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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)