The Nonlinear Optical Effects of Opening a Gap in Graphene

Graphene possesses remarkable electronic, optical and mechanical properties that have taken the research of two-dimensional relativistic condensed matter systems to prolific levels. However, the understanding of how its nonlinear optical properties are affected by relativistic-like effects has been broadly uncharted. It has been recently shown that highly-nontrivial currents can be generated in free-standing samples, notably leading to the generation of even harmonics. Since graphene monolayers are centrosymmetric media, for which such harmonic generation is deemed inaccessible, this light-driven phenomenon is both startling and promising. More realistically, graphene samples are often deposited on a dielectric substrate, leading to additional intricate interactions. Here, we present a treatment to study this instance by gapping the spectrum and we show this leads to the appearance of a Berry phase in the carrier dynamics. We analyse the role of such a phase in the generated nonlinear current and conclude that it suppresses odd-harmonic generation. The pump energy can be tuned to the energy gap to yield interference among odd harmonics mediated by interband transitions, allowing even harmonics to be generated. Our results and general methodology pave the way for understanding the role of gap-opening physical factors in the nonlinear optics of hexagonal two-dimensional lattices.Comment: 5 figure

Using theoretical-computational conflicts to enrich the concept name of derivative

Recent literature has pointed out pedagogical obstacles associated with the use of computational environments in the learning of mathematics. In this paper, we focus on the pedagogical role of the computer's inherent limitations in the development of learners' concept images of derivative. In particular, we intend to discuss how the approach to this concept can be designed to prompt a positive conversion of those limitations for the enrichment of concept images. We present results of a case study with six undergraduate students in Brazil, dealing with situation of theoretical-computational conflict

Polarization and valley switching in monolayer group-IV monochalcogenides

Group-IV monochalcogenides are a family of two-dimensional puckered materials with an orthorhombic structure that is comprised of polar layers. In this article, we use first principles calculations to show the multistability of monolayer SnS and GeSe, two prototype materials where the direction of the puckering can be switched by application of tensile stress or electric field. Furthermore, the two inequivalent valleys in momentum space, which are dictated by the puckering orientation, can be excited selectively using linearly polarized light, and this provides an additional tool to identify the polarization direction. Our findings suggest that SnS and GeSe monolayers may have observable ferroelectricity and multistability, with potential applications in information storage

KEYNES’ CRITIQUE OF THE CLASSICAL AND NEOCLASSICAL THEORIES OF THE RATE OF INTEREST

The classical theory of the rate of interest is the theory that mainstream economists inherited chiefly from Marshall, Ricardo and Wicksell, and is also this same theory that John Maynard Keynes criticizes in his General Theory for presenting an explanation centered solely on the special case of full employment. Despite the difficulties, Keynes offered a scathing critique of the theory of the rate of interest from both classical and neoclassical economists. This was only made possible because the traditional rationale of these economists remained imprisoned by the trap set by Say's Law. Therefore, within this context, the main objective of this paper is to undertake a critical analysis of Keynes regarding the classical general theory of the rate of interest, through which we may then demonstrate the points on which he was in disagreement with the neoclassical school. The main conclusion is that Keynes considered that traditional analysis is defective because it was unable to identify the independent variables of the system. Indeed, savings and investment are determined variables and not the determinants of the dynamics of the capitalist economic system. Such determined variables are the twin product of the true determinants, i.e., from the propensity to consume, from the scale of the marginal efficiency of capital and from the interest rates, and this is why the flow of investments tends to expand until the marginal efficiency of capital remains at the rate of interest.The classical theory of the rate of interest is the theory that mainstream economists inherited chiefly from Marshall, Ricardo and Wicksell, and is also this same theory that John Maynard Keynes criticizes in his General Theory for presenting an explanation centered solely on the special case of full employment. Despite the difficulties, Keynes offered a scathing critique of the theory of the rate of interest from both classical and neoclassical economists. This was only made possible because the traditional rationale of these economists remained imprisoned by the trap set by Say's Law. Therefore, within this context, the main objective of this paper is to undertake a critical analysis of Keynes regarding the classical general theory of the rate of interest, through which we may then demonstrate the points on which he was in disagreement with the neoclassical school. The main conclusion is that Keynes considered that traditional analysis is defective because it was unable to identify the independent variables of the system. Indeed, savings and investment are determined variables and not the determinants of the dynamics of the capitalist economic system. Such determined variables are the twin product of the true determinants, i.e., from the propensity to consume, from the scale of the marginal efficiency of capital and from the interest rates, and this is why the flow of investments tends to expand until the marginal efficiency of capital remains at the rate of interest

Robustness of Trans-European Gas Networks

Here we uncover the load and fault-tolerant backbones of the trans-European gas pipeline network. Combining topological data with information on inter-country flows, we estimate the global load of the network and its tolerance to failures. To do this, we apply two complementary methods generalized from the betweenness centrality and the maximum flow. We find that the gas pipeline network has grown to satisfy a dual-purpose: on one hand, the major pipelines are crossed by a large number of shortest paths thereby increasing the efficiency of the network; on the other hand, a non-operational pipeline causes only a minimal impact on network capacity, implying that the network is error-tolerant. These findings suggest that the trans-European gas pipeline network is robust, i.e., error tolerant to failures of high load links.Comment: 11 pages, 8 figures (minor changes