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Related Concept Videos

Singularity Functions for Shear01:26

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In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous  variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...
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Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented using a...
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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
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Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
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Magic of high-order van Hove singularity.

Noah F Q Yuan1, Hiroki Isobe1, Liang Fu2

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.

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Summary

Researchers discovered a new type of van Hove singularity in 2D materials, arising from high-order saddle points. This finding offers a new way to engineer electronic properties in materials like graphene by tuning a single parameter.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Solid-State Physics

Background:

  • Van Hove singularities (VHS) are crucial features in the electronic density of states (DOS) of periodic systems.
  • They typically arise from saddle points in the energy dispersion relation in momentum space.
  • Understanding VHS is key to predicting and controlling material properties.

Purpose of the Study:

  • To introduce and characterize a novel type of van Hove singularity in two-dimensional (2D) systems.
  • To demonstrate a general method for achieving these high-order van Hove singularities (HOVHS) by tuning material parameters.
  • To explore the implications of HOVHS on electronic properties, including correlation effects.

Main Methods:

  • Theoretical analysis of energy dispersion relations in 2D periodic systems.
  • Identification of high-order saddle points in the band structure.
  • Modeling of moiré superlattices, specifically twisted bilayer graphene and trilayer graphene.
  • Investigation of parameter tuning effects (twist angle, pressure, electric field) on band structure and DOS.

Main Results:

  • A new class of van Hove singularities, termed high-order van Hove singularities (HOVHS), was identified.
  • HOVHS exhibit a power-law divergence in the density of states.
  • These HOVHS can be controllably induced in moiré superlattices like twisted bilayer graphene and trilayer graphene by tuning a single parameter.
  • The impact of HOVHS on electronic correlations near the Fermi level was discussed.

Conclusions:

  • High-order van Hove singularities represent a significant new feature in the electronic structure of 2D materials.
  • Tunable band structures in moiré superlattices provide a versatile platform for realizing and studying HOVHS.
  • This work opens avenues for engineering novel electronic and correlated phenomena in advanced materials.