26 research outputs found
Quantized Fermi-arc-mediated transport in Weyl semimetal nanowires
We study longitudinal transport in Weyl semimetal nanowires, both in the
absence and in the presence of a magnetic flux threading the nanowires. We
identify two qualitatively different regimes of transport with respect to the
chemical potential in the nanowires. In the "surface regime", for low doping,
most of the conductance occurs through the Fermi-arc surface states, and it
rises in steps of one quantum of conductance as a function of the chemical
potential; furthermore, with varying flux the conductance changes in steps of
one quantum of conductance with characteristic Fabry-P\'erot interference
oscillations. In the "bulk-surface regime", for highly-doped samples, the
dominant contribution to the conductance is quadratic in the chemical
potential, and mostly conditioned by the bulk states; the flux dependence shows
clearly that both the surface and the bulk states contribute. The two
aforementioned regimes prove that the contribution of the Fermi-arc surface
states is salient and, therefore, crucial for understanding transport
properties of finite-size Weyl semimetal systems. Last but not least, we
demonstrate that both regimes are robust to disorder.Comment: 13 pages, 6 figure
Characterizing unconventional superconductors from the spin structure of impurity-induced bound states
Cooper pairs in two-dimensional unconventional superconductors with broken
inversion symmetry are in a mixture of an even-parity spin-singlet pairing
state with an odd-parity spin-triplet pairing state. We study the magnetic
properties of the impurity bound states in such superconductors and find
striking signatures in their spin polarization which allow to unambiguously
discriminate a non-topological superconducting phase from a topological one.
Moreover, we show how these properties, which could be measured using
spin-polarized scanning tunneling microscopy (STM), also enable to determine
the direction of the spin-triplet pairing vector of the host material and thus
to distinguish between different types of unconventional pairing.Comment: 11 pages + 9 pages of supplementary information, 9 figures + 8
figures (SI
Asymptotic behavior of impurity-induced bound states in low-dimensional topological superconductors
We study theoretically the asymptotic behavior of the Shiba bound states
associated with magnetic impurities embedded in both 2D and 1D anomalous
superconductors. We calculate analytically the spatial dependence of the local
density of states together with the spin polarization associated with the Shiba
bound states. We show that the latter quantity exhibits drastic differences
between s-wave and different types of p-wave superconductors. Such properties,
which could be measured using spin-polarized STM, offer therefore a way to
discriminate between singlet and triplet pairing in low-dimensional
superconductors, as well as a way to estimate the amplitude of the triplet
pairing in these systems.Comment: 18 pages, 5 figure
Controlling topological superconductivity by magnetization dynamics
We study theoretically a chain of precessing classical magnetic impurities in
an -wave superconductor. Utilizing a rotating wave description, we derive an
effective Hamiltonian that describes the emergent Shiba band. We find that this
Hamiltonian shows non-trivial topological properties, and we obtain the
corresponding topological phase diagrams both numerically and analytically. We
show that changing the precession frequency offers a control over topological
phase transitions and the emergence of Majorana bound states. We propose
driving the magnetic impurities or magnetic texture into precession by means of
spin-transfer torque in a spin-Hall setup, and manipulate it using spin
superfluidity in the case of planar magnetic order.Comment: 5 pages+9 pages supplementary materia
Analytical and semianalytical tools to determine the topological character of Shiba chains
We introduce three new analytical and semi-analytical tools that allow one to
determine the topological character of impurity Shiba chains. The analytical
methods are based on calculating the effective Green's function of an infinite
embedded chain using the T-matrix formalism and describing the chain as a {\it
line impurity}. We thus provide a solution to the longstanding size-effects
problem affecting the only general alternative method, the numerical
tight-binding analysis. As an example we consider a chain of magnetic
impurities deposited on an s-wave superconducting substrate with Rashba
spin-orbit and we calculate its topological phase diagram as a function of the
magnetic impurity strength and the chemical potential. We find a perfect
agreement between all our new techniques and a numerical analysis
Polarisation en spin et propriétés topologiques des états de Yu-Shiba-Rusinov
In this manuscript we first revisit the physics of Yu-Shiba-Rusinov subgap states, focusing on their spin polarisation. We start by showing theoretically that we can extract a considerable amount of information about the host superconductor, by analysing spin-polarised local density of states related to the presence of magnetic impurities. First, we demonstrate that the spin-orbit coupling in two-dimensional and one-dimensional systems, both superconducting and metallic, can be read-off directly and unambiguously via spin-resolved STM. We analyse the impurity-induced oscillations in the local density of states. In particular, we focus on the Fourier transform (FT) of the Friedel oscillations and we note that high-intensity FT features appear at a wave vector given by twice the inverse spin-orbit length. Second, in unconventional superconductors with both s-wave and p-wave pairing, by analysing the spin-resolved spectral structure of the Yu-Shiba-Rusinov states it is possible to determine the dominating pairing mechanism. Most strikingly, we demonstrate that a careful analysis of spin-polarised density of states allows not only to unambiguously characterise the degree of triplet pairing, but also to define the orientation of the triplet pairing vector, also known as the d-vector.Finally, we discuss two different ways of engineering and controlling topological phases with both scalar and magnetic impurities. We start with providing a microscopic theory of scalar impurity structures on chiral superconductors. We show that given a non-trivial chiral superconductor, the scalar impurities give rise to a complex hierarchy of distinct non-trivial phases with high Chern numbers. Second, we propose and study theoretically a new promising platform that we call 'dynamical Shiba chain', i.e. a chain of classical magnetic impurities in an s-wave superconductor with precessing spins. We have shown that it can be employed not only for engineering a topological superconducting phase, but most remarkably for controlling topological phase transitions by means of magnetisation texture dynamics.This manuscript is organised as follows. In the first part, the essential introductory information on superconductivity, Friedel oscillations and Yu-Shiba-Rusinov states is provided. The second part is dedicated to spin polarisation of Yu-Shiba-Rusinov states and the properties that could be extracted by means of spin-resolved STM measurements. In the last part, two setups proposed for topological phase engineering based on impurity-induced states are presented, followed by conclusions with a brief summary of the thesis achievements and further directions to pursue.Dans ce manuscrit de thèse, nous revisitons d'abord la physique des états de Yu-Shiba-Rusinov, en nous concentrant sur leur polarisation en spin. Nous commençons par montrer théoriquement que nous pouvons extraire beaucoup d'informations sur le supraconducteur hôte, en analysant la densité locale d'états électroniques liée à la présence d'impuretés magnétiques. Tout d'abord, nous démontrons que le couplage spin-orbite peut être lu directement et sans ambiguïté par la spectroscopie par effet tunnel résolu en spin dans les systèmes bidimensionnels et unidimensionnels, qu’ils soient supraconducteurs ou métalliques. Nous analysons les oscillations induites par les impuretés dans la densité d'états électroniques. En particulier, nous nous concentrons sur la transformation de Fourier (TF) des oscillations de Friedel et nous notons que les caractéristiques à haute intensité apparaissent pour un vecteur d'onde donné par deux fois la longueur inverse du spin-orbite. Ensuite, nous montrons qu'il est possible de déterminer le mécanisme d’appariement dominant, qu’il soit en ondes s ou en ondes p, dans les supraconducteurs non conventionnels en analysant la structure spectrale résolue en spin des états liés de Yu-Shiba-Rusinov. De manière frappante, nous démontrons qu'une analyse minutieuse de la densité d'états électroniques polarisée en spin ne permet pas seulement de caractériser sans équivoque le degré d’appariement de type triplet, mais également son orientation, a.k.a. le vecteur d. Enfin, nous proposons et discutons deux approches différentes d'ingénierie et de contrôle des phases topologiques à l’aide d’impuretés scalaires et magnétiques. Nous commençons par fournir une théorie microscopique des réseaux d'impuretés scalaires sur les supraconducteurs chiraux. Nous montrons que pour un supraconducteur topologique de type chiral, les impuretés scalaires donnent lieu à une hiérarchie complexe de phases non triviales distinctes avec des nombres de Chern élevés. Deuxièmement, nous proposons et étudions théoriquement une nouvelle plate-forme prometteuse que nous appelons «la chaîne dynamique de Shiba», c'est-à -dire une chaîne d'impuretés magnétiques classiques dans un supraconducteur en ondes s avec des spins qui précessent. Nous montrons que cette approche peut être utilisée non seulement pour créer une phase supraconductrice topologique, mais surtout pour contrôler les transitions de phase topologiques au moyen de la dynamique de la texture de la magnétisation. Ce manuscrit est organisé comme suit. Dans la première partie, les informations d'introduction essentielles sur la supraconductivité, les oscillations de Friedel et les états de Yu-Shiba-Rusinov sont fournies. La deuxième partie est consacrée à la polarisation en spin des états Yu-Shiba-Rusinov et aux propriétés qui pourraient être extraites au moyen de la microscopie par effet tunnel résolu en spin. Dans la dernière partie, deux configurations proposées pour l'ingénierie de phases topologiques, basées sur les états induits par les impuretés, sont présentées, suivies de conclusions, d’un bref résumé des réalisations de cette thèse et enfin d’une discussion de possibles directions futures
Formation of Majorana fermions in finite-size graphene strips
We investigate the formation of Majorana fermions in finite-size graphene
strips with open boundary conditions in both directions, in the presence of an
in-plane magnetic field and in the proximity of a superconducting substrate. We
show that for long enough strips the Majorana states can form in the presence
of a Rashba-like spin-orbit coupling, as well as in the presence of an
inhomogeneous magnetic field. We find that, unlike infinite graphene ribbons in
which Majorana states arise solely close to the bottom of the band and the Van
Hove singularities, for finite-size systems this can happen also at much
smaller doping values, close to the Dirac points, and depends strongly on the
type of the short edges of the systems (e.g. armchair vs. zigzag), as well as
on the width of the ribbons
Obtaining Majorana and other boundary modes from the metamorphosis of impurity-induced states: Exact solutions via the T-matrix
We provide here a direct and exact formalism to describe the formation of edge or surface states, as well as to calculate boundary Green's functions. Modeling the boundary as an impurity potential, we show via the T-matrix formalism that the impurity states evolve into boundary modes when the impurity potential goes to infinity. We apply this technique to obtain Majorana states in one- (1D) and two-dimensional Kitaev systems. For the 1D case we also calculate the corresponding boundary Green's functions. We argue that our formalism can be applied to other topological models, as well as to any model exhibiting edge states
Formation of Majorana fermions in finite-size graphene strips
8 pages, 12 figuresInternational audienceWe investigate the formation of Majorana fermions in finite-size graphene strips with open boundary conditions in both directions, in the presence of an in-plane magnetic field and in the proximity of a superconducting substrate. We show that for long enough strips the Majorana states can form in the presence of a Rashba-like spin-orbit coupling, as well as in the presence of an inhomogeneous magnetic field. We find that, unlike infinite graphene ribbons in which Majorana states arise solely close to the bottom of the band and the Van Hove singularities, for finite-size systems this can happen also at much smaller doping values, close to the Dirac points, and depends strongly on the type of the short edges of the systems (e.g. armchair vs. zigzag)
Modeling long imperfect SNS junctions and Andreev bound states using two impurities and the -matrix formalism
We provide an analytical tool to calculate the energies of Andreev bound states (ABSs) in long imperfect SNS junctions, which at present can only be described using numerical tools. We model an NS junction as a δ-function “Andreev” impurity, i.e., a localized potential that scatters an electron into a hole with opposite spin. We show using the scattering matrix formalism that, quite surprisingly, an “Andreev” impurity is equivalent to an NS junction characterized by both Andreev reflection and a finite amount of normal scattering. The ABS energies are then calculated using the T-matrix formalism applied to a system with two Andreev impurities. Our results lie between those for a perfect long SNS junction limit described by the Andreev approximation (ABS energies depend linearly on the phase and are independent of the chemical potential) and the particle-in-the-box limit (bound state energies are independent of the phase and have a linear dependence on the chemical potential). Moreover, we recover a closed-form expression for the ABS energies by expanding around the particle-in-the-box limit