[Paper Review] Two-dimensional parabolic Dirac system in the presence of non-magnetic and magnetic impurities

Chen-Huan Wu|arXiv (Cornell University)|Sep 25, 2018

Topological Materials and Phenomena44 references4 citations

TL;DR

This paper investigates the effects of non-magnetic and magnetic impurities on two-dimensional parabolic Dirac systems using linear response theory and random phase approximation (RPA). It derives the screened Coulomb potential and calculates the RKKY interaction between magnetic impurities, showing that anisotropic dispersion in materials like black phosphorus leads to anisotropic RKKY interactions sensitive to lattice parameters and Berry curvature, serving as a signature of topological phase transitions.

ABSTRACT

We theoretically investigate the effect of the non-magnetic and magnetic impurities to the 2D parabolic Dirac system. The induced charge density by the charged impuri- ty is obtained by the linear response theory within the random phase approximation. We also detailly calculate the RKKY interaction between two magnetic impurities placed within the 2D sheet of the Dirac materials with isotropic and anisotropic dis- persion. For the anisotropic dispersion, the RKKY interaction is also anisotropic and related to the lattice parameters which can be obtained throuh the DFT calculation or the experiments. The fearures of the RKKY interaction also can be treated as a signature of the topological phase transition as well as the change of Berry curvature. Our results are also illuminating to the study of the static screening and the RKKY interaction of the isotropic or anisotropic 3D Dirac or Weyl systems.

Motivation & Objective

• To understand the screening of charged impurities in 2D parabolic Dirac systems using linear response theory and RPA.
• To investigate the RKKY interaction between magnetic impurities in 2D Dirac materials with isotropic and anisotropic band dispersions.
• To explore how anisotropy in dispersion, influenced by lattice parameters or strain, affects the RKKY interaction and its relation to topological phase transitions.
• To establish the RKKY interaction as a probe of Berry curvature and topological order in 2D Dirac materials.
• To extend insights to 3D Dirac and Weyl systems with anisotropic or isotropic dispersions.

Proposed method

• Employed linear response theory within the random phase approximation (RPA) to compute the induced charge density from a charged impurity.
• Derived the screened Coulomb potential using the Thomas-Fermi approximation and RPA, incorporating the screening wave vector $k_s$.
• Calculated the retarded real-space Green’s function for anisotropic 2D Dirac systems with momentum-dependent effective mass and Rashba coupling.
• Used the Green’s function to compute spin susceptibility components $\chi_{xx}$, $\chi_{xy}$, and $\chi_{zz}$, which encode the RKKY interaction.
• Extracted Heisenberg, Ising, and Dzyaloshinskii-Moriya (DM) interaction terms from the spin susceptibility via a Hamiltonian mapping.
• Accounted for Rashba coupling by preserving pseudospin component separation despite spin mixing, enabling analytical treatment of the Green’s function.

Experimental results

Research questions

• RQ1 How does the RKKY interaction between two magnetic impurities depend on the anisotropy of the band dispersion in 2D Dirac materials?
• RQ2 What is the role of Berry curvature and topological phase transitions in shaping the RKKY interaction in anisotropic 2D Dirac systems?
• RQ3 How does the induced charge density from a non-magnetic impurity respond to screening in a 2D parabolic Dirac system?
• RQ4 In what way does the anisotropy of the Fermi velocity and effective mass influence the spatial dependence of the RKKY interaction?
• RQ5 Can the RKKY interaction serve as a detectable signature of topological phase transitions in 2D Dirac materials?

Key findings

• The RKKY interaction in anisotropic 2D Dirac systems, such as black phosphorus, exhibits directional dependence, with stronger coupling along the direction of higher Fermi velocity.
• For electron-doped systems, the RKKY interaction is stronger along the armchair direction, while for hole-doped systems, it is enhanced along the zigzag direction.
• The RKKY interaction is anisotropic and directly related to the lattice parameters and effective mass anisotropy, which can be extracted from DFT or experimental measurements.
• The spin susceptibility components $\chi_{xx}$ and $\chi_{zz}$ are non-zero and momentum-dependent, while $\chi_{xy}$ vanishes due to symmetry, indicating a dominant Ising-like character.
• The RKKY interaction is sensitive to the sign of the Fermi energy and changes sign across the topological phase transition, serving as a signature of nontrivial topology.
• The presence of Rashba coupling does not break the pseudospin component separation, allowing analytical treatment of the Green’s function and enabling derivation of the RKKY interaction in spin-orbit coupled systems.