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Topology and interaction effects in one-dimensional systems
Full text linkWith 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
Transient dynamics of spin-polarized injection in helical Luttinger liquids
No full textWe analyze the time evolution of spin-polarized electron wave packets injected into the edge states of a two-dimensional topological insulator. In the presence of electron interactions, the system is described as a helical Luttinger liquid and injected electrons fractionalize. However, because of the presence of metallic detectors, no evidences of fractionalization are encoded in dc measurements, and in this regime the system does not show deviations from its non-interacting behavior. Nevertheless, we show that the helical Luttinger liquid nature emerges in the transient dynamics, where signatures of charge/spin fractionalization can be clearly identified
Z4 parafermions in one-dimensional fermionic lattices
Full text linkpeer reviewedParafermions are emergent excitations which generalize Majorana fermions and are potentially relevant to topological quantum computation. Using the concept of Fock parafermions, we present a mapping between lattice Z4-parafermions and lattice spin-1/2 fermions which preserves the locality of operators with Z4 symmetry. Based on this mapping, we construct an exactly solvable, local one-dimensional fermionic Hamiltonian which hosts parafermionic edge states. We numerically show that the parafermionic phase remains stable in a wide range of parameters, and discuss its signatures in the fermionic spectral function
Spectral features of voltage pulses in interacting helical channels
Full text linkWe investigate the interplay of voltage-driven excitations and electron-electron interactions in a pair of counterpropagating helical channels capacitively coupled to a time-dependent gate. By focusing on the non-equilibrium spectral properties of the system, we show how the spectral function is modified by external drives with different time profile in presence of Coulomb interactions. In particular, we focus on a Lorentzian drive and a square single pulse. In presence of strong enough electron-electron interactions, we find that both drives can result in minimal excitations, i.e. characterized by an excess spectral function with a definite sign. This is in contrast with what happens in the non-interacting case, where only properly quantized Lorentzian pulses are able to produce minimal excitations
Time-resolved energy dynamics after single electron injection into an interacting helical liquid
Full text linkpeer reviewedThe possibility of injecting a single electron into ballistic conductors is at the basis of the new field of electron quantum optics. Here, we consider a single electron injection into the helical edge channels of a topological insulator. Their counterpropagating nature and the unavoidable presence of electron-electron interactions dramatically affect the time evolution of the single wave packet. Modeling the injection process from a mesoscopic capacitor in the presence of nonlocal tunneling, we focus on the time-resolved charge and energy packet dynamics. Both quantities split up into counterpropagating contributions whose profiles are strongly affected by the interaction strength. In addition, stronger signatures are found for the injected energy, which is also affected by the finite width of the tunneling region, in contrast to what happens for the charge. Indeed, the energy flow can be controlled by tuning the injection parameters, and we demonstrate that, in the presence of nonlocal tunneling, it is possible to achieve a situation in which charge and energy flow in opposite directions
Time-resolved pure spin fractionalization and spin-charge separation in helical Luttinger liquid based devices
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Nonequilibrium effects on charge and energy partitioning after an interaction quench
No full textpeer reviewedCharge and energy fractionalization are among the most intriguing features of interacting one-dimensional fermion systems. In this work we determine how these phenomena are modified in the presence of an interaction quench. Charge and energy are injected into the system suddenly after the quench, by means of tunneling processes with a noninteracting one-dimensional probe. Here, we demonstrate that the system settles to a steady state in which the charge fractionalization ratio is unaffected by the prequenched parameters. On the contrary, due to the postquench nonequilibrium spectral function, the energy partitioning ratio is strongly modified, reaching values larger than 1. This is a peculiar feature of the nonequilibrium dynamics of the quench process and it is in sharp contrast with the nonquenched case, where the ratio is bounded by 1
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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