-based conductors like carbon nanotubes (CNTs) and graphene nanoribbons (GNRs) have many properties, which make them relevant for potential electronic applications. Among them are high conductances and tunable band gap sizes. These properties make CNTs and GNRs useful in many circumstances, e.g. as channel material in transistors or transparent electrodes in solar cells. Plenty of literature can be found on the topic of single linear CNTs/GNRs. Some applications however require a large network of these conductors. In addition, a single conductor has only a small impact on the network conductance, which reduces the need to control the properties of each individual nanotube/-ribbon. This leads to networks being easier to apply. In this work, the conductance of large networks of GNRs is calculated using the quantum-transport formalism (QT). This has not been done before in literature. In order to apply QT to such a large amount of atoms, the recursive Green's function formalism is used. For this the networks are devided into subcells, which are represented by tight-binding matrices. Similar networks are also examined using two different nodal analysis (NA) approaches, where the nanoribbons are treated as ohmic conductors. For NA with one-dimensional conductors, major discrepancies are found in regards to the QT model. However, networks consisting of two-dimensional conductors (NA-2D) have many properties similar to the QT networks. A recipe to approximate the QT results with NA-2D is presented.:1. Introduction 2. Theoretical Principles 2.1 Carbon-based Conductors 2.1.1 Structure and Properties 2.1.2 Networks 2.2 Tight-Binding Model 2.3 Quantum Transport 2.3.1 Introduction 2.3.2 Level Broadening 2.3.3 Current Flow 2.3.4 Transmission 2.4 Nodal Analysis 3. Implementation 3.1 Quantum Tranport 3.1.1 Network Generation 3.1.2 Density-Functional based Tight-Binding Method 3.1.3 Recursive Green's Function Algorithm 3.1.4 Conductance 3.2 Nodal Analysis 3.2.1 One-dimensional Conductors 3.2.2 Two-dimensional Conductors 4. Results 4.1 Quantum Transport 4.1.1 Band Structures and Fermi Energies 4.1.2 Ideal Transmission and Consistency Tests 4.1.3 Percolation 4.1.4 Transmission 4.1.5 Conductance 4.1.6 Power Law Scaling 4.1.7 Size Dependence and Confinement Effects 4.1.8 Calculation Time 4.2 Nodal Analysis 4.2.1 One-dimensional Conductors 4.2.2 Two-dimensional Conductors 4.2.3 Calculation Time 4.3 Approximating QT with NA 4.3.1 Optimal Parameters 4.3.2 Percolation 4.3.3 Conductance 4.3.4 Power Law Scaling 5. Conclusions / Graphenbasierte Leiter wie Kohlenstoff-Nanoröhrchen (engl. 'carbon nanotubes', CNTs) oder Graphen-Nanobänder (engl. 'graphene nanoribbons', GNRs) haben viele Eigenschaften, die sie für potenzielle elektronische Anwendungen interessant machen. Darunter sind hohe Leitfähigkeiten und einstellbare Bandlückengrößen. Dadurch sind CNTs und GNRs in vielen Bereichen nützlich, z.B. als Kanalmaterial in Transistoren oder als transparente Elektroden in Solarzellen. Es gibt viel Literatur über einzelne, lineare CNTs/GNRs. Einige Anwendungen benötigen jedoch ein großes Netzwerk dieser Leiter. Zusätzlich hat ein einzelner Leiter wenig Einfluss auf die Leitfähigkeit des Netzwerks, wodurch die Eigenschaften der einzelnen Nanoröhrchen/-streifen weniger streng kontrolliert werden müssen. Dies führt dazu, dass es einfacher ist Netzwerke zu nutzen. In dieser Arbeit wird die Leitfähigkeit von großen GNR-Netzwerken mittels Quantentransport (QT) berechnet. Dies wurde in der Literatur noch nicht getan. Um QT auf eine so große Menge an Atomen anzuwenden wird der rekursive Greenfunktions-Formalismus benutzt. Dazu werden die Netzwerke in Unterzellen unterteilt, die durch Tight-Binding-Matrizen dargestellt werden. Ähnliche Netzwerke werden auch mit zwei Versionen der Knotenanalyse (engl. 'nodal analysis', NA) untersucht, welche die Nanobänder wie ohmische Leiter behandelt. Die Ergebnisse der NA mit eindimensionalen Leitern weisen deutliche Unterschiede zu den mit QT erzielten Ergebnissen auf. Wenn jedoch zweidimensionale Leiter in NA verwendet werden (NA-2D) gibt es viele parallelen zu den QT Ergebnissen. Zuletzt wird ein Vorgehen präsentiert, mit dem QT Resultate durch NA-2D Rechnungen genähert werden können.:1. Introduction 2. Theoretical Principles 2.1 Carbon-based Conductors 2.1.1 Structure and Properties 2.1.2 Networks 2.2 Tight-Binding Model 2.3 Quantum Transport 2.3.1 Introduction 2.3.2 Level Broadening 2.3.3 Current Flow 2.3.4 Transmission 2.4 Nodal Analysis 3. Implementation 3.1 Quantum Tranport 3.1.1 Network Generation 3.1.2 Density-Functional based Tight-Binding Method 3.1.3 Recursive Green's Function Algorithm 3.1.4 Conductance 3.2 Nodal Analysis 3.2.1 One-dimensional Conductors 3.2.2 Two-dimensional Conductors 4. Results 4.1 Quantum Transport 4.1.1 Band Structures and Fermi Energies 4.1.2 Ideal Transmission and Consistency Tests 4.1.3 Percolation 4.1.4 Transmission 4.1.5 Conductance 4.1.6 Power Law Scaling 4.1.7 Size Dependence and Confinement Effects 4.1.8 Calculation Time 4.2 Nodal Analysis 4.2.1 One-dimensional Conductors 4.2.2 Two-dimensional Conductors 4.2.3 Calculation Time 4.3 Approximating QT with NA 4.3.1 Optimal Parameters 4.3.2 Percolation 4.3.3 Conductance 4.3.4 Power Law Scaling 5. Conclusions

Das Transport- und Relaxationsverhalten verschiedener Quantenmodelle wird untersucht. Den ersten Teil der vorliegenden Arbeit bildet die Untersuchung der Transporteigenschaften von speziellen finiten modularen Quantensystemen bzgl. einer Boltzmann-Gleichung (BG). Diese Systeme, in denen unter bestimmten Bedingungen diffusiver Transport beobachtet werden kann, wurden mit verschiedenen Methoden zur Beschreibung von Quantentransport untersucht. Dabei zeigt sich, dass sich das diffusive Transportverhalten in diesen Systemen aus der zugrunde liegenden Schrödinger Dynamik heraus beschreiben lässt. Ob die diffusive Dynamik in diesen Systemen ebenfalls auf der Basis einer BG beschrieben werden kann, wird analytisch und numerisch untersucht. Im zweiten Teil wird die Relaxationsdynamik in quantenmechanischen Vielteilchensystemen untersucht. Speziell wird versucht, die Lebensdauern von angeregten Elektronen (Löchern) in Metallen, welche mit dem Fermi-See der Elektronen wechselwirken, mittels der zeitfaltungsfreien Projektionsoperator-Methode (TCL) zu bestimmen. Letztere liefert einen analytischen Ausdruck für die Dämpfungsrate (inverse Lebensdauer), welche temperaturabhängig ist und im Rahmen von Standard-Streuprozessen interpretiert werden kann. Um dieses analytische Ergebnis zu testen, wird es angewendet, um die Lebensdauern angeregter Elektronen (Löcher) in Aluminium zu bestimmen, für das ein Jellium Modell verwendet wird. Die Ergebnisse, die man über Monte-Carlo-Integration erhält, werden mit experimentellen und theoretischen Daten aus Selbstenergie-Rechnungen verglichen. Des Weiteren werden die Lebensdauern angeregter Elektronen in Kupfer ermittelt, für das ein Tight-Binding-Modell verwendet wird.

Our everyday experiences teach us that any imbalance like temperature gradients, non-uniform particle-densities etc. will approach some equilibrium state if not subjected to any external force. Phenomenological descriptions of these empirical findings reach back to the 19th century where Fourier and Fick presented descriptions of relaxation for macroscopic systems by stochastic approaches. However, one of the main goals of thermodynamics remained the derivation of these phenomenological description from basic microscopic principles. This task has gained much attraction since the foundation of quantum mechanics about 100 years ago. However, up to now no such conclusive derivation is presented. In this dissertation we will investigate whether closed quantum systems may show equilibration, and if so, to what extend such dynamics are in accordance with standard thermodynamic behavior as described by stochastic approaches. To this end we consider i.a. Markovian dynamics, Fokker-Planck and diffusion equations. Furthermore, we consider fluctuation theorems as given e.g. by the Jarzynski relation beyond strict Gibbsian initial states. After all we find indeed good agreement for selected quantum systems.

We present a novel approach to the investigation of transport coefficients in condensed matter systems, which is based on a pertinent time-convolutionless (TCL) projection operator technique. In this context we analyze in advance the convergence of the corresponding perturbation expansion and the influence of the occurring inhomogeneity. The TCL method is used to establish a formalism for a consistent derivation of a Boltzmann equation from the underlying quantum dynamics, which is meant to apply to non-ideal quantum gases. We obtain a linear(ized) collision term that results as a finite non-singular rate matrix and is thus adequate for further considerations, e.g., the calculation of transport coefficients. In the work at hand we apply the provided scheme to numerically compute the diffusion coefficient of an atomic wire and especially analyze its dependence on certain model properties, in particular on the width of the wire.

Questa tesi di dottorato studia l’interazione della cooperatività con il rumore in sistemi realistici, focalizzandosi principalmente sulla superradianza. Gli effetti cooperativi emergono dall’interazione collettiva di un insieme di elementi con un campo esterno. Esempi degni di nota sono la superconduttività, dove le coppie di Cooper elettroniche interagiscono con le vibrazioni reticolari, le eccitazioni di plasma, che sorgono dall'interazione collettiva degli elettroni in un metallo con il campo coulombiano, e la superradianza, ovvero quel processo di emissione spontanea cooperativa che sorge da un aggregato di emettitori identici. Gli effetti cooperativi sono tipicamente robusti al disordine e al rumore, cosa che li rende interessanti per delle applicazioni a dispositivi quantistici che possano operare a temperatura ambiente. In questo lavoro, inizialmente, introduciamo un formalismo di “master equations” che descrive l’accoppiamento collettivo di un aggregato di emettitori/assorbitori con il campo elettromagnetico, valido quando le dimensioni dell'aggregato sono sia maggiori che minori della lunghezza d’onda emessa/assorbita. Inoltre, il formalismo è valido per accoppiamento sia debole che forte con il campo elettromagnetico e, cosa più importante, permette di descrivere correttamente la superradianza in diversi regimi. In tale formalismo, studiamo l’interazione tra superradianza e rumore termico sia per nanotubi molecolari (di dimensioni minori della lunghezza d’onda associata alla transizione) che sono presenti nei complessi antenna fotosintetici dei Green Sulfur Bacteria, sia pure per superreticoli di quantum dots di nuova generazione, aventi dimensioni maggiori della lunghezza d’onda emessa. In entrambi i casi si dimostra che la coerenza può permanere in presenza di rumore termico alle temperature a cui questi sistemi sono stati analizzati sperimentalmente (temperatura ambiente per i nanotubi molecolari, e 6 K per i superreticoli di quantum dots). Nello specifico, nei nanotubi molecolari mostriamo che la macroscopica delocalizzazione coerente delle eccitazioni a temperatura ambiente, che copre centinaia di molecole, può essere considerata un effetto emergente che origina dall’effetto combinato della specifica disposizione geometrica delle molecole e della presenza di accoppiamenti tra subunità del cilindro, incrementati dagli effetti cooperativi. Questi risultati aprono la strada a nuovi modi per ingegnerizzare dei “quantum wires” robusti al rumore grazie alla cooperatività. Inoltre, la presente analisi di sistemi allo stato solido basati su superreticoli di “quantum dots” di perovskite (CsPbBr3) fornisce una base teorica in grado di comprendere recenti osservazioni di emissione superradiante. Sulla base della nostra teoria, suggeriamo che futuri esperimenti dove si utilizzino quantum dots più piccoli, potrebbe aumentare significativamente la robustezza del sistema al rumore termico, aprendo la strada verso la superradianza a temperatura ambiente in sistemi allo stato solido. Si considerano anche i complessi antenna dei Purple Bacteria, dove è ben risaputo che gli effetti cooperativi incrementano il trasferimento e l’accumulo di eccitazioni generate dalla luce assorbita. Mostriamo come queste proprietà possono essere sfruttate per creare un laser ispirato a sistemi biologici e basato su aggregati molecolari, dove la luce solare, benché debole, sarebbe utilizzata come sorgente di pompaggio. Il trasferimento efficiente di energia dentro questo sistema, all’atto pratico, focalizzerebbe l’eccitazione assorbita in direzione di un dimero molecolare, composto da una coppia di molecole interagenti, opportunamente scelte. L’orientazione dei momenti di dipolo di transizione in ciascun dimero è tale da concentrare tutta l’intensità del dipolo nel livello a più alta energia, lasciando lo stato eccitonico inferiore otticamente inattivo. Un dimero molecolare in tale configurazione, che è ideale per ottenere inversione di popolazione, è chiamato “H-dimer”. Tale H-dimer, nell’archittettura qui proposta per un laser ispirato a sistemi biologici, è posto al centro di un aggregato molecolare ispirato a sistemi biologici. Gli H-dimers, eccitati dagli aggregati molecolari circostanti, raggiungono inversione di popolazione e, dunque, possono emettere luce laser quando tali aggregati sono posti in una cavità ottica. Convertire l’energia incoerente fornita dal Sole in un fascio laser coerente supererebbe diverse limitazioni pratiche inerenti all’utilzzo della luce solare come sorgente di energia pulita. Per esempio, i fasci laser sono molto efficienti nell’avviare reazioni chimiche che convertono la luce solare in energia chimica. Inoltre, dal momento che i complessi fotosintetici batterici tendono ad operare nella regione spettrale del vicino infrarosso, la nostra proposta si presta in modo naturale a realizzare laser a infrarossi a corta lunghezza d’onda, i cui fasci viaggerebbero per lunghe distanze senza quasi perdere energia, quindi distribuendo in modo efficiente l’energia solare raccolta. Nella ricerca di un meccanismo comune alla cooperatività e alla sua robustezza, abbiamo confrontato il modello delle coppie di Cooper della superconduttività con la superradianza in singola eccitazione, mostrando molte somiglianze tra i due fenomeni: in particolare, i sistemi superradianti presentano una “gap” immaginaria nel piano complesso (ovvero, una segregazione tra i tempi di vita degli autostati del sistema) che, in modo simile alla gap superconduttiva, rende questi sistemi robusti al rumore statico. Più in generale, mostriamo che ogni interazione a lungo raggio tra i costituenti di un sistema induce effetti collettivi, manifestati da delle gap nello spettro eccitonico. Perciò, la nostra analisi successiva considera l’effetto delle interazioni a lungo raggio sul trasporto eccitonico lungo catene disordinate. Dimostriamo che la presenza di uno stato collettivo ben separato dagli altri stati influenza tutto lo spettro del sistema, generando dei regimi molto controintuitivi dove il trasporto è incrementato dal disordine o è indipendente da esso, e tali regimi si estendono su molti ordini di grandezza nell’intensità del disordine. Dimostriamo anche che una catena fortemente accoppiata a un modo del campo elettromagnetico in una cavità ottica è equivalente a una catena con interazione a lungo raggio, mostrandosi dunque molto promettente per esperimenti e applicazioni future. Nello specifico, mostriamo che catene molecolari realistiche, ioni intrappolati realizzati allo stato dell’arte e atomi di Rydberg sono tutti in grado di raggiungere l’intensità di interazione a lungo raggio tale per cui il trasporto sarebbe incrementato dal disordine o indipendente da esso, puntando alla realizzazione di un trasporto di energia senza dissipazione in “quantum wires” disordinati. / This Ph.D. thesis studies the interplay of cooperativity and noise in realistic systems, largely focusing on superradiance. Cooperative effects emerge from the collective interaction of an ensemble of elements to an external field. Notable examples are superconductivity, where the electron Cooper pairs interact with the lattice vibrations, plasmon excitations, arising from the collective interaction of electrons in a metal with the Coulomb field, and superradiance, that is a cooperative spontaneous emission process stemming from an aggregate of identical emitters. Cooperative effects are typically robust to disorder and noise, making them interesting for applications to quantum devices operating at room temperature. In this work, we first present a general master equation formalism that describes the collective coupling of an aggregate of emitters/absorbers to the electromagnetic field, valid both when the size of the aggregate is larger or smaller than the emitted/absorbed wavelength. Also, the formalism is valid both for weak and strong coupling of the emitters to the electromagnetic field and, most importantly, it allows to correctly describe superradiance in different regimes. Within such formalism, the interplay of superradiance and thermal noise is studied both for molecular nanotubes (of size smaller than the transition wavelength) that are present in the antenna complexes of photosynthetic Green Sulfur Bacteria, and also for novel solid state quantum dot superlattices, having size larger than the emitted wavelength. In both cases it is shown that coherence can persist in presence of thermal noise at the temperatures where these systems have been experimentally analyzed (room temperature for molecular nanotubes, and 6 K for quantum dot superlattices). Specifically, in natural molecular nanotubes we show that the macroscopic coherent delocalization of the excitation at room temperature, covering hundreds of molecules, can be considered an emergent effect originating from the combined effect of the specific geometric disposition of the molecules and the presence of cooperatively enhanced couplings between cylinder subunits. These results open the path to new ways of engineering quantum wires robust to noise thanks to cooperativity. Moreover, our analysis of solid state systems based on perovskite (CsPbBr3) quantum dot superlattices provides a theoretical framework able to explain recent observations of superradiant emission. Based on our theory, we suggest that further experiments, using smaller quantum dots, could significantly increase the robustness of the system to thermal noise, paving the way towards room-temperature superradiance in solid-state systems. We also considered the antenna complexes of Purple Bacteria, where cooperative effects are well known to boost the transfer and storage of photo-absorbed excitations. We show how these properties can be exploited to create a bio-inspired molecular aggregate laser medium, where natural sunlight, although weak, would be used as a pumping source. The efficient energy transfer within this system would effectively focus the absorbed excitation on a suitably chosen molecular dimer, composed by a pair of interacting molecules. The orientation of the molecule transition dipole moment in each dimer is such to concentrate all the dipole strength in the highest energy level, leaving the lower excitonic state dark. A molecular dimer in such configuration, which is ideal to achieve population inversion, is called H-dimer. Such an H-dimer in our proposed architecture for a bio-inspired laser medium, is placed at the center of the bio-inspired molecular aggregates. The H-dimers, pumped by the surrounding molecular aggregates, reach population inversion and, therefore, can lase when such aggregates are placed in an optical cavity. Turning the incoherent energy supply provided by the Sun into a coherent laser beam would overcome several of the practical limitations inherent in using sunlight as a source of clean energy. For example, laser beams are highly effective at driving chemical reactions which convert sunlight into chemical energy. Further, since bacterial photosynthetic complexes tend to operate in the near-infrared spectral region, our proposal naturally lends itself for realising short-wavelength infrared lasers which would allow their beams to travel nearly losslessly over large distances, thus efficiently distributing the collected sunlight energy. In search of a common mechanism to cooperativity and its robustness, we have compared the Cooper pair model of superconductivity and single-excitation superradiance, showing many similarities between the two: in particular, superradiant systems present an imaginary gap in the complex plane (that is, a segregation between the lifetimes of the system eigenstates) that, similarly to the superconducting gap, makes these systems robust to static disorder. More in general, we show that any long-range interaction between the constituents of a system generates collective behaviours, manifested by gaps in the excitonic spectrum. Therefore, our further analysis considers the effect of long-range interactions on excitation transport along disordered chains. We show that the presence of a gapped, collective state affects the whole spectrum of the system, generating quite counter-intuitive disorder-enhanced and disorder-independent transport regimes, that extend over many orders of magnitude of the disorder strength. We also prove that a chain strongly coupled to a cavity mode is equivalent to a long-range interacting chain, thus being very promising for future experiments and applications. Specifically, we show that realistic molecular chains, state-of-the-art trapped ions and Rydberg atoms are all able to reach the needed long-range interaction strength that would show disorder-enhanced or disorder-independent transport, aiming to the realization of dissipationless transport of energy in disordered quantum wires.

<p dir="ltr">Photovoltaics are leading devices in green energy production. Understanding the fundamental physics behind energy transport in candidate materials for future photovoltaic and optoelectronic devices is necessary to both realize material limitations and improve efficiency. Excitons, which are bound electron-hole pairs, are central to determining how energy propagates throughout semiconductors. Exciton transport is greatly influenced by material dimensionality. In highly ordered quantum dot (QD) systems, electronic coupling between individual QDs can lead to coherent exciton transport, whereas in two-dimensional heterostructures, excitons can form at the interface of a heterojunction, creating charge-transfer excitons.</p><p dir="ltr">This dissertation is dedicated to summarizing the studies of exciton transport and behavior in two systems: perovskite QD superlattices and transition metal dichalcogenide (TMDC)/polyacene heterostructures. Chapter 1 provides readers with details on these materials in addition to information on the fundamental concepts (i.e., excitons, phonons, energy transfer) needed to best appreciate further chapters. Chapter 2 summarizes the spectroscopic techniques (photoluminescence and transient absorption spectroscopy and microscopy) used to examine exciton behavior. Next, the effects of disorder and dephasing pathways on the ability of perovskite QDs to coherently couple is investigated through the lens of superradiance in Chapter 3. After this, the temperature-dependent exciton transport within perovskite QD superlattices is imaged with high spatial and temporal resolutions in Chapter 4. The experimental transport data on these superlattices provides evidence for environment-assisted quantum transport, which, until this study, had yet to be realized in solid-state systems. In Chapter 5, attention is switched to verifying the existence and deepening the understanding of the behavior of several spatially separated interlayer excitons in a tungsten disulfide/tetracene heterostructure. Finally, Chapter 6 summarizes the preliminary results obtained through transient absorption spectroscopy on other TMDC/polyacene heterostructures where separation of the triplet pair state is attempted. </p><p dir="ltr">It is this author’s hope that this dissertation will not only summarize their graduate work but will also serve as inspiration for others to continue learning and contribute to the advancement of the energy research field.</p>