This repository contains WannierTools [1] input files used for the tight-binding
band structure calculations of twisted double bilayer graphene (TDBG) models
characterized by different twist angles and performed in presence of intrinsic
symmetric polarization (ISP). Calculations have been performed for both rigid
and relaxed structures organized in two separate folders: "Rigid-SE9mVpA" and
"Relaxed-SE9mVpA". Each folder contains 34 subfolders that correspond to
different angles.

Figures 2 and 3 of Ref. [2] can be reproduced with the calculations performed
using these input files.

Each twist angle corresponds to a commensuration parameter (m) (see Ref. [2] for
details). The folders are named as "mN", in which N is the corresponding
commensuration parameter for the respective twist angle. For example, folder "m3" 
corresponds to m=3 and 9.43 degrees twist angle. In each folder, the angle is 
given in the first line of the hr.dat file.

The hr.dat files contains the tight-binding parameters used in the calculations.
For more information please visit http://www.wanniertools.org/
Note, the version of WannierTools used in these cacluations was not released to the
public at the time of publishing this archive. The original source of this 
version can be obtained upon a reasonable request from Dr. QuanSheng Wu 
(wuquansheng@gmail.com).

References:
[1] Q. Wu, S. Zhang, H.F. Song, M. Troyer, A. A. Soluyanov, WannierTools: An 
open-source software package for novel topological materials, Computer 
Physics Communications 224, 405 (2018)
[2] F. Haddadi, Q. Wu, A.J. Kruchkov, O. V. Yazyev, Moiré Flat Bands in Twisted
Double Bilayer Graphene, Nano Letters 20, 2410 (2020)