Generalized Bloch band theory for non-Hermitian bulk–boundary correspondence

Bulk–boundary correspondence is the cornerstone of topological physics. In some non-Hermitian topological systems this fundamental relation is broken in the sense that the topological number calculated for the Bloch energy band under the periodic boundary condition fails to reproduce the boundary properties under the open boundary. To restore the bulk–boundary correspondence in such non-Hermitian systems a framework beyond the Bloch band theory is needed. We develop a non-Hermitian Bloch band theory based on a modified periodic boundary condition that allows a proper description of the bulk of a non-Hermitian topological insulator in a manner consistent with its boundary properties. Taking a non-Hermitian version of the Su–Schrieffer–Heeger model as an example, we demonstrate our scenario, in which the concept of bulk–boundary correspondence is naturally generalized to non-Hermitian topological systems.

Novel indicators for evaluating topological threats to populations from pandemics applied to COVID-19

ABSTRACTBACKGROUNDTo deal with pandemics, evaluating the temporal status of an outbreak is important. However, prevailing standards in this respect are mostly empirical and arbitrary. As an alternative, we focus on a novel approach which configures indicators that evaluate topological threats to populations due to the COVID-19 pandemic.METHODSWe extended the current PzDom model to calculate a threshold of the model for accelerated growth, an indicator of growth extent Re(v), covariance Re(s), a topological number E(l), and expected sums of possibly increasing numbers of infected people. We term this the exPzDom model.RESULTSThe indicators in the exPzDom model adhere well to the empirical dynamics of SARS-CoV-2 infected people and align appropriately with actual policies instituted by the Japanese government.CONCLUSIONSThe described indicators could be leveraged pursuant of objective evaluation based on mathematics. Further testing of the reliability and robustness of exPzDom model in other pandemic contexts is warranted.

Three-Dimensional Skyrmions with Arbitrary Topological Number in a Ferromagnetic Spin-1 Bose-Einstein Condensate

We propose a new scheme for creating three-dimensional Skyrmions in a ferromagnetic spin-1 Bose-Einstein condensate by manipulating a multipole magnetic field and a pair of counter-propagating laser beams. The result shows that a three-dimensional Skyrmion with topological number Q = 2 can be created by a sextupole magnetic field and the laser beams. Meanwhile, the vortex ring and knot structure in the Skyrmion are found. The topological number can be calculated analytically in our model, which implies that the method can be extended to create Skyrmions with arbitrary topological number. As the examples, three-dimensional Skyrmions with Q = 3, 4 are also demonstrated and are distinguishable by the density distributions with a specific quantization axis. These topological objects have the potential to be realized in ferromagnetic spin-1 Bose-Einstein condensates experimentally.

Dynamical magnetoelectric phenomena of skyrmions in multiferroics

Magnetic skyrmions, nanoscopic spin vortices carrying a quantized topological number in chiral-lattice magnets, are recently attracting great research interest. Although magnetic skyrmions had been observed only in metallic chiral-lattice magnets such as B20 alloys in the early stage of the research, their realization was discovered in 2012 also in an insulating chiral-lattice magnet $\textrm{Cu}_2\textrm{OSeO}_3$. A characteristic of the insulating skyrmions is that they can host multiferroicity, that is, the noncollinear magnetization alignment of skyrmion induces electric polarizations in insulators with a help of the relativistic spin-orbit interaction. It was experimentally confirmed that the skyrmion phase in $\textrm{Cu}_2\textrm{OSeO}_3$ is indeed accompanied by the spin-induced ferroelectricity. The resulting strong magnetoelectric coupling between magnetizations and electric polarizations can provide us with a means to manipulate and activate magnetic skyrmions by application of electric fields. This is in sharp contrast to skyrmions in metallic systems, which are driven through injection of electric currents. The magnetoelectric phenomena specific to the skyrmion-based multiferroics are attracting intensive research interest, and, in particular, those in dynamical regime are widely recognized as an issue of vital importance because their understanding is crucial both for fundamental science and for technical applications. In this article, we review recent studies on multiferroic properties and dynamical magnetoelectric phenomena of magnetic skyrmions in insulating chiral-lattice magnet $\textrm{Cu}_2\textrm{OSeO}_3$. It is argued that the multiferroic skyrmions show unique resonant excitation modes of coupled magnetizations and polarizations, so-called electromagnon excitations, which can be activated both magnetically with a microwave magnetic field and electrically with a microwave electric field. The interference between these two activation processes gives rise to peculiar phenomena in the gigahertz regime. As its representative example, we discuss a recent theoretical prediction of unprecedentedly large nonreciprocal directional dichroism of microwaves in the skyrmion phase of $\textrm{Cu}_2\textrm{OSeO}_3$. This phenomenon can be regarded as a one-way window effect on microwaves, that is, the extent of microwave absorption changes significantly when its incident direction is reversed. This dramatic effect was indeed observed by subsequent experiments. These studies demonstrated that the multiferroic skyrmions can be a promising building block for microwave devices.

Extracting topological information from momentum space propagators

A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from non-perturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement.