2018, Liu, Z., Lou, R., Guo, P., Wang, Q., Sun, S., Li, C., Thirupathaiah, S., Fedorov, A., Shen, D., Liu, K., Lei, H., Wang, S.

The topological nodal-line semimetal state, serving as a fertile ground for various topological quantum phases, where a topological insulator, Dirac semimetal, or Weyl semimetal can be realized when the certain protecting symmetry is broken, has only been experimentally studied in very few materials. In contrast to discrete nodes, nodal lines with rich topological configurations can lead to more unusual transport phenomena. Utilizing angle-resolved photoemission spectroscopy and first-principles calculations, here, we provide compelling evidence of nodal-line fermions in centrosymmetric semimetal TiB2 with a negligible spin-orbit coupling effect. With the band crossings just below the Fermi energy, two groups of Dirac nodal rings are clearly observed without any interference from other bands, one surrounding the Brillouin zone (BZ) corner in the horizontal mirror plane σh and the other surrounding the BZ center in the vertical mirror plane σv. The linear dispersions forming Dirac nodal rings are as wide as 2 eV. We further observe that the two groups of nodal rings link together along the Γ-K direction, composing a nodal-link configuration. The simple electronic structure with Dirac nodal links mainly constituting the Fermi surfaces suggests TiB2 as a remarkable platform for studying and applying the novel physical properties related to nodal-line fermions.

2018, Zhang, Y., Železný, J., Sun, Y., Van Den Brink, J., Yan, B.

The spin Hall effect (SHE), which converts a charge current into a transverse spin current, has long been believed to be a phenomenon induced by spin-orbit coupling. Here, we identify an alternative mechanism to realize the intrinsic SHE through a noncollinear magnetic structure that breaks the spin rotation symmetry. No spin-orbit coupling is needed even when the scalar spin chirality vanishes, different from the case of the topological Hall effect and topological SHE reported previously. In known noncollinear antiferromagnetic compounds Mn3X (X = Ga, Ge, and Sn), for example, we indeed obtain large spin Hall conductivities based on ab initio calculations.

2014, Klimm, F., Borge-Holthoefer, J., Wessel, N., Kurths, J., Zamora-Lopez, G.

The analysis of complex networks is devoted to the statistical characterization of the topology of graphs at different scales of organization in order to understand their functionality. While the modular structure of networks has become an essential element to better apprehend their complexity, the efforts to characterize the mesoscale of networks have focused on the identification of the modules rather than describing the mesoscale in an informative manner. Here we propose a framework to characterize the position every node takes within the modular configuration of complex networks and to evaluate their function accordingly. For illustration, we apply this framework to a set of synthetic networks, empirical neural networks, and to the transcriptional regulatory network of the Mycobacterium tuberculosis. We find that the architecture of both neuronal and transcriptional networks are optimized for the processing of multisensory information with the coexistence of well-defined modules of specialized components and the presence of hubs conveying information from and to the distinct functional domains.

2020, Xu, Q., Zhang, Y., Koepernik, K., Shi, W., van den Brink, J., Felser, C., Sun, Y.

First-principles calculations have recently been used to develop comprehensive databases of nonmagnetic topological materials that are protected by time-reversal or crystalline symmetry. However, owing to the low symmetry requirement of Weyl points, a symmetry-based approach to identifying topological states cannot be applied to Weyl semimetals (WSMs). To date, WSMs with Weyl points in arbitrary positions are absent from the well-known databases. In this work, we develop an efficient algorithm to search for Weyl points automatically and establish a database of nonmagnetic WSMs with Weyl points near the Fermi level based on the experimental non-centrosymmetric crystal structures in the Inorganic Crystal Structure Database (ICSD). In total, 46 Weyl semimetals were discovered to have nearly clean Fermi surfaces and Weyl points within 300 meV of the Fermi level. Nine of them are chiral structures which may exhibit the quantized circular photogalvanic effect. In addition, the nonlinear optical response is studied and the giant shift current is explored. Besides nonmagnetic WSMs, our powerful tools can also be used in the discovery of magnetic topological materials.

2010, Donner, R.V., Zou, Y., Donges, J.F., Marwan, N., Kurths, J.

This paper presents a new approach for analysing the structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

2014, Traxl, D., Boers, N., Kurths, J.

The effects of white noise and global coupling strength on the maximum degree of synchronization in complex networks are explored. We perform numerical simulations of generic oscillator models with both linear and non-linear coupling functions on a broad spectrum of network topologies. The oscillator models include the Fitzhugh-Nagumo model, the Izhikevich model and the Kuramoto phase oscillator model. The network topologies range from regular, random and highly modular networks to scale-free and small-world networks, with both directed and undirected edges. We then study the dependency of the maximum degree of synchronization on the global coupling strength and the noise intensity. We find a general scaling of the synchronizability, and quantify its validity by fitting a regression model to the numerical data.

2017, Mitra, C., Kittel, T., Choudhary, A., Kurths, J., Donner, R.V.

Maintaining the synchronous motion of dynamical systems interacting on complex networks is often critical to their functionality. However, real-world networked dynamical systems operating synchronously are prone to random perturbations driving the system to arbitrary states within the corresponding basin of attraction, thereby leading to epochs of desynchronized dynamics with a priori unknown durations. Thus, it is highly relevant to have an estimate of the duration of such transient phases before the system returns to synchrony, following a random perturbation to the dynamical state of any particular node of the network. We address this issue here by proposing the framework of single-node recovery time (SNRT) which provides an estimate of the relative time scales underlying the transient dynamics of the nodes of a network during its restoration to synchrony. We utilize this in differentiating the particularly slow nodes of the network from the relatively fast nodes, thus identifying the critical nodes which when perturbed lead to significantly enlarged recovery time of the system before resuming synchronized operation. Further, we reveal explicit relationships between the SNRT values of a network, and its global relaxation time when starting all the nodes from random initial conditions. Earlier work on relaxation time generally focused on investigating its dependence on macroscopic topological properties of the respective network. However, we employ the proposed concept for deducing microscopic relationships between topological features of nodes and their respective SNRT values. The framework of SNRT is further extended to a measure of resilience of the different nodes of a networked dynamical system. We demonstrate the potential of SNRT in networks of Rössler oscillators on paradigmatic topologies and a model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics illustrating the conceivable practical applicability of the proposed concept.

2019, Haubold, E., Fedorov, A., Pielnhofer, F., Rusinov, I.P., Menshchikova, T.V., Duppel, V., Friedrich, D., Weihrich, R., Pfitzner, A., Zeugner, A., Isaeva, A., Thirupathaiah, S., Kushnirenko, Y., Rienks, E., Kim, T., Chulkov, E.V., Büchner, B., Borisenko, S.

We report experimental and theoretical evidence that GaGeTe is a basic Z2 topological semimetal with three types of charge carriers: bulk-originated electrons and holes as well as surface state electrons. This electronic situation is qualitatively similar to the classic 3D topological insulator Bi2Se3, but important differences account for an unprecedented transport scenario in GaGeTe. High-resolution angle-resolved photoemission spectroscopy combined with advanced band structure calculations show a small indirect energy gap caused by a peculiar band inversion at the T-point of the Brillouin zone in GaGeTe. An energy overlap of the valence and conduction bands brings both electron and holelike carriers to the Fermi level, while the momentum gap between the corresponding dispersions remains finite. We argue that peculiarities of the electronic spectrum of GaGeTe have a fundamental importance for the physics of topological matter and may boost the material's application potential.

2014, Schultz, P., Heitzig, J., Kurths, J.

To analyse the relationship between stability against large perturbations and topological properties of a power transmission grid, we employ a statistical analysis of a large ensemble of synthetic power grids, looking for significant statistical relationships between the single-node basin stability measure and classical as well as tailormade weighted network characteristics. This method enables us to predict poor values of single-node basin stability for a large extent of the nodes, offering a node-wise stability estimation at low computational cost. Further, we analyse the particular function of certain network motifs to promote or degrade the stability of the system. Here we uncover the impact of so-called detour motifs on the appearance of nodes with a poor stability score and discuss the implications for power grid design.

2012, Ge, T., Cui, Y., Lin, W., Kurths, J., Liu, C.

In this paper, we propose a new approach to characterize time series with noise perturbations in both the time and frequency domains by combining Granger causality and complex networks. We construct directed and weighted complex networks from time series and use representative network measures to describe their physical and topological properties. Through analyzing the typical dynamical behaviors of some physical models and the MIT-BIH 7 human electrocardiogram data sets, we show that the proposed approach is able to capture and characterize various dynamics and has much potential for analyzing real-world time series of rather short length.