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Abstract Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimetal CeAlSi, where the magnetization introduces a pronounced directionality in the nonlinear optical second-harmonic generation (SHG). We demonstrate a six-fold change of the measured SHG intensity between opposite propagation directions over a bandwidth exceeding 250 meV. Supported by density-functional theory, we establish the linearly dispersive bands emerging from Weyl nodes as the origin of this broadband effect. We further demonstrate current-induced magnetization switching and thus electrical control of the NODE. Our results advance ongoing research to identify novel nonlinear optical/transport phenomena in magnetic topological materials and further opens new pathways for the unidirectional manipulation of light. 

Synopsis New biophysical theory and electronic databases raise the prospect of deriving fundamental rules of life, a conceptual framework for how the structures and functions of molecules, cells, and individual organisms give rise to emergent patterns and processes of ecology, evolution, and biodiversity. This framework is very general, applying across taxa of animals from 10–10 g protists to 108 g whales, and across environments from deserts and abyssal depths to rain forests and coral reefs. It has several hallmarks: (1) Energy is the ultimate limiting resource for organisms and the currency of biological fitness. (2) Most organisms are nearly equally fit, because in each generation at steady state they transfer an equal quantity of energy (˜22.4 kJ/g) and biomass (˜1 g/g) to surviving offspring. This is the equal fitness paradigm (EFP). (3) The enormous diversity of life histories is due largely to variation in metabolic rates (e.g., energy uptake and expenditure via assimilation, respiration, and production) and biological times (e.g., generation time). As in standard allometric and metabolic theory, most physiological and life history traits scale approximately as quarter-power functions of body mass, m (rates as ∼m–1/4 and times as ∼m1/4), and as exponential functions of temperature. (4) Time is the fourth dimension of life. Generation time is the pace of life. (5) There is, however, considerable variation not accounted for by the above scalings and existing theories. Much of this “unexplained” variation is due to natural selection on life history traits to adapt the biological times of generations to the clock times of geochronological environmental cycles. (6) Most work on biological scaling and metabolic ecology has focused on respiration rate. The emerging synthesis applies conceptual foundations of energetics and the EFP to shift the focus to production rate and generation time. 

Abstract Here we review and extend the equal fitness paradigm (EFP) as an important step in developing and testing a synthetic theory of ecology and evolution based on energy and metabolism. The EFP states that all organisms are equally fit at steady state, because they allocate the same quantity of energy, ~ 22.4 kJ/g/generation to the production of offspring. On the one hand, the EFP may seem tautological, because equal fitness is necessary for the origin and persistence of biodiversity. On the other hand, the EFP reflects universal laws of life: how biological metabolism – the uptake, transformation and allocation of energy – links ecological and evolutionary patterns and processes across levels of organisation from: (1) structure and function of individual organisms, (2) life history and dynamics of populations, and (3) interactions and coevolution of species in ecosystems. The physics and biology of metabolism have facilitated the evolution of millions of species with idiosyncratic anatomy, physiology, behaviour and ecology but also with many shared traits and tradeoffs that reflect the single origin and universal rules of life.