Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Topological electric field-defined quantum dots in bilayer graphene: An atomistic approach

Wlodzimierz Jaskolski

Abstract

We study topological bound states in quantum dots defined by an electric field in bilayer graphene. An external field is perpendicular to the bilayer and changes sign in a finite region that defines the quantum dot. The electric field opens a gap in the bilayer graphene, and the reversed field creates a domain wall with one-dimensional chiral gapless bands localized therein. The finite size of dots leads to the quantization of these bands and the appearance of discrete bound states localized at the dot boundary. We consider rectangular dots oriented along the armchair and zigzag directions. We go beyond a simple continuum one-valley model and use an atomistic tight-binding approach. This allows us to identify new effects related to the atomic structure of graphene, strengths of the electric field, valley mixing, and valley asymmetry.

Topological electric field-defined quantum dots in bilayer graphene: An atomistic approach

Abstract

We study topological bound states in quantum dots defined by an electric field in bilayer graphene. An external field is perpendicular to the bilayer and changes sign in a finite region that defines the quantum dot. The electric field opens a gap in the bilayer graphene, and the reversed field creates a domain wall with one-dimensional chiral gapless bands localized therein. The finite size of dots leads to the quantization of these bands and the appearance of discrete bound states localized at the dot boundary. We consider rectangular dots oriented along the armchair and zigzag directions. We go beyond a simple continuum one-valley model and use an atomistic tight-binding approach. This allows us to identify new effects related to the atomic structure of graphene, strengths of the electric field, valley mixing, and valley asymmetry.
Paper Structure (7 sections, 2 equations, 6 figures)

This paper contains 7 sections, 2 equations, 6 figures.

Table of Contents

  1. Introduction and model description
  2. Computational method
  3. Results and discussion
  4. Two parallel EFWs
  5. Two parallel EFWs of finite width
  6. Rectangual QD
  7. Summary and Conclusions

Figures (6)

  • Figure 1: Schematic representations of electrically defined rectangle BLG QD (a) and a system of two parallel EFWs separated by $d$ (b). The dot is defined as a region in gated BLG, where the voltages $\pm V$ applied to the layers (red and blue) are reversed.
  • Figure 2: Energy bands close to $\Gamma$ ($k=0$) for two parallel EFWs along the armchair direction. In (a) and (c), the walls are separated by 140 unit cells; in (b) and (d), they are separated by 20 unit cells. Voltage applied to the layers is $V=\pm0.1\,$V in (a) and (b), and $V=\pm0.5\,$V in (c) and (d).
  • Figure 3: Energy bands close to $k=\frac{2\pi}{3a_z}$ for two parallel EFWs along the zigzag direction. In (a) and (c), the walls are separated by 80 unit cells; in (b) and (d), they are separated by 20 unit cells. Voltages applied to the layers are $V=\pm0.1\,$V in (a) and (b), and $V=\pm0.5\,$V in (c) and (d).
  • Figure 4: Energy levels of two parallel EFWs of finite width $W$. The voltages applied to the layers are $V=\pm0.1\,$V. Upper panels: EFWs along the armchair direction, separated by 160 unit cells (a) and by 40 unit cells (b). Lower panels: EFWs along the zigzag direction, separated by 80 and 40 unit cells in (c) and (d), respectively.
  • Figure 5: Energy levels of two parallel EFWs of finite width $W$. The voltages applied to the layers are $V=\pm0.5\,$V. (a) EFWs in armchair direction separated by 80 unit cells; (b) EFWs in zigzag direction separated by 40 unit cells
  • ...and 1 more figures