High-mobility graphene in 2D periodic potentials

This work focuses on hBN-graphene van der Waals heterostructures and their investigation via transport experiments. In this way, we could probe and characterize different commensurability effects stemming from the induced superlattice potential and report their influence on transport properties in graphene. The encapsulation of graphene between hBN significantly increases the bulk carrier mobility of graphene and were able to investigate interaction-driven quantum Hall effects, such as quantum Hall ferromagnetism and the fractional quantum Hall effect. Any further top-down patterning steps do not necessarily degrade the intrinsic quality of the graphene sheet. The high sample quality can be preserved in graphene-based antidot lattices and we successfully probed pronounced commensurability features in antidot arrays. Moreover, we study the interplay between a moiré and an imposed antidot superlattice potential and discuss their influence on magnetotransport measurements. In the end, we discuss a new method for imposing lateral superlattice potentials, employing a local few-layer graphene patterned bottom gate. In this way, we are able to report Weiss oscillations in the weakly modulated unipolar regime and antidot peaks for strong modulation in a bipolar gate configuration

Strong coupling regime of semiconductor quantum dot embedded in the nano-cavity

Photonic lattices represent suitable systems for investigation of wave propagation in periodic structures [1]. However, different unavoidable defects may arise either during their process of fabrication or as result of misusage, accidental damage, etc. Although undesirable in the first place, these imperfections enable the existence of different types of stable, localized defect modes [2]. In this paper, we investigate light propagation through composite photonic lattice composed of two identical linear and lossless lattices. The interface between them represents a geometric defect, while each lattice contains a single nonlinear defect that is placed symmetrically with respect to the interface. Depending on the input light beam parameters (its position, width and transverse tilt), the width of geometric defect, strength and position of the nonlinear defects, different dynamical regimes have been identified. These dynamical regimes are caused by the balance of photonic lattice potentials’ contributions originating from the presence of the geometric and two nonlinear defects. We have found numerically conditions under which dynamically stable bounded modes can exist in the area between nonlinear defects or between a nonlinear and a geometric defect. Various types of localized modes such as: two-hump, multi-hump, one- and multicomponent moving breathers localized at a certain area among defects have been observed. The parameters can be adjusted to capture light and to prevent light launched inside the area among defects to leave it, i.e. this corresponds to the appearance of the modes trapped inside this area. Since the configuration of the lattice prevents transmission of the light through the area confined by defects, these modes can formally be related to Fano resonances and Fano- blockade [3, 4]. When light is launched outside the area among defects, different dynamical regimes have been distinguished: total reflection, single and double partial reflection and full transmission through the area among defects. These numerical findings may lead to interesting applications such as blocking, filtering and transporting light beams through the optical medium. Photonic devices based on resonant tunneling such as waveguides interacting through the area between defects, may be applied as add-drop filters.V International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 and the Second international workshop "Control of light and matter waves propagation and localization in photonic lattices" : PHOTONICA2015 : book of abstracts; August 24-28, 2015; Belgrad

Linear scaling quantum transport methodologies

Altres ajuts: SR, AWC and JHG acknowledge PRACE and the Barcelona Supercomputing Center (Project No. 2015133194). ICN2 is funded by the CERCA Programme/Generalitat de Catalunya.In recent years, predictive computational modeling has become a cornerstone for the study of fundamental electronic, optical, and thermal properties in complex forms of condensed matter, including Dirac and topological materials. The simulation of quantum transport in realistic models calls for the development of linear scaling, or order-N, numerical methods, which then become enabling tools for guiding experimental research and for supporting the interpretation of measurements. In this review, we describe and compare different order-N computational methods that have been developed during the past twenty years, and which have been used extensively to explore quantum transport phenomena in disordered media. We place particular focus on the zero-frequency electrical conductivities derived within the Kubo-Greenwood​ and Kubo-Streda formalisms, and illustrate the capabilities of these methods to tackle the quasi-ballistic, diffusive, and localization regimes of quantum transport in the noninteracting limit. The fundamental issue of computational cost versus accuracy of various proposed numerical schemes is addressed in depth. We then illustrate the usefulness of these methods with various examples of transport in disordered materials, such as polycrystalline and defected graphene models, 3D metals and Dirac semimetals, carbon nanotubes, and organic semiconductors. Finally, we extend the review to the study of spin dynamics and topological transport, for which efficient approaches for calculating charge, spin, and valley Hall conductivities are described

Fermionic Quantum Information in Surface Acoustic Waves

Quantum computers are on the verge of revolutionising modern technology by providing scientists with unparalleled computational resources. With quantum-mechanical phenomena such as the superposition principle and entanglement, these computers could solve certain computational problems that are otherwise impossible for even the most powerful classical supercomputers. One of the major challenges standing in the way of this computing revolution is the accurate control of quantum bits. Quantum systems are extremely fragile and, by their nature, cannot be measured without destroying their quantum state. I wrote a numerical program to solve the time-dependent Schrödinger equation, the differential equation that describes the evolution of wave functions. The advantage of my code over other solvers is its speed. I used graphics processing units (GPUs), a technology that has only recently matured, to accelerate high-performance computing. Hardware- acceleration allows me to solve complex time-evolution problems within days rather than years. Such an exceptional speedup has enabled me to calculate the behaviour of single electrons in semiconductor devices. Electrons are particularly interesting because they are ubiquitous in modern technology, as well as being fundamental quantum particles. Using the simulations produced by my code, I track the time evolution of an electron wave function as it propagates along quantum circuits. By animating the evolution of the wave function, I am able to visualise the wave function of electrons propagating in space and time. This is a remarkable tool for studying the behaviour of quantum particles in nanodevices. I focused my thesis on the realistic modelling of devices that are readily available in a laboratory or on designs that could be fabricated in the near future. I began by modelling single electrons as quantum bits. I provide a definition for an optimal qubit and lay out the set of operations required to manipulate the quantum information carried by the electron. In all my simulations, I aim to model experimentally realistic devices. I calculated the electrostatic potential of a real nanodevice and simulated the time-evolution of a single electron. I show that it is possible to create a single-electron beam splitter by tuning the voltages applied to various parts of the device and I calculate the range of voltages in which quantum information is preserved and manipulated accurately. These results were verified experimentally by collaborators at the Institut Néel and were published in Nature Communications 10, 4557 (2019). Using my code, I developed a framework for general measurements of electron qubits and provided a design for a semiconductor device capable of performing positive-operator valued measures (POVMs). A POVM is a powerful measurement technique in quantum mechanics that allows quantum information to be manipulated in interesting ways. The proposed setup is suggested as an implementation of entanglement distillation, which is a useful error correction tool that transforms an arbitrary entangled state into a pure Bell pair. Entanglement is one of the most fascinating aspects of quantum mechanics and it remains a challenge to generate perfectly entangled particle pairs. An experimentally viable method for distilling – or perfecting – entanglement is crucial for the design of quantum computers or quantum communication systems. Using this design, I introduced a protocol to use electrons, rather than photons, in quantum-optics-like systems. These results were published in Phys. Rev. A 96, 052305 (2017). Going beyond single-particle behaviour, I compare different methods for generating entanglement between electron-spin qubits using the power-of-SWAP operation. By using realistic experimental parameters in my simulations, I demonstrate that generating entan- glement via electron-electron collisions in a harmonic channel cannot be implemented for multidimensional systems. These findings go against what researchers thought was possible and put forward the need for new solutions to particle entanglement. I provide an alternative by demonstrating that a method based on the exchange energy is more viable than previously thought. I present a semiconductor device structure and an electrostatic potential that experi- mental groups can use in order to obtain the most efficient entangling quantum logic gates. These findings were published in Phys. Rev. A 101, 022329 (2020). The results presented in this thesis provide a comprehensive description of the control of single electrons in a surface-acoustic-wave-based quantum circuit. However, work in this field is far from over. I present various research paths for future projects. These include going beyond the time-dependent Schrödinger equation to capture more complicated dynamics, using different hardware solutions to further accelerate numerical problem solving, and studying new systems of interest to extend this project beyond semiconductor physics.In all my simulations, I aim to model experimentally realistic devices. I calculated the electrostatic potential of a real nanodevice and simulated the time-evolution of a single electron. I show that it is possible to create a single-electron beam splitter by tuning the voltages applied to various parts of the device and I calculate the range of voltages in which quantum information is preserved and manipulated accurately. These results were verified experimentally by collaborators at the Institut Néel and were published in Nature Communications 10, 4557 (2019). Using my code, I developed a framework for general measurements of electron qubits and provided a design for a semiconductor device capable of performing positive-operator valued measures (POVMs). A POVM is a powerful measurement technique in quantum mechanics that allows quantum information to be manipulated in interesting ways. The proposed setup is suggested as an implementation of entanglement distillation, which is a useful error correction tool that transforms an arbitrary entangled state into a pure Bell pair. Entanglement is one of the most fascinating aspects of quantum mechanics and it remains a challenge to generate perfectly entangled particle pairs. An experimentally viable method for distilling – or perfecting – entanglement is crucial for the design of quantum computers or quantum communication systems. Using this design, I introduced a protocol to use electrons, rather than photons, in quantum-optics-like systems. These results were published in Phys. Rev. A 96, 052305 (2017). Going beyond single-particle behaviour, I compare different methods for generating entanglement between electron-spin qubits using the power-of-SWAP operation. By using realistic experimental parameters in my simulations, I demonstrate that generating entan- glement via electron-electron collisions in a harmonic channel cannot be implemented for multidimensional systems. These findings go against what researchers thought was possible and put forward the need for new solutions to particle entanglement. I provide an alternative by demonstrating that a method based on the exchange energy is more viable than previously thought. I present a semiconductor device structure and an electrostatic potential that experi- mental groups can use in order to obtain the most efficient entangling quantum logic gates. These findings were published in Phys. Rev. A 101, 022329 (2020). The results presented in this thesis provide a comprehensive description of the control of single electrons in a surface-acoustic-wave-based quantum circuit. However, work in this field is far from over. I present various research paths for future projects. These include going beyond the time-dependent Schrödinger equation to capture more complicated dynamics, using different hardware solutions to further accelerate numerical problem solving, and studying new systems of interest to extend this project beyond semiconductor physics.The Institute of Physics Horizon 2020 Marie Skłodowska Curie Actions Fonds de Recherche du Québec – Nature et technologies St Edmund’s College, Cambridge Canadian Imperial Bank of Commerce Canadian Centennial Scholarship Fund Institute of Engineering and Technolog

Local measurements of cyclotron states in graphene

Multilayer epitaxial graphene has been shown to contain "massless Dirac fermions" and is believed to provide a possible route to industrial-scale graphene electronics. We used scanning tunneling microscopy (STM) and spectroscopy (STS) in high magnetic fields to obtain local information on these fermions. A new STS technique was developed to directly measure graphene's energy-momentum relationship and resulted in the highest precision measurement of graphene's Dirac cone. STS spectra similar to ideal graphene were observed, but additional anomalies were also found. Extra peaks and an asymmetry between electron and hole states were shown to be caused by the work function difference between the Iridium STM tip and graphene. This tip effect was extracted using modeled potentials and performing a least square fit using degenerate perturbation theory on graphene's eigenstates solved in the symmetric gauge. Defects on graphene were then investigated and magnetic field effects were shown to be due to a mixture of potential effect from defects and the tip potential. New defect states were observed to localize around specific defects, and are believed to interact with the STM tip by Stark shifting in energy. This Stark shift gives a direct measurement of the capacitive coupling between the tip and graphene and agrees with the modeled results found when extracting the tip potential.Ph.D.Committee Chair: First, Phillip; Committee Member: Jiang, Zhigang; Committee Member: Kindermann, Markus; Committee Member: Stroscio, Joseph,; Committee Member: Zangwill, Andre

Photo-magnonics in two-dimensional antidot lattices

Wesentlicher Gegenstand der vorliegenden (kumulativen) Dissertation ist die ausschließlich optische Erzeugung und Detektion sowie gezielte Manipulation magnetischer Anregungen, sogenannter Spinwellen oder Magnonen. Insbesondere werden die Mechanismen und Prozesse diskutiert, die zur Beobachtung wohldefinierter Spinwellenmoden in dünnen magnetischen Filmen führen, nachdem ein intensiver, ultrakurzer Laserpuls absorbiert wurde. Eine langreichweitig geordnete, periodische Strukturierung der magnetischen Filme (in diesem Fall mit Löchern) ist sodann gleichbedeutend mit der Schaffung magnetischer Metamaterialien (d.h. magnonischer Kristalle). Abhängig von Wirtsmaterial (Nickel oder Kobalt-Eisen-Bor) und strukturellen Eigenschaften der Lochgitter (Periodizität, strukturelle Einheit) ist die Erzeugung oder Unterdrückung bestimmter magnetischer Moden möglich. So führt die vergleichsweise große intrinsische magnetische Dämpfung in Nickel zur Ausbildung lokalisierter Spinwellen, während wegen der geringen Dämpfung in Kobalt-Eisen-Bor ausgedehnte Blochwellen beobachtet werden. Deren Wellenlänge ist zudem einstellbar mittels der Periodizität des Metamaterials und wird anhand numerischer Berechnungen der (magnonischen) Bandstrukturen nachvollzogen. Zuletzt werden auf Basis dieser Ergebnisse mögliche Anwendungen magnonischer Kristalle diskutiert. Hierbei liegt ein Schwerpunkt auf anisotropen Lochgittern und deren Perspektive als Spinwellenfilter

Topology and interaction effects in one-dimensional systems

With the discovery of the integer quantum Hall effect by von Klitzing and collaborators in 1980, the mathematical field of topology entered the world of condensed matter physics. Almost three decades later, this eventually led to the theoretical prediction and the experimental realization of many intriguing topological materials and topology-based devices. In this Ph.D. thesis, we will study the interplay between topology and another key topic in condensed matter physics, namely the study of inter-particle interactions in many-body systems. This interplay is analyzed from two different perspectives. Firstly, we studied how the presence of electron-electron interactions affects single-electron injection into a couple of counter-propagating one-dimensional edge channels. The latter appear at the edges of topologically non-trivial systems in the quantum spin Hall regime and they can also be engineered by exploiting the integer quantum Hall effect. Because of inter-channel interactions, the injected electron splits up into a couple of counter-propagating fractional excitations. Here, we carefully study and discuss their properties by means of an analytical approach based on the Luttinger liquid theory and the bosonization method. Our results are quite relevant in the context of the so-called electron quantum optics, a fast developing field which deeply exploits the topological protection of one-dimensional edge states to study the coherent propagation of electrons in solid-state devices. As an aside, we also showed that similar analytical techniques can also be used to study the time-resolved dynamics of a Luttinger liquid subject to a sudden change of the interaction strength, a protocol known as quantum quench which is gaining more and more attention, especially within the cold-atoms community. Secondly, we study how inter-particle interactions can enhance the topological properties of strictly one-dimensional fermionic systems. More precisely, the starting point is the seminal Kitaev chain, a free-fermionic lattice model which hosts exotic Majorana zero-energy modes at its ends. The latter are extremely relevant in the context of topological quantum computation because of their non-Abelian anyonic exchange statistics. Here we show that, by properly adding electron-electron interactions to the Kitaev chain, it is possible to obtain lattice models which feature zero-energy parafermionic modes, an even more intriguing generalization of Majoranas. To this end, we develop at first an exact mapping between Z4 parafermions and ordinary fermions on a lattice. We subsequently exploit this mapping to analytically obtain an exactly solvable fermionic model hosting zero-energy parafermions. We study their properties and numerically investigate their signatures and robustness even when parameters are tuned away from the exactly solvable point

Advanced Quantum Electronic and Spin Systems: Artificial Graphene and Nitrogen-Vacancy Centers in Diamond

When nature is observed at the nanoscale, quantum physics is typically the most accurate model to describe and predict its behavior. Furthermore, quantum effects are increasingly at the core of the operation of new advanced electronic and photonic devices, which, in some cases, are designed on the basis of controlling quantum systems. This thesis focuses on two such systems, united by the methods used to realize them. These methods represent the cutting-edge of nanofabrication, which is the structuring of matter at ultra-small dimensions with a degree of precision and control that has not been previously attained. Pushing these methods to their limits enables the emergence of unique phenomena in the quantum systems explored here. The first system involves the realization of artificial graphene in an AlGaAs/GaAs quantum heterostructure. The appearance of massless charge carriers in graphene, which are described by the relativistic Dirac equation, originates from the linear energy-momentum dispersion of the electronic states in proximity to the K and K’ points of the hexagonal Brillouin zone. This unique quantum behavior is a direct result of the honeycomb symmetry of the graphene lattice. The prospect of reproducing this physics in an adjustable, artificial honeycomb lattice, known as artificial graphene, offers a platform for the exploration of novel quantum regimes of massless Dirac fermions beyond the limits imposed by the inability to manipulate the lattice of the natural material. The electronic properties of a two-dimensional electron gas whose density is modulated by a periodic potential with honeycomb symmetry have been predicted to generate massless Dirac-fermions with tunable Fermi velocity. This thesis reports the observation of a graphene-like band structure in a modulation-doped AlGaAs/GaAs quantum well engineered with a honeycomb lateral surface superlattice. This was accomplished by reactive ion etching of the surface to within a few tens of nanometers from the quantum well. A metal hard-mask, patterned by electron beam lithography combined with metal deposition and lift-off, was used to form a honeycomb artificial lattice with a variable lattice period, down to 40 nm. This is a three-fold reduction with respect to the smallest reported to date in pertinent literature. The BCl3-based shallow etching produces cylindrical pillars below which the two-dimensional electron gas is expected to form quantum dots, where the electron density is higher than in the surrounding etched regions. Low-temperature resonant inelastic light scattering measurements reveal new electronic transitions. An accurate interpretation of these can be found in the joint density of states derived from the calculated graphene-like linearly-dispersed energy bands, induced by the honeycomb potential modulation. The second system comprises the nanoscale engineering of individual electron spin qubits in diamond. Spin systems in solid-state have been intensively investigated as an outstanding pathway towards quantum information processing. One of the advantages of solid-state spintronics is the possibility of applying nanofabrication techniques commonly used by the semiconductor industry to produce and integrate spin qubits. The negatively charged nitrogen-vacancy (NV-) center in diamond stands out because of its optically addressable spin, which shows long coherence time and viable spin initiation, manipulation and read-out. A central challenge has been the positioning of NV- centers with nanometer scale control, that would allow for efficient and consistent dipolar coupling and the integration within an optoelectronic device. I demonstrate a method for chip-scale fabrication of arrays of closely-spaced NV- centers with record spatial localization of approximately 10 nm in all three dimensions and controllable inter-NV spacing as small as 40 nm. This is the highest spatial resolution realized to date in positioning NV- centers at the nanoscale with high throughput, and approaches the length scale of strong dipolar coupling. This method used masked implantation of nitrogen in an ultra-pure CVD-grown diamond substrate through nano-apertures in a thin gold film, patterned via electron-beam lithography and dry etching. The high-density and high-atomic weight of gold results in a mask which is significantly thinner than polymer films used in other works, whilst still successfully impeding ion penetration, with a mask contrast of more than 40 dB. This process allows for the creation of apertures with lower aspect ratio which are therefore easier to pattern in close proximity to one another, i.e., within the dipolar coupling range. The position and spin coherence properties of the resulting near-surface NVs were measured through wide-field super-resolution optically detected magnetic resonance imaging, Hahn echo and CPMG pulsed microwave spectroscopy. The patterning methodology demonstrated here is optimally suited to functional integration with plasmonic nanostructures, which can enhance our ability to control single-photon emission with the prospect of creating near-surface nanoscale sensors of electric or magnetic fields and quantum optoelectronic devices