Duality between atomic configurations and Bloch states in twistronic materials

The relative orientation (twist) of successive layers of stacked two-dimensional (2D) materials creates variations in the interlayer atomic registry. The variations often form a super lattice, called a moir\'e pattern, which can alter electronic properties. In this work we introduce a classification of the single-particle electronic structures that can occur in twisted stacks of 2D layers by characterizing them as "moir\'e molecules" or "moir\'e crystals". The molecules generate localized electronic states and moir\'e flat bands, while the crystals are sometimes unconventional and produce electronic banding in the configuration basis. The underpinning of this classification is the duality between interlayer configuration and monolayer Bloch momentum in moir\'e Hamiltonians. We apply this understanding to diagrams of local electron density in untwisted geometries to produce intuitive and quantitative predictions of twistronic properties. We provide a conceptual introduction to this framework through a one-dimensional model, and then apply it to 2D twisted bilayers of the semi-metal graphene, and of MoS$_2$, a representative material of the transition metal dichalcogenide (TMDC) family of semiconductors. This level of thorough understanding of twistronic phenomena is vital in the search for new material platforms for localized moir\'e electrons.Comment: 13 pages, 9 figure

The Catalan simplicial set

The Catalan numbers are well-known to be the answer to many different counting problems, and so there are many different families of sets whose cardinalities are the Catalan numbers. We show how such a family can be given the structure of a simplicial set. We show how the low-dimensional parts of this simplicial set classify, in a precise sense, the structures of monoid and of monoidal category. This involves aspects of combinatorics, algebraic topology, quantum groups, logic, and category theory.Comment: 15 pages. Replaces and expands upon parts of arXiv:1307.0265; remaining parts of arXiv:1307.0265 will be incorporated into a sequel. Version 2: minor revision; to appear in Math. Proc. Camb. Phil. So

Social Security Money's Worth

This paper describes how three money's worth measures the benefit-to-tax ratio, the internal rate of return, and the net present value are calculated and used in analyses of social security reforms, including systems with privately managed individual accounts invested in equities. Declining returns from the U.S. social security system prove to be the inevitable result of having instituted an unfunded (pay-as-you-go) retirement system that delivered $7.9 trillion of net transfers (in 1997 present value dollars) to people born before 1917, and will deliver another$1.8 trillion to people born between 1918 and 1937. But young and future workers cannot necessarily do better by investing their payroll taxes in capital markets. If the old system were closed down, massive unfunded liabilities of $9-10 trillion would still have to be paid unless already accrued benefits were cut. Alternative methods of calculating these accrued benefits yield somewhat different numbers: the straight line calculation is$800 billion less than the constant benefit calculation we propose as the benchmark. Using this benchmark in a world with no uncertainty, we show that privatization without prefunding would not increase returns at all, net of the new taxes needed to pay for unfunded liabilities. These new taxes would amount to 3.6 percent of payroll, or about 29 percent of social security contributions. Prefunding, implemented by reducing accrued benefits or by raising taxes, would eventually increase money's worth for later generations, but at the cost of lower money's worth for today's workers and/or retirees. Computing money's worth when there is uncertainty is much more difficult unless four conditions hold prices into stocks and out of bonds has no effect whatsoever on money's worth when it i adjusted for risk: a dollar of stock is worth no more than a dollar of bonds. diversification can raise welfare for constrained households, but the exact money's worth must depend on specific assumptions about household attitudes toward risk. Calculations lik the Social Security Advisory Council that attribute over $2.85 of net present va$1 shifted from bonds to stocks completely overlook the disutility of risk. By estimate that a 2 percent of payroll equity fund carved out of social security w present value by about 59 cents per dollar of bonds switched into equities When the likely reductions in income and longevity insurance are factored in privatization and diversification is substantially less than popularly perceived

Valuing the Roundup Ready® Soybean Weed Management Program

This study examines soybean grower adoption of the Roundup Ready® (RR) weed management program with and without a residual herbicide application, and grower concerns regarding weed resistance to herbicides using telephone survey data from of 357 growers in 2007. It also estimates the pecuniary and non-pecuniary benefits enjoyed by growers from their RR program. The results indicate that soybean growers planned to treat 29 percent of their RR acres with a residual herbicide in 2008. More than half (53%) of the growers survey were concerned about weed resistance. The estimated expected benefit of the RR program in 2008 was $10.17 per acre, which translates into about$727 million with 75.7 million acres of soybean in the U.S. in 2008. The estimated value per acre of the RR program with and without a residual was $8.78 and$12.83. The estimates also suggest that if growers were not using residual herbicides with the RR program, their benefits would be 28.4% lower. Alternatively, if all growers were required to use residual herbicides on their RR acres, the value of the RR program would be 46% lower. Simply increasing grower weed resistance concerns could increase residual herbicide use on RR acres by up to 7%. The same increase in residual herbicide use could be accomplished by decreasing the cost of residual herbicide applications on RR acres by $0.81 per acre.Roundup Ready, Soybean, Glyphosate, Weed Resistance, Benefits, Crop Production/Industries, Demand and Price Analysis, Farm Management, Research and Development/Tech Change/Emerging Technologies,

The Role of Company Stock in Defined Contribution Plans

This paper explores the risks and benefits of holding company stock in employer-sponsored defined contribution (DC) retirement plans. We address three questions: (1) What is the role and function of company stock in such plans? (2) Who might be affected by enhanced portfolio diversification in such plans? and (3) What mechanisms exist, or might be developed, to enhance portfolio diversification if more diversification were deemed useful? Firms offer company stock within DC plans in an effort to enhance economic performance, though evidence is mixed on productivity gains from stock ownership. We demonstrate that concentrated stock positions arise most often in larger firms' DC plans where sponsors direct employer contributions and restrict diversification. Stock concentration also arises because participants systematically underestimate the risk of employer stock and over-rely on its past performance in making investment decisions. In a retirement system with concentrated stock positions, there will always be some participants who forfeit DC plan savings to firm bankruptcy. Encouraging plan diversification mitigates this risk, but it could also induce some companies to redirect plan contributions to other forms of stock compensation or to replace stock contributions with cash compensation. We conclude by describing policy tools that might be used to encourage diversification and discuss conditions for their effective implementation.