Achromatic optical phase shifter/modulator

We propose and demonstrate, theoretically and experimentally, a novel achromatic optical phase shifter modulator based on a frequency-domain optical delay line configured to maintain zero group delay as variable phase delay is generated by means of tilting a mirror. Compared with previously reported phase shifter modulators, e.g., based on the Pancharatnam (geometric) phase, our device is high speed and polarization insensitive and produces a large, bounded phase delay that, uniquely, is one-to-one mapped to a measurable parameter, the tilt angle.

Re-entrant phase behaviour of network fluids: A patchy particle model with temperature-dependent valence

We study a model consisting of particles with dissimilar bonding sites ("patches"), which exhibits self-assembly into chains connected by Y-junctions, and investigate its phase behaviour by both simulations and theory. We show that, as the energy cost epsilon(j) of forming Y-junctions increases, the extent of the liquid-vapour coexistence region at lower temperatures and densities is reduced. The phase diagram thus acquires a characteristic "pinched" shape in which the liquid branch density decreases as the temperature is lowered. To our knowledge, this is the first model in which the predicted topological phase transition between a fluid composed of short chains and a fluid rich in Y-junctions is actually observed. Above a certain threshold for epsilon(j), condensation ceases to exist because the entropy gain of forming Y-junctions can no longer offset their energy cost. We also show that the properties of these phase diagrams can be understood in terms of a temperature-dependent effective valence of the patchy particles. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3605703]

Landau analog levels for dipoles in non-commutative space and phase space - Landau analog levels for dipoles

We investigate the analog of Landau quantization, for a neutral polarized particle in the presence of homogeneous electric and magnetic external fields, in the context of non-commutative quantum mechanics. This particle, possessing electric and magnetic dipole moments, interacts with the fields via the Aharonov-Casher and He-McKellar-Wilkens effects. For this model we obtain the Landau energy spectrum and the radial eigenfunctions of the non-commutative space coordinates and non-commutative phase space coordinates. Also we show that the case of non-commutative phase space can be treated as a special case of the usual non-commutative space coordinates.

Impurity states in the quantum spin Hall phase in graphene

Two-dimensional insulators with time-reversal symmetry can have two topologically different phases, the quantum spin Hall and the normal phase. The former is revealed by the existence of conducting edge states that are topologically protected. Here we show that the reaction to impurity, in bulk, is radically different in the two phases and can be used as a marker for the topological phase. Within the context of the Kane-Mele model for graphene, we find that strictly normalizable in-gap impurity states only occur in the quantum spin Hall phase and carry a dissipationless current whose chirality is determined by the spin and pseudospin of the residing electron.

Topological massive Dirac edge modes and long-range superconducting Hamiltonians

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower-band eigenvector and the winding number of the Hamiltonians. For exponentially decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive nonlocal Dirac fermion localized at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.

Interferência de Fano e uma ligeira flutuação da marca Majorana

Pós-graduação em Ciência dos Materiais - FEIS

Fano interference and a slight fluctuation of the Majorana hallmark

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Probing the antisymmetric Fano interference assisted by a Majorana fermion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Interferência Fano antissimétrica assistida por um férmion de Majorana

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Crystallisation behaviours of Al-based metallic glasses: Compositional and topological aspects

The different types of thermal crystallisation behaviours observed during continuous heating of M-based metallic glasses have been successfully associated with the topological instability. criterion, which is simply calculated from the alloy composition and metallic radii of the alloying elements and aluminium. In the present work, we report on new results evidencing the correlation between the values of X and the crystallisation behaviours in Al-based alloys of the Al-Ni-Ce system and we compare the glass-forming abilities of alloys designed with compositions corresponding to the same topological instability condition. The results are discussed in terms of compositional and topological aspects emphasizing the relevance of the different types of clusters in the amorphous phase in defining the stability of the glass and the types of thermal crystallisation. (C) 2008 Elsevier B.V. All rights reserved.

Thermodynamic and topological instability approaches for forecasting glass-forming ability in the ternary Al-Ni-Y system

A thermodynamic approach to predict bulk glass-forming compositions in binary metallic systems was recently proposed. In this approach. the parameter gamma* = Delta H-amor/(Delta H-inter - Delta H-amor) indicates the glass-forming ability (GFA) from the standpoint of the driving force to form different competing phases, and Delta H-amor and Delta H-inter are the enthalpies for-lass and intermetallic formation, respectively. Good glass-forming compositions should have a large negative enthalpy for glass formation and a very small difference for intermetallic formation, thus making the glassy phase easily reachable even under low cooling rates. The gamma* parameter showed a good correlation with GFA experimental data in the Ni-Nb binary system. In this work, a simple extension of the gamma* parameter is applied in the ternary Al-Ni-Y system. The calculated gamma* isocontours in the ternary diagram are compared with experimental results of glass formation in that system. Despite sonic misfitting, the best glass formers are found quite close to the highest gamma* values, leading to the conclusion that this thermodynamic approach can lie extended to ternary systems, serving as a useful tool for the development of new glass-forming compositions. Finally the thermodynamic approach is compared with the topological instability criteria used to predict the thermal behavior of glassy Al alloys. (C) 2007 Elsevier B. V. All rights reserved.

Topological instability and electronegativity effects on the glass-forming ability of metallic alloys

The glass-forming ability (GFA) of metallic alloys is associated with a topological instability criterion combined with a new parameter based on the average electronegativity difference of an element and its surrounding neighbours. In this model, we assume that during solidification the glassy phase competes directly with the supersaturated solid solution having the lowest topological instability factor for a given composition. This criterion is combined with the average electronegativity difference among the elements in the alloy, which reflects the strength of the liquid. The GFA is successfully correlated with this combined criterion in several binary glass-forming systems.

Topological charge and angular momentum of light beams carrying optical vortices

We analyze the properties of light beams carrying phase singularities, or optical vortices. The transformations of topological charge during free-space propagation of a light wave, which is a combination of a Gaussian beam and a multiple charged optical vortex within a Gaussian envelope, are studied both in theory and experiment. We revise the existing knowledge about topological charge conservation, and demonstrate possible scenarios where additional vortices appear or annihilate during free propagation of such a combined beam. Coaxial interference of optical vortices is also analyzed, and the general rule for angular-momentum density distribution in a combined beam is established. We show that, in spite of any variation in the number of vortices in a combined beam, the total angular momentum is constant during the propagation. [S1050-2947(97)09910-1].

Solid-phase synthesis and NMR studies of modified oligonucleotides forming triplex helix and of oligonucleopeptides mimicking the topoisomerase I-DNA covalent complex

Report for the scientific sojourn carried out at the Institut de Biologia Molecular de Barcelona of the CSIC –state agency – from april until september 2007. Topoisomerase I is an essential nuclear enzyme that modulates the topological status of DNA, facilitating DNA helix unwinding during replication and transcription. We have prepared the oligonucleotide-peptide conjugate Ac-NLeu-Asn-Tyr(p-3’TTCAGAAGC5’)-LeuC-CONH-(CH2)6-OH as model compound for NMR studies of the Topoisomerase I- DNA complex. Special attention was made on the synthetic aspects for the preparation of this challenging compound especially solid supports and protecting groups. The desired peptide was obtained although we did not achieve the amount of the conjugate needed for NMR studies. Most probably the low yield is due to the intrinsic sensitive to hydrolysis of the phosphate bond between oligonucleotide and tyrosine. We have started the synthesis and the structural characterization of oligonucleotides carrying intercalating compounds. At the present state we have obtained model duplex and quadruplex sequences modified with acridine and NMR studies are underway. In addition to this project we have successfully resolved the structure of a fusion peptide derived from hepatitis C virus envelope synthesized by the group of Dr. Haro and we have synthesized and started the characterization of a modified G-quadruplex.