37 research outputs found

    Quantized shift response in multi-gap topological phases

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    We show that certain 3D multi-gap topological insulators can host quantized shift photoconductivities due to bulk invariants that are defined under reality conditions imposed by additional symmetries. We recast the quantization in terms of the integrated torsion tensor and the non-Abelian Berry connection constituting Chern-Simons forms. Physically, we recognize that the topological quantization emerges purely from virtual transitions contributing to the optical response. Our findings provide another quantized electromagnetic DC response due to the non-trivial band topology, beyond the quantum anomalous Hall effect of Chern insulators and quantized circular photogalvanic effect found in Weyl semimetals.Comment: 7+7 pages; 3+1 figure

    Disorder-induced topological quantum phase transitions in Euler semimetals

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    We study the effect of disorder in systems having a non-trivial Euler class. As these recently proposed multi-gap topological phases come about by braiding non-Abelian charged band nodes residing between different bands to induce stable pairs within isolated band subspaces, novel properties that include a finite critical phase under the debraiding to a metal rather than a transition point and a modified stability may be expected when the disorder preserves the underlying C2TC_2\cal{T} or PT\cal{P}\cal{T} symmetry on average. Employing elaborate numerical computations, we verify the robustness of associated topology by evaluating the changes in the average densities of states and conductivities for different types of disorders. Upon performing a scaling analysis around the corresponding quantum critical points we retrieve a universality for the localization length exponent of ν=1.4±0.1\nu = 1.4 \pm 0.1 for Euler-protected phases, relating to 2D percolation models. We generically find that quenched disorder drives Euler semimetals into critical metallic phases. Finally, we show that magnetic disorder can also induce topological transitions to quantum anomalous Hall plaquettes with local Chern numbers determined by the initial value of the Euler invariant.Comment: 6+7 pages, 4+6 figure

    Optical manifestations of topological Euler class in electronic materials

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    We analyze quantum-geometric bounds on optical weights in topological phases with pairs of bands hosting non-trivial Euler class, a multi-gap invariant characterizing non-Abelian band topology. We show how the bounds constrain the combined optical weights of the Euler bands at different dopings and further restrict the size of the adjacent band gaps. In this process, we also consider the associated interband contributions to DC conductivities in the flat-band limit. We physically validate these results by recasting the bound in terms of transition rates associated with the optical absorption of light, and demonstrate how the Euler connections and curvatures can be determined through the use of momentum and frequency-resolved optical measurements, allowing for a direct measurement of this multi-band invariant. Additionally, we prove that the bound holds beyond the degenerate limit of Euler bands, resulting in nodal topology captured by the patch Euler class. In this context, we deduce optical manifestations of Euler topology within kp\vec{k} \cdot \vec{p} models, which include AC conductivity, and third-order jerk photoconductivities in doped Euler semimetals. We showcase our findings with numerical validation in lattice-regularized models that benchmark effective theories for real materials and are themselves directly realizable in metamaterials and optical lattices.Comment: 8+9 pages, 3 figure

    On the search for the right definition of heart failure with preserved ejection fraction

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    The definition of heart failure with preserved ejection fraction (HFpEF) has evolved from a clinically based “diagnosis of exclusion” to definitions focused on objective evidence of diastolic dysfunction and/or elevated left ventricular filling pressures. Despite advances in our understanding of HFpEF pathophysiology and the development of more sophisticated imaging modalities, the diagnosis of HFpEF remains challenging, especially in the chronic setting, given that symptoms are provoked by exertion and diagnostic evaluation is largely conducted at rest. Invasive hemodynamic study, and in particular — invasive exercise testing, is considered the reference method for HFpEF diagnosis. However, its use is limited as opposed to the high number of patients with suspected HFpEF. Thus, diagnostic criteria for HFpEF should be principally based on non-invasive measurements. As no single non-invasive variable can adequately corroborate or refute the diagnosis, different combinations of clinical, echocardiographic, and/or biochemical parameters have been introduced. Recent years have brought an abundance of HFpEF definitions. Here, we present and compare four of them: 1) the 2016 European Society of Cardiology criteria for HFpEF; 2) the 2016 echocardiographic algorithm for diagnosing diastolic dysfunction; 3) the 2018 evidence-based H2FPEF score; and 4) the most recent, 2019 Heart Failure Association HFA-PEFF algorithm. These definitions vary in their approach to diagnosis, as well as sensitivity and specificity. Further studies to validate and compare the diagnostic accuracy of HFpEF definitions are warranted. Nevertheless, it seems that the best HFpEF definition would originate from a randomized clinical trial showing a favorable effect of an intervention on prognosis in HFpEF
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