2016, Klein, Olaf, Recupero, Vincenzo

Sweeping processes are a class of evolution differential inclusions arising in elastoplasticity and were introduced by J.J. Moreau in the early seventies. The solution operator of the sweeping processes represents a relevant example of rate independent operator. As a particular case we get the so called play operator, which is a typical example of a hysteresis operator. The continuity properties of these operators were studied in several works. In this note we address the continuity with respect to the strict metric in the space of functions of bounded variation with values in the metric space of closed convex subsets of a Hilbert space. We provide counterexamples showing that for all BV-formulations of the sweeping process the corresponding solution operator is not continuous when its domain is endowed with the strict topology of BV and its codomain is endowed with the L1-topology. This is at variance with the play operator which has a BV-extension that is continuous in this case.

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.

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.

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.

2021, Bannies, J., Razzoli, E., Michiardi, M., Kung, H.-H., Elfimov, I.S., Yao, M., Fedorov, A., Fink, J., Jozwiak, C., Bostwick, A., Rotenberg, E., Damascelli, A., Felser, C.

Several early transition metal dipnictides (TMDPs) have been found to host topological semimetal states and exhibit large magnetoresistance (MR). In this paper, we use angle-resolved photoemission spectroscopy (ARPES) and magnetotransport to study the electronic properties of a TMDP ZrP2. We find that ZrP2 exhibits an extremely large and unsaturated MR of up to 40 000% at 2 K, which originates from an almost perfect electron-hole (e-h) compensation. Our band structure calculations further show that ZrP2 hosts a topological nodal loop in proximity to the Fermi level. Based on the ARPES measurements, we confirm the results of our calculations and determine the surface band structure. This paper establishes ZrP2 as a platform to investigate near-perfect e-h compensation and its interplay with topological band structures.

2023, Liu, Huimei, Hirschmann, Moritz M., Sawatzky, George A., Khaliullin, Giniyat, Schnyder, Andreas P.

SmB6 is a mixed-valence compound with flat f-electron bands that have a propensity to magnetism. Here, using a realistic Γ8 quartet model, we investigate the dynamical spin susceptibility and describe the in-gap collective mode observed in neutron scattering experiments. We show that as the Sm valence increases with pressure, the magnetic correlations enhance and SmB6 undergoes a first-order phase transition into a metallic antiferromagnetic state, whose symmetry depends on the model parameters. The magnetic orderings give rise to distinct band topologies: while the A-type order leads to an overlap between valence and conduction bands in the form of Dirac nodal lines, the G-type order has a negative indirect gap with weak Z2 indices. We also consider the spin polarized phase under a strong magnetic field, and find that it exhibits Weyl points as well as nodal lines close to the Fermi level. The magnetic phases show markedly different surface states and tunable bulk transport properties, with important implications for experiments. Our theory predicts that a magnetic order can be stabilized also by lifting the Γ8 cubic symmetry, thus explaining the surface magnetism reported in SmB6.

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.

2018, Heidemann, Knut M., Sageman-Furnas, Andrew O., Sharma, Abhinav, Rehfeldt, Florian, Schmidt, Christoph F., Wardetzky, Max

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N,z). Despite the universal properties of such (N,z) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.

2022, Leonov, A.O., Pappas, C.

Cu2OSeO3 represents a unique example in the family of B20 cubic helimagnets with a tilted spiral and a low-temperature skyrmion phase arising for magnetic fields applied along the easy crystallographic (100) axes. Although the stabilization mechanism of these phases can be accounted for by cubic magnetic anisotropy, the skyrmion nucleation process is still an open question, since the stability region of the skyrmion phase displays strongly hysteretic behavior with different phase boundaries for increasing and decreasing magnetic fields. Here, we address this important point using micromagnetic simulations and come to the conclusion that skyrmion nucleation is underpinned by the reorientation of spiral domains occurring near the critical magnetic fields of the phase diagrams: HC1, the critical field of the transition between the helical and conical/tiled spiral phase, and HC2, the critical field between the conical/tiled spiral and the homogenous phase. By studying a wide variety of cases we show that domain walls may have a 3D structure. Moreover, they can carry a finite topological charge stemming from half-skyrmions (merons) also permitting along-the-field and perpendicular-to-the-field orientation. Thus, domain walls may be envisioned as nucleation source of skyrmions that can form thermodynamically stable and metastable lattices as well as skyrmion networks with misaligned skyrmion tubes. The results of numerical simulations are discussed in view of recent experimental data on chiral magnets, in particular, for the bulk cubic helimagnet Cu2OSeO3.

2022, Siegfried, Peter E., Bhandari, Hari, Jones, David C., Ghimire, Madhav P., Dally, Rebecca L., Poudel, Lekh, Bleuel, Markus, Lynn, Jeffrey W., Mazin, Igor I., Ghimire, Nirmal J.

The Fermi surface (FS) is essential for understanding the properties of metals. It can change under both conventional symmetry-breaking phase transitions and Lifshitz transitions (LTs), where the FS, but not the crystal symmetry, changes abruptly. Magnetic phase transitions involving uniformly rotating spin textures are conventional in nature, requiring strong spin-orbit coupling (SOC) to influence the FS topology and generate measurable properties. LTs driven by a continuously varying magnetization are rarely discussed. Here we present two such manifestations in the magnetotransport of the kagome magnet YMn6Sn6: one caused by changes in the magnetic structure and another by a magnetization-driven LT. The former yields a 10% magnetoresistance enhancement without a strong SOC, while the latter a 45% reduction in the resistivity. These phenomena offer a unique view into the interplay of magnetism and electronic topology, and for understanding the rare-earth counterparts, such as TbMn6Sn6, recently shown to harbor correlated topological physics.