{{indexmenu_n>999}}
====== Tight binding ======
###
The object tight-binding defines the tight-binding structure of a crystal or a molecule, including the onsite energy of spin-orbitals and the local and non-local hopping among the spin-orbitals. The tight-binding object can be created directly in Lua using the function //[[documentation:language_reference:functions:NewTightBinding|NewTightBinding()]]// or can be generated from the output of DFT calculation (see, for example, //[[documentation:language_reference:functions:TightBindingDefFromDresdenFPLO|TightBindingDefFromDresdenFPLO()]]//).
The tight-binding objects are used to more efficiently generate cluster Hamiltonians (see //[[documentation:language_reference:functions:CreateClusterHamiltonian|CreateClusterHamiltonian()]]//).
For more details see the [[documentation:language_reference:objects:tightbinding:properties:start|properties]] of tight-binding objects.
-- set parameters
dAB = 0.2
tnn = 1.1
-- create the tight binding Hamiltonian
HTB = NewTightBinding()
HTB.Name = "dichalcogenide tight binding"
HTB.Cell = {{sqrt(3),0,0},
{sqrt(3/4),3/2,0},
{0,0,1}}
HTB.Atoms = { {"A", {0,0,0}, {{"p", {"0"}}}},
{"B", {sqrt(3),1,0}, {{"p", {"0"}}}}}
HTB.Hopping = {{"A.p","A.p",{ 0, 0,0},{{-dAB/2}}},
{"B.p","B.p",{ 0, 0,0},{{ dAB/2}}},
{"A.p","B.p",{ 0, 1,0},{{ tnn }}},
{"B.p","A.p",{ 0, -1,0},{{ tnn }}},
{"A.p","B.p",{ sqrt(3/4),-1/2,0},{{ tnn }}},
{"B.p","A.p",{-sqrt(3/4), 1/2,0},{{ tnn }}},
{"A.p","B.p",{-sqrt(3/4),-1/2,0},{{ tnn }}},
{"B.p","A.p",{ sqrt(3/4), 1/2,0},{{ tnn }}}
}
print("Tight-binding object:")
print(HTB)
print("create a periodic cluster Hamiltonian with 4 unit-cells along the z-axis:")
HCl = CreateClusterHamiltonian(HTB, {"periodic", {{1,0,0},{0,1,0},{0,0,4}}})
print(HCl)
###
Tight-binding object:
Settings of a tight binding model: dichalcogenide tight binding
printout of Crystal Structure
Units: 2Pi (g.r=2Pi) Angstrom Absolute atom positions
Unit cell parameters:
a: 1.7320508 0.0000000 0.0000000
b: 0.8660254 1.5000000 0.0000000
c: 0.0000000 0.0000000 1.0000000
Reciprocal latice:
a: 3.6275987 -2.0943951 0.0000000
b: 0.0000000 4.1887902 0.0000000
c: 0.0000000 0.0000000 6.2831853
Number of atoms 2
# 0 | A ( 0 ) at position { 0.0000000 , 0.0000000 , 0.0000000 }
| p shell with 1 orbitals { 0 }
# 1 | B ( 5 ) at position { 1.7320508 , 1.0000000 , 0.0000000 }
| p shell with 1 orbitals { 0 }
Containing a total number of 2 orbitals
Hopping definitions ( 8 )
Hopping from 0 : A - p to 0 : A - p with translation vector in unit cells: { 0 , 0 , 0 } ({ 0.00000000E+00 0.00000000E+00 0.00000000E+00 })
Matrix =
Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
[ 0]
[ 0] -1.00000000E-01
Hopping from 1 : B - p to 1 : B - p with translation vector in unit cells: { 0 , 0 , 0 } ({ 0.00000000E+00 0.00000000E+00 0.00000000E+00 })
Matrix =
Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
[ 0]
[ 0] 1.00000000E-01
Hopping from 0 : A - p to 1 : B - p with translation vector in unit cells: { -1 , 0 , 0 } ({ 0.00000000E+00 1.00000000E+00 0.00000000E+00 })
Matrix =
Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
[ 0]
[ 0] 1.10000000E+00
Hopping from 1 : B - p to 0 : A - p with translation vector in unit cells: { 1 , 0 , 0 } ({ 0.00000000E+00 -1.00000000E+00 0.00000000E+00 })
Matrix =
Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
[ 0]
[ 0] 1.10000000E+00
Hopping from 0 : A - p to 1 : B - p with translation vector in unit cells: { 0 , -1 , 0 } ({ 8.66025404E-01 -5.00000000E-01 0.00000000E+00 })
Matrix =
Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
[ 0]
[ 0] 1.10000000E+00
Hopping from 1 : B - p to 0 : A - p with translation vector in unit cells: { 0 , 1 , 0 } ({-8.66025404E-01 5.00000000E-01 0.00000000E+00 })
Matrix =
Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
[ 0]
[ 0] 1.10000000E+00
Hopping from 0 : A - p to 1 : B - p with translation vector in unit cells: { -1 , -1 , 0 } ({-8.66025404E-01 -5.00000000E-01 0.00000000E+00 })
Matrix =
Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
[ 0]
[ 0] 1.10000000E+00
Hopping from 1 : B - p to 0 : A - p with translation vector in unit cells: { 1 , 1 , 0 } ({ 8.66025404E-01 5.00000000E-01 0.00000000E+00 })
Matrix =
Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
[ 0]
[ 0] 1.10000000E+00
create a periodic cluster Hamiltonian with 4 unit-cells along the z-axis:
Operator: Operator
QComplex = 0 (Real==0 or Complex==1 or Mixed==2)
MaxLength = 2 (largest number of product of lader operators)
NFermionic modes = 8 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)
NBosonic modes = 0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)
Operator of Length 2
QComplex = 0 (Real==0 or Complex==1)
N = 16 (number of operators of length 2)
C 0 A 0 | -1.00000000000000E-01
C 1 A 1 | 1.00000000000000E-01
C 0 A 1 | 3.30000000000000E+00
C 1 A 0 | 3.30000000000000E+00
C 2 A 2 | -1.00000000000000E-01
C 3 A 3 | 1.00000000000000E-01
C 2 A 3 | 3.30000000000000E+00
C 3 A 2 | 3.30000000000000E+00
C 4 A 4 | -1.00000000000000E-01
C 5 A 5 | 1.00000000000000E-01
C 4 A 5 | 3.30000000000000E+00
C 5 A 4 | 3.30000000000000E+00
C 6 A 6 | -1.00000000000000E-01
C 7 A 7 | 1.00000000000000E-01
C 6 A 7 | 3.30000000000000E+00
C 7 A 6 | 3.30000000000000E+00
===== Table of contents =====
{{indexmenu>.#1|msort}}