A topological insulator, as originally proposed for electrons governed by quantum mechanics, is characterized by a dichotomy between the interior and the edge of a finite system: The bulk has an ...energy gap, and the edges sustain excitations traversing this gap. However, it has remained an open question whether the same physics can be observed for systems obeying Newton's equations of motion. We conducted experiments to characterize the collective behavior of mechanical oscillators exhibiting the phenomenology of the quantum spin Hall effect. The phononic edge modes are shown to be helical, and we demonstrate their topological protection via the stability of the edge states against imperfections. Our results may enable the design of topological acoustic metamaterials that can capitalize on the stability of the surface phonons as reliable wave guides.
Topological phononic crystals, alike their electronic counterparts, are characterized by a bulk–edge correspondence where the interior of a material dictates the existence of stable surface or ...boundary modes. In the mechanical setup, such surface modes can be used for various applications such as wave guiding, vibration isolation, or the design of static properties such as stable floppy modes where parts of a system move freely. Here, we provide a classification scheme of topological phonons based on local symmetries. We import and adapt the classification of noninteracting electron systems and embed it into the mechanical setup. Moreover, we provide an extensive set of examples that illustrate our scheme and can be used to generate models in unexplored symmetry classes. Our work unifies the vast recent literature on topological phonons and paves the way to future applications of topological surface modes in mechanical metamaterials.
The current rate of species extinction is rapidly approaching unprecedented highs, and life on Earth presently faces a sixth mass extinction event driven by anthropogenic activity, climate change, ...and ecological collapse. The field of conservation genetics aims at preserving species by using their levels of genetic diversity, usually measured as neutral genome-wide diversity, as a barometer for evaluating population health and extinction risk. A fundamental assumption is that higher levels of genetic diversity lead to an increase in fitness and long-term survival of a species. Here, we argue against the perceived importance of neutral genetic diversity for the conservation of wild populations and species. We demonstrate that no simple general relationship exists between neutral genetic diversity and the risk of species extinction. Instead, a better understanding of the properties of functional genetic diversity, demographic history, and ecological relationships is necessary for developing and implementing effective conservation genetic strategies.
Learning phase transitions by confusion van Nieuwenburg, Evert P. L.; Liu, Ye-Hua; Huber, Sebastian D.
Nature physics,
05/2017, Letnik:
13, Številka:
5
Journal Article
Recenzirano
Odprti dostop
Classifying phases of matter is key to our understanding of many problems in physics. For quantum-mechanical systems in particular, the task can be daunting due to the exponentially large Hilbert ...space. With modern computing power and access to ever-larger data sets, classication problems are now routinely solved using machine-learning techniques1. Here, we propose a neural-network approach to finding phase transitions, based on the performance of a neural network after it is trained with data that are deliberately labelled incorrectly. We demonstrate the success of this method on the topological phase transition in the Kitaev chain2, the thermal phase transition in the classical Ising model3, and the many-body-localization transition in a disordered quantum spin chain4. Our method does not depend on order parameters, knowledge of the topological content of the phases,or any other specics of the transition at hand. It therefore paves the way to the development of a generic tool for identifying unexplored phase transitions.
The modern theory of charge polarization in solids is based on a generalization of Berry's phase. The possibility of the quantization of this phase arising from parallel transport in momentum space ...is essential to our understanding of systems with topological band structures. Although based on the concept of charge polarization, this same theory can also be used to characterize the Bloch bands of neutral bosonic systems such as photonic or phononic crystals. The theory of this quantized polarization has recently been extended from the dipole moment to higher multipole moments. In particular, a two-dimensional quantized quadrupole insulator is predicted to have gapped yet topological one-dimensional edge modes, which stabilize zero-dimensional in-gap corner states. However, such a state of matter has not previously been observed experimentally. Here we report measurements of a phononic quadrupole topological insulator. We experimentally characterize the bulk, edge and corner physics of a mechanical metamaterial (a material with tailored mechanical properties) and find the predicted gapped edge and in-gap corner states. We corroborate our findings by comparing the mechanical properties of a topologically non-trivial system to samples in other phases that are predicted by the quadrupole theory. These topological corner states are an important stepping stone to the experimental realization of topologically protected wave guides in higher dimensions, and thereby open up a new path for the design of metamaterials.
In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of the superfluid weight D_{s}, does not draw from the curvature of the band but has ...a purely band-geometric origin. In a mean-field description, a nonzero Chern number or fragile topology sets a lower bound for D_{s}, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG). For fragile topology, relevant for the bilayer system, the fate of this bound for finite temperature and beyond the mean-field approximation remained, however, unclear. Here, we numerically use exact Monte Carlo simulations to study an attractive Hubbard model in flat bands with topological properties akin to those of MATBG. We find a superconducting phase transition with a critical temperature that scales linearly with the interaction strength. Then, we investigate the robustness of the superconducting state to the addition of trivial bands that may or may not trivialize the fragile topology. Our results substantiate the validity of the topological bound beyond the mean-field regime and further stress the importance of fragile topology for flat-band superconductivity.
Phononic crystals and metamaterials can sculpt elastic waves, controlling their dispersion using different mechanisms. These mechanisms are mostly Bragg scattering, local resonances, and inertial ...amplification, derived from ad hoc, often problem-specific geometries of the materials' building blocks. Here, we present a platform that ultilizes a lattice of spiraling unit cells to create phononic materials encompassing Bragg scattering, local resonances, and inertial amplification. We present two examples of phononic materials that can control waves with wavelengths much larger than the lattice's periodicity. (1) A wave beaming plate, which can beam waves at arbitrary angles, independent of the lattice vectors. We show that the beaming trajectory can be continuously tuned, by varying the driving frequency or the spirals' orientation. (2) A topological insulator plate, which derives its properties from a resonance-based Dirac cone below the Bragg limit of the structured lattice of spirals.
Arguments about how ethnic diversity affects governance typically posit that groups differ from each other in substantively important ways and that these differences make effective governance more ...difficult. But existing cross-national empirical tests typically use measures of ethnolinguistic fractionalization (ELF) that have no information about substantive differences between groups. This article examines two important ways that groups differ from each other—culturally and economically—and assesses how such differences affect public goods provision. Across 46 countries, the analysis compares existing measures of cultural differences with a new measure that captures economic differences between groups: between-group inequality (BGI). We show that ELF, cultural fractionalization (CF), and BGI measure different things, and that the choice between them has an important impact on our understanding of which countries are most ethnically diverse. Furthermore, empirical tests reveal that BGI has a large, robust, and negative relationship with public goods provision, whereas CF, ELF, and overall inequality do not.
Flat-band superconductivity has theoretically demonstrated the importance of band topology to correlated phases. In two dimensions, the superfluid weight, which determines the critical temperature ...through the Berezinksii-Kosterlitz-Thouless criteria, is bounded by the Fubini-Study metric at zero temperature. We show this bound is nonzero within flat bands whose Wannier centers are obstructed from the atoms-even when they have identically zero Berry curvature. Next, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. We find that the bounds can be naturally expressed using the formalism of real space invariants (RSIs) that highlight the separation between electronic and atomic degrees of freedom. Finally, using exact Monte Carlo simulations on a model with perfectly flat bands and strictly local obstructed Wannier functions, we find that an attractive Hubbard interaction results in superconductivity as predicted by the RSI bound beyond mean field. Hence, obstructed bands are distinguished from trivial bands in the presence of interactions by the nonzero lower bound imposed on their superfluid weight.
I develop four related measures of the "ethnicization" of electoral behavior. Each measure increases as ethnic identity becomes more central to vote choice, but the measures differ along two ...theoretical dimensions. The first dimension contrasts a group-based perspective (which focuses on cohesion in the voting patterns of group members) with a party-based perspective (which focuses on the composition of groups supporting political parties). The second dimension contrasts a fractionalization perspective (which assumes that more groups or parties cause more problems) with a polarization perspective (which assumes that problems are greatest when there are two equal-sized groups or parties). Using survey data to implement the measures in 43 countries, the article shows that proportional electoral laws are associated with lower levels of ethnicization—the opposite of what is widely assumed. I argue that the lower levels of ethnicization in PR systems should be unsurprising.
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