Twistronics

Julia codes for computing electronic bandstructure in twisted 2D systems

Installation

Download the repository, which is compatible with Julia 1.7

Disclaimer

This package is still under heavy development

Examples

Codes can be found in the examples folder

Twisted bilayer graphene (TBG)

Supercell and bandstructure

(a) Supercell of TBG at twist angle $1.89^\circ$. (b)-(d) Bandstructure of TBG at twist angle (b) $\theta=21.79^\circ$, (c) $\theta=9.43^\circ$ and (d) $\theta=1.89^\circ$.

Interlayer bias and layer operator

Bandstructure of TBG with interlayer bias $V=0.1t$ at twist angle (a) $\theta=9.43^\circ$ and (b) $\theta=1.89^\circ$. The color indicates either the bands belong to the first/second layer ($\langle L\rangle=\pm 1$) or mixed ($\langle L\rangle=0$).

Interlayer bias and valley operator

(a) Bandstructure of TBG with a small valley potential $0.05\mathcal{V}_z$. (b) Bandstructure of TBG with an interlayer bias $V=0.1t$. The color indicates the valley polarization.

Twisted Dirac quantum spin liquid

(a) Part of the supercell of the twisted $\pi$-flux model at twist angle $3.48^\circ$ under a fixed gauge. (b)-(d) Bandstructure of the twisted $\pi$-flux model at twist angle (b) $\theta=21.79^\circ$, (c) $\theta=9.43^\circ$ and (d) $\theta=3.48^\circ$.