Fractional Charge Research Articles

A new criterion for self-healing quantification of structured light beams

This paper introduces a new approach to the self-healing quantification of structured light beams. The self-healing is quantitatively determined by defining a self-healing degree (SHD) and a similarity function based on comparing the intensity distributions of the perturbed and unperturbed beams. In addition, the SHD is employed for two other intensity-based methods to compare the methods’ performance. The Bessel beams (BBs) with integer and fractional topological charges (TCs) are examined numerically to verify the method. Further, the effect of superposition of the Bessel and mirrored BBs with respect to the x-axis on the self-healing property is investigated. The perturbation of the beams is applied using a pair of circular masks as a symmetric perturbation. The propagating of perturbed and unperturbed beams is simulated by the angular spectrum method. The obtained quantitative results are confirmed by the intuitive results and also the accuracy of the proposed method is similar to the other used methods. On the other hand, due to using fewer calculations with respect to them and so is less time-consuming (about 57% and 67% reduction in computational time), it can be used as an adequate alternative method. As a result of this method, it is shown that the superposition of BBs with their mirrored ones is an effective factor to improve the self-healing property, in which the SHD of the superposed beams is more than the BBs for each TC. It is also shown that using the fractional TC beams is another advantageous improvement to increase the SHD.

Free-space creation of a perfect vortex beam with fractional topological charge.

Perfect vortex beams can only propagate stably with integer topological charges. Thus, creating perfect fractional vortex beams capable of stable propagation in free space, as perfect integer vortex beams, is crucial. This study proposed perfect vortex beams carrying fractional topological charge of l + 0.5, which are special solutions of the wave equation, and can maintain stable propagation with physical laws same as integer topological charge. Perfect fractional vortex beams were created in free space, which can break the cognition of traditional fractional perfect vortex beams and promote the development of scientific fields such as optical communication, quantum sensing, and optical imaging.

A survey of family unification models with bifundamental matter

Extensions of the Standard Model have been attempted from the bottom up and from the top down, yet there remains a largely unexplored middle ground. In this paper, using the Mathematica package LieART, we exhaustively enumerate embeddings of the Standard Model within the class of theories with bifundamental fermions in product gauge group SU(a)×SU(b)×SU(c) with no more generators than E6, while achieving SM family unification rather than replication. We incorporate simple phenomenological constraints and find 151 unique models, including 9 that have only vector-like particle content beyond-the-Standard Model (BSM) particles, which we conjecture belong to 5 infinite families of such models. We describe the potentially most viable models: namely, the 9 with strictly vector-like BSM content along with the 29 models we found with no more than 30 additional BSM chiral particles. These include models with fractional electric charge color singlets, and hence magnetic monopoles with multiple Dirac charge. This latter collection of models predicts chiral particles with masses near the electroweak scale accessible to current and future collider experiments.

High-accuracy identification of interferograms between two vortex beams via deep learning without adequate experimental data

The on-axis interference intensity patterns between a vortex beam and its conjugated beam can be used to measure the fractional topological charge of vortex beams. However, it is still challenging to efficiently recognize these intensity diagrams. On one hand, the difference of the patterns for adjacent modes with interval 0.1 is too subtle to be identified precisely. On the other hand, the interferograms are susceptible to undesirable experimental conditions such as the misalignment of the beams, the unequal arms of the interferometer and the deviation of splitting ratio of the beam splitters in the interferometer. Here, we propose a deep learning method to recognize these intensity diagrams with up to accuracy. In particular, our method has reference values for deep learning model training when there is not adequate experimental data.

Measurement of the fractional topological charge of an optical vortex beam through interference fringe dislocation.

An optical vortex beam carrying fractional topological charge (TC) has become an immerging field of interest due to its unique intensity distribution and fractional phase front in a transverse plane. Potential applications include micro-particle manipulation, optical communication, quantum information processing, optical encryption, and optical imaging. In these applications, it is necessary to know the correct information of the orbital angular momentum, which is related to the fractional TC of the beam. Therefore, the accurate measurement of fractional TC is an important issue. In this study, we demonstrate a simple technique to measure the fractional TC of an optical vortex with a resolution of 0.05 using a spiral interferometer and fork-shaped interference patterns. We further show that the proposed technique provides satisfactory results in cases of low to moderate atmospheric turbulences, which has relevance in free-space optical communications.

Thermoelectric properties of topological chains coupled to a quantum dot

Topological one-dimensional superconductors can sustain zero energy modes protected by different kinds of symmetries in their extremities. Observing these excitations in the form of Majorana fermions is one of the most intensive quests in condensed matter physics. We are interested in another class of one-dimensional topological systems in this work, namely topological insulators. Which present symmetry-protected end modes with robust properties and do not require the low temperatures necessary for topological superconductivity. We consider a device in the form of a single electron transistor coupled to the simplest kind of topological insulators, namely chains of atoms with hybridized sp orbitals. We study the thermoelectric properties of the device in the trivial, non-trivial topological phases and at the quantum topological transition of the chains. We show that the device’s electrical conductance and the Wiedemann–Franz ratio at the topological transition have universal values at very low temperatures. The conductance and thermopower of the device with diatomic sp-chains, at their topological transition, give direct evidence of fractional charges in the system. The former has an anomalous low-temperature behavior, attaining a universal value that is a consequence of the double degeneracy of the system due to the presence of zero energy modes. On the other hand, the system can be tuned to exhibit high values of the thermoelectric figure of merit and the power factor at high temperatures.

Anyonic interference and braiding phase in a Mach-Zehnder interferometer

Fractional quantum Hall states have long been predicted to be a testing ground of fractional—anyonic—exchange statistics. These topological states, which can have either an Abelian or non-Abelian character, harbour quasiparticles with fractional charges. The charge of the quasiparticles can be measured by shot noise measurements, whereas their quantum statistics can be revealed by appropriate interference experiments. The multipath Fabry–Pérot electronic interferometer is easier to fabricate, but it is often plagued by Coulomb interactions, area breathing with the magnetic field and fluctuating charges. Yet, recent experiments with an adequately screened Fabry–Pérot interferometer allowed the observation of anyonic interference at a bulk filling factor of ν = 1/3. Here we demonstrate the interference and braiding of anyons in an interaction-free two-path Mach–Zehnder interferometer tuned to bulk filling of ν = 2/5 with an outermost ν = 1/3 edge mode. Interference with this mode reveals a phase dependence that corresponds to the predicted anyonic braiding. This proves that a Mach–Zehnder interferometer is a powerful tool that probes the quantum statistics of complex anyonic states.

The gaugino condensate from asymmetric four-torus with twists

We calculate the gaugino condensate in SU(2) super Yang-Mills theory on an asymmetric four-torus \U0001d54b4 with ’t Hooft’s twisted boundary conditions. The \U0001d54b4 asymmetry is controlled by a dimensionless detuning parameter ∆, proportional to L3L4 − L1L2, with Li denoting the \U0001d54b4 periods. We perform our calculations via a path integral on a \U0001d54b4. Its size is taken much smaller than the inverse strong scale Λ and the theory is well inside the semi-classical weak-coupling regime. The instanton background, constructed for ∆ ≪ 1 in [1], has fractional topological charge Q=frac{1}{2} and supports two gaugino zero modes, yielding a non-vanishing bilinear condensate, which we find to be ∆-independent. Further, the theory has a mixed discrete chiral/1-form center anomaly leading to double degeneracy of the energy eigenstates on any size torus with ’t Hooft twists. In particular, there are two vacua, ∣0〉 and ∣1〉, that are exchanged under chiral transformation. Using this information, the ∆-independence of the condensate, and assuming further that the semi-classical theory is continuously connected to the strongly-coupled large-\U0001d54b4 regime, we determine the numerical coefficient of the gaugino condensate: 〈0|trλλ|0〉 = ∣〈1|trλλ|1〉∣ = 32π2Λ3, a result equal to twice the known ℝ4 value. We discuss possible loopholes in the continuity approach that may lead to this discrepancy.

Fractional topological charge in lattice Abelian gauge theory

AbstractWe construct a non-trivial $U(1)/\mathbb {Z}_q$ principal bundle on T4 from the compact U(1) lattice gauge field by generalizing Lüscher’s constriction so that the cocycle condition contains $\mathbb {Z}_q$ elements (the ’t Hooft flux). The construction requires an admissibility condition on lattice gauge field configurations. From the transition function so constructed, we have the fractional topological charge that is $\mathbb {Z}_q$ one-form gauge invariant and odd under the lattice time reversal transformation. Assuming a rescaling of the vacuum angle θ → qθ suggested from the Witten effect, our construction provides a lattice implementation of the mixed ’t Hooft anomaly between the $\mathbb {Z}_q$ one-form symmetry and the time reversal symmetry in the U(1) gauge theory with matter fields of charge $q\in 2\mathbb {Z}$ when θ = π, which was studied by Honda and Tanizaki [J. High Energy Phys. 12, 154 (2020)] in the continuum framework.

Fractional Josephson effect versus fractional charge in superconducting–normal metal hybrid circuits

Fractionally charged excitations play a central role in condensed matter physics, and can be probed in different ways. If transport occurs via dissipationless supercurrents, they manifest as a fractional Josephson effect, whereas in dissipative transport they can be revealed by the transport statistics. However, in a regime where supercurrents and lossy currents coincide, a full understanding of the relationship between these two transport phenomena is still missing. Moreover, especially for superconducting circuits, the question of how noninteger quasicharges can be reconciled with charge quantization is still not fully resolved, and plays an important role for the circuit dynamics. Here, we aim to unify the above concepts by studying the system-detector dynamics in terms of a Lindbladian capturing both coherent and dissipative transport. Charge quantization is here a conserved property of the detector basis of the Lindbladian, while charge fractionalization is a topological property of its complex-valued eigenspectrum. We show that already conventional superconductor-normal metal hybrid circuits exhibit a variety of topological phases, including an open quantum system version of a fractional Josephson effect. Surprisingly, quasiparticles, usually considered a detrimental side effect, are here a necessary ingredient to observe nontrivial transport behavior.

Emergent XY* transition driven by symmetry fractionalization and anyon condensation

Anyons in a topologically ordered phase can carry fractional quantum numbers with respect to the symmetry group of the considered system, one example being the fractional charge of the quasiparticles and quasiholes in the fractional quantum Hall effect. When such symmetry-fractionalized anyons condense, the resulting phase must spontaneously break the symmetry and display a local order parameter. In this paper, we study the phase diagram and anyon condensation transitions of a \mathbb{Z}_2ℤ2 topological order perturbed by Ising interactions in the Toric Code. The interplay between the global (``onsite’’) Ising (\mathbb{Z}_2ℤ2) symmetry and the lattice space group symmetries results in a non-trivial symmetry fractionalization class for the anyons, and is shown to lead to two characteristically different confined, symmetry-broken phases. To understand the anyon condensation transitions, we use the recently introduced critical torus energy spectrum technique to identify a line of emergent 2+1D XY* transitions ending at a fine-tuned (Ising^22)* critical point. We provide numerical evidence for the occurrence of two symmetry breaking patterns predicted by the specific symmetry fractionalization class of the condensed anyons in the explored phase diagram. In combination with large-scale quantum Monte Carlo simulations we measure unusually large critical exponents \etaη for the scaling of the correlation function at the continuous anyon condensation transitions, and we further identify lines of (weakly) first order transitions in the phase diagram. As an important additional result, we discuss the phase diagram of a resulting 2+1D Ashkin-Teller model, where we demonstrate that torus spectroscopy is capable of identifying emergent XY/O(2) critical behaviour, thereby solving some longstanding open questions in the domain of the 3D Ashkin-Teller models. To establish the generality of our results, we propose a field theoretical description capturing the transition from a \mathbb{Z}_2ℤ2 topological order to either \mathbb{Z}_2ℤ2 symmetry broken phase, which is in excellent agreement with the numerical results.

Systemic cascades on inhomogeneous random financial networks

This article presents a model of the financial system as an inhomogeneous random financial network (IRFN) with N nodes that represent different types of institutions such as banks or funds and directed weighted edges that signify counterparty relationships between nodes. The onset of a systemic crisis is triggered by a large exogenous shock to banks’ balance sheets. Their behavioural response is modelled by a cascade mechanism that tracks the propagation of damaging shocks and possible amplification of the crisis, and leads the system to a cascade equilibrium. The mathematical properties of the stochastic framework are investigated for the first time in a generalization of the Eisenberg–Noe solvency cascade mechanism that accounts for fractional bankruptcy charges. New results include verification of a “tree independent cascade property” of the solvency cascade mechanism, and culminate in an explicit recursive stochastic solvency cascade mapping conjectured to hold in the limit as the number of banks N goes to infinity. It is shown how this cascade mapping can be computed numerically, leading to a rich picture of the systemic crisis as it evolves toward the cascade equilibrium.

Fractional Topological Charge Construction in a U(1) Lattice Gauge Theory Framework

We have constructed a fractional topological charge in the lattice Abelian gauge theory formalism, which avoids the issue of infinite degrees of freedom in continuum spacetime quantum field theory.

Fractional Disclination Charge and Discrete Shift in the Hofstadter Butterfly.

In the presence of crystalline symmetries, topological phases of matter acquire a host of invariants leading to nontrivial quantized responses. Here we study a particular invariant, the discrete shift 𝒮, for the square lattice Hofstadter model of free fermions. 𝒮 is associated with a Z_{M} classification in the presence of M-fold rotational symmetry and charge conservation. 𝒮 gives quantized contributions to (i)the fractional charge bound to a lattice disclination and (ii)the angular momentum of the ground state with an additional, symmetrically inserted magnetic flux. 𝒮 forms its own "Hofstadter butterfly," which we numerically compute, refining the usual phase diagram of the Hofstadter model. We propose an empirical formula for 𝒮 in terms of density and flux per plaquette for the Hofstadter bands, and we derive a number of general constraints. We show that bands with the same Chern number may have different values of 𝒮, although odd and even Chern number bands always have half-integer and integer values of 𝒮, respectively.

Multidimensional Interface Topology Induced by Acoustic Wannier Configurations

Recently, real-space representations, revealing in depth the duality of topological descriptions in real and momentum space, have been applied to show multidimensional crystalline topology. Here we propose nontrivial phononic crystals by constructing different Wannier configurations based on real-space representations. We experimentally achieve the symmetry-protected interface topology in multiple dimensions containing anomalous interface states and higher-order corner states. Nontrivial acoustic pseudospin polarizations are critical to the interface states and have been directly observed in experiment. In a consistent frame, the higher-order corner states arising from the fractional charge anomaly are further observed. Our study provides a scheme based on Wannier configurations for designing topological metamaterials, which is fruitful for characterizing and manipulating multidimensional topological states and can be generalized to other classical systems.

Higher-Order Topological States in Photonic Thue-Morse Quasicrystals: Quadrupole Insulator and the Origin of Corner States

Corner states (CSs) in higher-order topological insulators (HOTIs) have recently been of great interest in both crystals and quasicrystals. In contrast to electronic systems, HOTIs have not been found in photonic quasicrystals (PQCs). Here, we systemically study the higher-order topology in the two-dimensional Thue-Morse photonic quasicrystals (TM PQCs). Not only the topological phase transition and the nontrivial CSs with fractional charge induced by multipole moments, but also another type of CSs are found due to the complex structure of TM PQCs near corners. The different origins of these CSs are also analyzed based on the tight-binding model. Our work opens the door to explore richer HOT physics beyond photonic crystals and the robustness of CSs in PQC shows the potential for applications.

Skyrmion and meron ordering in quasi-two-dimensional chiral magnets

We revisit the well-known theoretical phase diagram for a two-dimensional chiral magnet with an easy-axis uniaxial anisotropy and an applied magnetic field. A particular emphasis is given to merons---quanta of the phase transition between the cycloid and the hexagonal skyrmion lattice, which possess fractional topological charges $\ifmmode\pm\else\textpm\fi{}1/2$. A localized state of two coupled merons with opposite topological charges exhibits the nonreciprocal current-driven dynamics: it experiences no skyrmion Hall effect, but due to the asymmetry of the attracting intermeron potential gives rise to asymmetric current-velocity characteristics. We also address the problem of skyrmion ordering into hexagonal and square skyrmion crystals. In an entire field range, the square lattice turns out a saddle point state between differently oriented hexagonal lattices. Merons separating elongated skyrmions were also shown to form a local energy minimum by forming a hexagonal lattice shadowing the ordinary lattice of skyrmions. In addition, we focus on the anisotropy-driven transformations of modulated phases and their isolated counterparts, which exist as detached branches of solutions on both sides from the critical anisotropy value. Moreover, a family of isolated skyrmions with both rotational senses can be found near this anisotropy value. Our results are useful from both the fundamental point of view, since they complement previous findings, and from the point of view of applications, since they provide guidelines for developing meron-based spintronic devices.

Generating elliptic perfect optical vortex beams with efficient dielectric metasurface in the ultraviolet spectrum

Due to the helical phase profile as well as the topological charge-independent doughnut spatial structure, perfect vortex beams have attract attentions in fiber communications and particle manipulations. However, for some advanced applications such as optical cage and optical microfluidic sorting and acceleration, it is more meaningful to generate asymmetric optical vortex fields such as elliptic perfect optical vortex (EPOV) beams. Herein we utilize silicon nitride nanopillars, functioning as half-wave plates, to construct high-efficiency geometric phase metasurfaces for the generation of EPOV beams with the integer and fractional topological charges in the ultraviolet range. By adjusting scaling factor, the shape of beams can be freely changed from circle to ellipse. In addition, multi-channel EPOV beams with arbitrary shape and different topological charges are produced with the help of the superposition principle of phase in Fourier space. We envision that this ultraviolet metasurface-based generator of EPOV beams can be used for manipulation of microscopic particle along an ellipse with acceleration and for the generation OAM-entangled photons.

SU(N) fractional instantons and the Fibonacci sequence

We study, by means of numerical methods, new SU(N) self-dual instanton solutions on R × T3 with fractional topological charge Q = 1/N. They are obtained on a box with twisted boundary conditions with a very particular choice of twist: both the number of colours and the ’t Hooft ZN fluxes piercing the box are taken within the Fibonacci sequence, i.e. N = Fn (the nth number in the series) and left|overrightarrow{m}right| = left|overrightarrow{k}right| = Fn−2. Various arguments based on previous works and in particular on ref. [1], indicate that this choice of twist avoids the breakdown of volume independence in the large N limit. These solutions become relevant on a Hamiltonian formulation of the gauge theory, where they represent vacuum-to-vacuum tunneling events lifting the degeneracy between electric flux sectors present in perturbation theory. We discuss the large N scaling properties of the solutions and evaluate various gauge invariant quantities like the action density or Wilson and Polyakov loop operators.

On magnetic monopole and Dirac quantization condition in the minimal length formalism

In this article, we study the effects of minimal length corrections on the cyclotron acceleration and radiation of a charged particle moving in a magnetic monopole field. Using the modified Hamiltonian describing the dynamics of a charged particle moving in a magnetic monopole field, we derive the modified cyclotron frequency and modified acceleration. Also, we derive the modified power for the cyclotron radiation using the modified acceleration. We find that all modified quantities are dependent on the deformation parameter α. In addition, we find that the modified electromagnetic angular momentum and magnetic charges are not quantized as an integer multiple; thus, we establish that the modified Dirac quantization condition and the usual Dirac quantization condition is just the term of zero order in α. The modified Dirac quantization condition allows fractional charges that arise from vacuum fluctuations. In the Born approximation, we derive the modified scattering cross-section and then we estimate the upper bound on the minimal length.