Friedel oscillation near a van Hove singularity in two-dimensional Dirac materials

Area of Science:

• Condensed Matter Physics
• Materials Science

Background:

• Two-dimensional Dirac materials, like twisted graphene bilayers and topological crystalline insulators, possess low-energy saddle points near van Hove singularities.
• These saddle points are experimentally accessible via gating, making them ideal for studying electronic properties.

Purpose of the Study:

• To investigate Friedel oscillations in 2D Dirac materials when the Fermi level is near a van Hove singularity.
• To determine the charge density decay behavior around an impurity in these materials.

Main Methods:

• Approximation of the Fermi surface near the saddle point with a hyperbola.
• Calculation of the static Lindhard response function.
• Application of Lighthill's theorem to derive the induced charge density.

Main Results:

• The static Lindhard response function exhibits a singularity similar to that of a circular Fermi surface, leading to an algebraic decay of charge density.
• The charge density decay shows distinct dependencies on Fermi energy, transitioning from behavior near the Dirac point to that above the saddle point.

Conclusions:

• Friedel oscillations in 2D Dirac materials near van Hove singularities display an algebraic decay, similar to systems with circular Fermi surfaces.
• The study predicts an observable evolution in the charge density decay in twisted graphene bilayers, verifiable by scanning tunneling microscopy.