Creation and annihilation of mobile fractional solitons in atomic chains

Localized modes in one-dimensional (1D) topological systems, such as Majonara modes in topological superconductors, are promising candidates for robust information processing. While theory predicts mobile integer and fractional topological solitons in 1D topological insulators, experiments so far have unveiled immobile, integer solitons only. Here we observe fractionalized phase defects moving along trimer silicon atomic chains formed along step edges of a vicinal silicon surface. By means of tunnelling microscopy, we identify local defects with phase shifts of 2π/3 and 4π/3 with their electronic states within the band gap and with their motions activated above 100 K. Theoretical calculations reveal the topological soliton origin of the phase defects with fractional charges of ±2e/3 and ±4e/3. Additionally, we create and annihilate individual solitons at desired locations by current pulses from the probe tip. Mobile and manipulable topological solitons may serve as robust, topologically protected information carriers in future information technology.

Unveiling the three-dimensional magnetic texture of skyrmion tubes

Magnetic skyrmions are stable topological solitons with complex non-coplanar spin structures. Their nanoscopic size and the low electric currents required to control their motion has opened a new field of research, skyrmionics, that aims for the usage of skyrmions as information carriers. Further advances in skyrmionics call for a thorough understanding of their three-dimensional (3D) spin texture, skyrmion–skyrmion interactions and the coupling to surfaces and interfaces, which crucially affect skyrmion stability and mobility. Here, we quantitatively reconstruct the 3D magnetic texture of Bloch skyrmions with sub-10-nanometre resolution using holographic vector-field electron tomography. The reconstructed textures reveal local deviations from a homogeneous Bloch character within the skyrmion tubes, details of the collapse of the skyrmion texture at surfaces and a correlated modulation of the skyrmion tubes in FeGe along their tube axes. Additionally, we confirm the fundamental principles of skyrmion formation through an evaluation of the 3D magnetic energy density across these magnetic solitons.

Magnetic particle-antiparticle creation and annihilation

A fundamental property of particles and antiparticles, such as electrons and positrons, is their ability to annihilate one another. Similar behavior is predicted for magnetic solitons~\cite{Kovalev_90}-- localized spin textures that can be distinguished by their topological index Q.Theoretically, magnetic topological solitons with opposite values of Q, such as skyrmions~\cite{Bogdanov_89} and their antiparticles -- antiskyrmions -- are expected to be able to merge continuously and to annihilate~\cite{Kuchkin_20i}. However, experimental verification of such particle-antiparticle pair production and annihilation processes has been lacking. Here, we report the creation and annihilation of skyrmion-antiskyrmion pairs in an exceptionally thin film of the cubic chiral magnet B20-type FeGe observed using transmission electron microscopy. Our observations are highly reproducible and are fully consistent with micromagnetic simulations. Our findings provide a new platform for fundamental studies of particles and antiparticles based on magnetic solids and open new perspectives for practical applications of thin films of isotropic chiral magnets.

Proca Q-balls and Q-shells

Non-topological solitons such as Q-balls and Q-shells have been studied for scalar fields invariant under global and gauged U(1) symmetries. We generalize this frame-work to include a Proca mass for the gauge boson, which can arise either from spontaneous symmetry breaking or via the Stückelberg mechanism. A heavy (light) gauge boson leads to solitons reminiscent of the global (gauged) case, but for intermediate values these Proca solitons exhibit completely novel features such as disconnected regions of viable parameter space and Q-shells with unbounded radius. We provide numerical solutions and excellent analytic approximations for both Proca Q-balls and Q-shells. These allow us to not only demonstrate the novel features numerically, but also understand and predict their origin analytically.

About the Solution of the Numerical Instability for Topological Solitons with Long Range Interaction

The computations of solutions of the field equations in the Model of Topological Particles, formulated with a scalar SU(2)-field, have shown instabilities leading to discrepancies between the numerical and analytical solutions. We identify the origin of these deviations in misalignments of the rotational axes corresponding to the SU(2) elements. The system of a single soliton we use as an example to show that a constraint suppressing the wave-like disturbances is able to lead to excellent agreement between the result of the numerical minimisation procedure and the analytical solution.

From Center-Vortex Ensembles to the Confining Flux Tube

In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.