CHERN_NUMBER¶
introduction¶
Chern number is a topological invariant used to explain the quantized Hall conductivity. The Chern invariant is the total Berry flux in the 2D Brillouin zone,
where \(n\) is an integer, \(\mathbf{S}\) is any closed 2D manifold, \(\boldsymbol{\Omega}\) is total Berry curvature (flux).
To calculate the Chern number, you must first select a closed 2D surface in the Brillouin.
example¶
An example (refer to folder examples/MnBi2Te4-weyl
) of calculating Chern number of the Weyl semimetal MnBi\(_2\)Te\(_4\) is given here.
The Input
file is:
INPUT_PARAMETERS
{
nspin 4
package ABACUS
fermi_energy 9.2309138700265265
fermi_energy_unit eV
HR_route data-HR-sparse_SPIN0.csr
SR_route data-SR-sparse_SPIN0.csr
rR_route data-rR-sparse.csr
HR_unit Ry
rR_unit Bohr
}
LATTICE
{
lattice_constant 1.8897162
lattice_constant_unit Bohr
lattice_vector
4.3773399999000002 0.0000000000000000 0.0000000000000000
2.1886700000000001 3.7908876409999999 0.0000000000000000
2.1886700000000001 1.2636292099999999 13.7730333333000008
}
CHERN_NUMBER
{
method 0
occ_band 109
integrate_mode Grid
integrate_grid 100 100 1
adaptive_grid 20 20 1
adaptive_grid_threshold 100
k_start 0 0 0
k_vect1 1 0 0
k_vect2 0 1 0
}
method
: Method for calculating berry curvature. 0
means direct calculation, 1
means calculation by Kubo formula.
occ_band
: The number of occupied energy bands of an insulator. When this value is not set, it will be determined according to the Fermi energy.
To determine a plane of k-space requires an origin (k_start
) and two vectors that are not parallel to each other (k_vect1
, k_vect2
).
k_start
: The origin point coordinates used to describe a Brillouin zone plane.
k_vect1
: The expansion vector used to describe a Brillouin zone plane.
k_vect2
: The expansion vector used to describe a Brillouin zone plane.
For k-point integration, please refer to the [Setting of integration] section.
After the task calculation is completed, the chern_number.dat
file will appear in the Out/Chern_Num
folder which contains the Chern number specific results.