Topolectric circuits: Theory and construction

We highlight a general theory to engineer arbitrary Hermitian tight-binding lattice models in electrical LC circuits, where the lattice sites are replaced by the electrical nodes, connected to its neighbors and to the ground by capacitors and inductors. In particular, by supplementing each node with n subnodes, where the phases of the current and voltage are the n distinct roots of unity, one can in principle realize arbitrary hopping amplitude between the sites or nodes via the shift capacitor coupling between them. This general principle is then implemented to construct a plethora of topological models in electrical circuits, topolectric circuits, where the robust zero-energy topological boundary modes manifest through a large boundary impedance, when the circuit is tuned to the resonance frequency. The simplicity of our circuit constructions is based on the fact that the existence of the boundary modes relies only on the Clifford algebra of the corresponding Hermitian matrices entering the Hamiltonian and not on their particular representation. This in turn enables us to implement a wide class of topological models through rather simple topolectric circuits with nodes consisting of only two subnodes. We anchor these outcomes from the numerical computation of the on-resonance impedance in circuit realizations of first-order (m = 1), such as Chern and quantum spin Hall insulators, and second- (m = 2) and third- (m = 3) order topological insulators in different dimensions, featuring sharp localization on boundaries of codimensionality d(c) = m. Finally, we subscribe to the stacked topolectric circuit construction to engineer three-dimensional Weyl, nodal-loop, quadrupolar Dirac, and Weyl semimetals, respectively, displaying surface- and hinge-localized impedance

Переяславська рада у сучасній російській навчальній літературі

Topological band-insulators (TBIs) represent a new class of quantum materials that in the presence of time-reversal symmetry (TRS) feature an insulating bulk bandgap together with metallic edge or surface states protected by a Z 2 topological invariant [1,2,3,4]. Recently, an extra layer in this Z 2 classification of TBIs has been uncovered by considering the crystal symmetries [5]. Dislocation lines being the unique topological defects related to the lattice translations play a fundamental role in this endeavor. We here elucidate the general rule governing their response in three-dimensional TBIs and uncover their role in this classification. According to that K-b-t rule, the lattice topology, represented by dislocation lines oriented in the direction t with the Burgers vector b , conspires with the electronic-band topology, characterized by the band-inversion momentum K inv , to produce gapless propagating modes along these line defects, which were discovered in Ref. [6]. For sufficiently symmetric crystals, this conspiracy leads to the topologically-protected metallic states inside the dislocation loops, which could also be important for applications. Finally, these findings are experimentally consequential as dislocation defects are ubiquitous in the real crystals

Massive CP1^1 theory from a microscopic model for doped antiferromagnets

A path-integral for the t-J model in two dimensions is constructed based on Dirac quantization, with an action found originally by Wiegmann (Phys. Rev. Lett. {\bf 60}, 821 (1988); Nucl. Phys. B323, 311 (1989)). Concentrating on the low doping limit, we assume short range antiferromagnetic order of the spin degrees of freedom. Going over to a local spin quantization axis of the dopant fermions, that follows the spin degree of freedom, staggered CP$^1$ fields result and the constraint against double occupancy can be resolved. The staggered CP$^1$ fields are split into slow and fast modes, such that after a gradient expansion, and after integrating out the fast modes and the dopant fermions, a CP$^1$ field-theory with a massive gauge field is obtained that describes generically incommensurate coplanar magnetic structures, as discussed previously in the context of frustrated quantum antiferromagnets. Hence, the possibility of deconfined spinons is opened by doping a colinear antiferromagnet.Comment: 24 pages, no figure

Dissipative dynamics of topological defects in frustrated Heisenberg spin systems

We study the dynamics of topological defects of a frustrated spin system displaying spiral order. As a starting point we consider the SO(3) nonlinear sigma model to describe long-wavelength fluctuations around the noncollinear spiral state. Besides the usual spin-wave magnetic excitations, the model allows for topologically non-trivial static solutions of the equations of motion, associated with the change of chirality (clockwise or counterclockwise) of the spiral. We consider two types of these topological defects, single vortices and vortex-antivortex pairs, and quantize the corresponding solutions by generalizing the semiclassical approach to a non-Abelian field theory. The use of the collective coordinates allows us to represent the defect as a particle coupled to a bath of harmonic oscillators, which can be integrated out employing the Feynman-Vernon path-integral formalism. The resulting effective action for the defect indicates that its motion is damped due to the scattering by the magnons. We derive a general expression for the damping coefficient of the defect, and evaluate its temperature dependence in both cases, for a single vortex and for a vortex-antivortex pair. Finally, we consider an application of the model for cuprates, where a spiral state has been argued to be realized in the spin-glass regime. By assuming that the defect motion contributes to the dissipative dynamics of the charges, we can compare our results with the measured inverse mobility in a wide range of temperature. The relatively good agreement between our calculations and the experiments confirms the possible relevance of an incommensurate spiral order for lightly doped cuprates.Comment: 22 pages, 7 figures, final published versio

Antiferromagnetic Ising spin glass competing with BCS pairing interaction in a transverse field

The competition among spin glass (SG), antiferromagnetism (AF) and local pairing superconductivity (PAIR) is studied in a two-sublattice fermionic Ising spin glass model with a local BCS pairing interaction in the presence of an applied magnetic transverse field $\Gamma$. In the present approach, spins in different sublattices interact with a Gaussian random coupling with an antiferromagnetic mean $J_0$ and standard deviation $J$. The problem is formulated in the path integral formalism in which spin operators are represented by bilinear combinations of Grassmann variables. The saddle-point Grand Canonical potential is obtained within the static approximation and the replica symmetric ansatz. The results are analysed in phase diagrams in which the AF and the SG phases can occur for small $g$ ($g$ is the strength of the local superconductor coupling written in units of $J$), while the PAIR phase appears as unique solution for large $g$. However, there is a complex line transition separating the PAIR phase from the others. It is second order at high temperature that ends in a tricritical point. The quantum fluctuations affect deeply the transition lines and the tricritical point due to the presence of $\Gamma$.Comment: 16 pages, 6 figures, accepted Eur. Phys. J.

Vision in an abundant North American bird: The Red-winged Blackbird

Avian vision is fundamentally different from human vision; however, even within birds there are substantial between species differences in visual perception in terms of visual acuity, visual coverage, and color vision. However, there are not many species that have all these visual traits described, which can constrain our ability to study the evolution of visual systems in birds. To start addressing this gap, we characterized multiple traits of the visual system (visual coverage, visual acuity, centers of acute vision, and color vision) of the Red-winged Blackbird (Agelaius phoeniceus), one of the most abundant and studied birds in North America. We found that Red-winged Blackbirds have: wide visual coverage; one center of acute vision per eye (fovea) projecting fronto-laterally with high density of single and double cones, making it the center of both chromatic and achromatic vision; a wide binocular field that does not have the input of the centers of acute vision; and an ultraviolet sensitive visual system. With this information, we parameterized a Red-winged Blackbird-specific perceptual model considering different plumage patches. We found that the male red epaulet was chromatically conspicuous but with minimal achromatic signal, but the male yellow patch had a lower chromatic but a higher achromatic signal, which may be explained by the pigment composition of the feathers. However, the female epaulet was not visually conspicuous in both the chromatic and achromatic dimensions compared with other female feather patches. We discuss the implications of this visual system configuration relative to the foraging, antipredator, mate choice, and social behaviors of Red-winged Blackbirds. Our findings can be used for comparative studies as well as for making more species-specific predictions about different visual behaviors for future empirical testing

Binocular vision and foraging in ducks, geese and swans (Anatidae)

Wide variation in visual field configuration across avian species is hypothesized to be driven primarily by foraging ecology and predator detection. While some studies of selected taxa have identified relationships between foraging ecology and binocular field characteristics in particular species, few have accounted for the relevance of shared ancestry. We conducted a large-scale, comparative analysis across 39 Anatidae species to investigate the relationship between the foraging ecology traits of diet or behaviour and binocular field parameters, while controlling for phylogeny. We used phylogenetic models to examine correlations between traits and binocular field characteristics, using unidimensional and morphometric approaches. We found that foraging behaviour influenced three parameters of binocular field size: maximum binocular field width, vertical binocular field extent, and angular separation between the eye-bill projection and the direction of maximum binocular field width. Foraging behaviour and body mass each influenced two descriptors of binocular field shape. Phylogenetic relatedness had minimal influence on binocular field size and shape, apart from vertical binocular field extent. Binocular field differences are associated with specific foraging behaviours, as related to the perceptual challenges of obtaining different food items from aquatic and terrestrial environments

A framework for managing airport grasslands and birds amidst conflicting priorities

Management of modern airports is a task beset by conflicting priorities. Airports are vital to the global market economy, but impose costly environmental disturbances including habitat loss, noise, reduced air quality, erosion, introduction of invasive organisms, and polluted storm-water runoff (Blackwell et al. 2009). Airport environments also attract some wildlife hazardous to aviation safety, namely species involved in wildlife-aircraft collisions or ‘strikes’ (ICAO 2001, Blackwell et al. 2009, DeVault et al. 2011). Since 1912 at least 276 human lives have been lost due to bird strikes (Thorpe 2010), and from 1990 to 2010, more than 106 000 bird strikes involving civil aircraft were reported to the US Federal Aviation Administration (FAA; http://wildlife-mitigation. tc.faa.gov/wildlife/). Dolbeer (2006) reported that for strikes resulting in substantial aircraft damage (ICAO 1989), 66% occurred below 152 m altitude and within 1.5 km of a runway for airports servicing piston-powered aircraft only, and within 3 km of a runway for airports servicing turbine-powered aircraft (FAA 2009). Consequently, aviation authorities prioritize human safety over wildlife conservation in management of airport habitats (ICAO 2001, FAA 2009). Despite these problems, airports have been proposed as candidates for biodiversity conservation (Kelly & Allan 2006, Blackwell et al. 2009). For example, Kutschbach- Brohl et al. (2010) report that airport grasslands can provide habitat for a range of arthropod communities (e.g. Lepidoptera), and suggest the possibility of conserving these communities while minimizing provision of prey resources to birds recognized as hazardous to aviation. Moreover, declines in grassland bird populations in Europe and North America due to agricultural intensification and development have focused attention on enhancing quality and quantity of remnant grasslands (Herkert 1994, Vickery et al. 2004), including airport grasslands. In North America, airport properties have been identified as key areas of remnant grasslands important to obligate grassland bird species; species that both nest and forage in grasslands (Vickery et al. 1994, Askins et al. 2007). Airport properties in the contiguous USA include \u3e 330 000 ha of grassland, mostly annually mown areas, constituting 39–50% of airport property (DeVault et al. 2012). However, there is little research specific to airport environments that considers food resources for birds (Bernhardt et al. 2010, Kutschbach-Brohl et al. 2010), how birds perceive and react to predation risk (Baker & Brooks 1981) or disturbance (Kershner & Bollinger 1996), and no adequate assessment of how grassland management might affect strike risk (Blackwell et al. 2009, Martin et al. 2011). In this context, we contend that promoting conservation of obligate grassland birds and managing to reduce bird hazards to aviation safety combines two potentially conflicting objectives in a single management framework. Ecologically based guidance to solve this potential conflict is limited, if not oversimplified. Here, we question the potential use of airports to conserve grassland birds, and assess the challenges in managing airport grasslands in light of current ecological and behavioral frameworks. We consider conditions for conservation of obligate grassland birds on airports, and evidence on the use of airports by frequently struck, grassland birds (both obligate and facultative). We also provide a framework to manage grassland birds at airports, given current information and uncertainty. Because of the availability of strike data via the FAA, our focus is on North America. However, problems associated with bird use of airport grasslands are international (ICAO 2001). Therefore, our ultimate purpose is better to inform current management, but also identify research gaps and establish specific predictions that will guide future studies on the ecological basis of use of airport grasslands by birds