twistwanTB

twistwanTB is an open-source code for building the Ab initio four-band Wannier tight-binding model for generic twisted multilayer graphene (TMG).

Build Wannier TB model for generic TMG

1. set parameters in build_wanTB.py.

Parameters	Description
m and n	They control the twist angle.
NG	NG controls the num of plane waves, default is 3.
w1 and w2	Layer coupling constant
Umax	Displacement field
enable_hBN	If consider BN substrate
U_BN_u(d)	hBN potential for the upper (lower) parts
htbfname_u(d)	htb filename for the upper (lower) part
mp_grid	Wigner-Seitz grid used for interpolating Wannier TB model
if_cal_wfs	If give real-space Wannier functions
fname_wfs	Filename for the Wannier functions

2. python build_wanTB.py, all of the Wannier tight-binding information will be saved in a single file htb.twistTMG.h5.
3. The .dat formated tight-binding model can be obtained by

from twistwanTB.wanpy.structure import Htb
# create Htb instance
htb = Htb()
# load data from .h5 file
htb.load('htb.twistTMG.h5')
# save the wannier charge center in POSCAR.vasp file
htb.save_wcc()
# save the Hamiltonian H(R)=<m0|H|nR> in wannier90_hr.dat formate
htb.save_wannier90_hr_dat()
# save the valley operators V(R)=<m0|V|nR> in wanpy_symmOP_xx.dat formate
htb.save_D_dat()

Estimate Coulomb parameters

1. Set if_cal_wfs = True in build_wanTB.py to obtain the real-space Wannier functions. It will be saved in fname_wfs=wfs.npz by default.
2. Set the filename fname_wfs of the calculated Wannier functions in cal_coulomb.py, and run the python code python cal_coulomb.py. The results will be saved in xxx.dat file.

Examples

• Magic angle twist bilayer graphene (mTBG) (theta=1.08 degree)
• Magic angle twist bilayer graphene (mTBG) with h-BN substrate (theta=1.08 degree)
• Twist double bilayer graphene (TDBG) (theta=2.0 degree)
• Magic angle twist double bilayer graphene (mTDBG) with displacement field turned on (theta=1.248 degree)
• Magic angle twist trilayer graphene (mTTG) with h-BN substrate and displacement field turned on (theta=1.248 degree)
• Twist multilayer graphene (theta=2.646 degree)
• The real-space Wannier functions for magic angle TBG, TDBG and TTG.

Reference

Jin Cao, Maoyuan Wang, Shi-Feng Qian, Cheng-Cheng Liu, and Yugui Yao, Phys. Rev. B 104, L081403 (2021).