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 NewTightBinding() or can be generated from the output of DFT calculation (see, for example, TightBindingDefFromDresdenFPLO()). The tight-binding objects are used to more efficiently generate cluster Hamiltonians (see CreateClusterHamiltonian()).

Example.Quanty

-- 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("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)

-- 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("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)