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====== Hopping ======

//TB.Hopping//: A list of local and non-local hoppings among atomic shells. Each element has the format {Atom1.Shell_i, Atom2.Shell_j, {a,b,c}, T}, where here {a,b,c} is the distance between the two atoms and T is an array defines the hopping matrix elements among the spin-orbitals of Atom1.Shell_i and Atom1.Shell_j . (in second-quantization language: $ \Sigma t_{\sigma, \sigma'} a^{\dagger}_{\sigma} a_{\sigma'} $)

===== Example =====

###
Two simple examples (with and without spin):
###

==== Input ====
<code Quanty 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("HTB.Name:")
print(HTB.Name)
    
print("\nHTB.Cell:")
print(HTB.Cell)
    
print("\nHTB.Atoms:")
print(HTB.Atoms)

print("\nHTB.NAtoms:")
print(HTB.NAtoms)
    
print("\nHTB.Hopping:")
print(HTB.Hopping)
    
print("\nHTB.Units:")
print(HTB.Units)
    
print("\nHTB.NF:")
print(HTB.NF)

print("\nHTB.Hk:")
print(HTB.Hk)

print("\nHTB.ReciprocalCell:")
print(HTB.ReciprocalCell)                              
    
-- create the tight binding Hamiltonian
HTB = NewTightBinding()
HTB.Name = "dichalcogenide tight binding (with spin)"
HTB.Cell = {{sqrt(3),0,0},
            {sqrt(3/4),3/2,0},
            {0,0,1}}
HTB.Atoms = { {"A", {0,0,0},       {{"p", {"^{dn}","^{up}"}}}},
                {"B", {sqrt(3),1,0}, {{"p", {"^{dn}","^{up}"}}}}}
HTB.Hopping = {{"A.p","A.p",{         0,   0,0},{{-dAB/2, 0}, {0, -dAB/2}}},
                {"B.p","B.p",{         0,   0,0},{{-dAB/2, 0}, {0, -dAB/2}}},
                {"A.p","B.p",{         0,   1,0},{{ tnn, 0  }, { 0, tnn  }}},
                {"B.p","A.p",{         0,  -1,0},{{ tnn, 0  }, { 0, tnn  }}},
                {"A.p","B.p",{ sqrt(3/4),-1/2,0},{{ tnn, 0  }, { 0, tnn  }}},
                {"B.p","A.p",{-sqrt(3/4), 1/2,0},{{ tnn, 0  }, { 0, tnn  }}},
                {"A.p","B.p",{-sqrt(3/4),-1/2,0},{{ tnn, 0  }, { 0, tnn  }}},
                {"B.p","A.p",{ sqrt(3/4), 1/2,0},{{ tnn, 0  }, { 0, tnn  }}}
                }
    
print("HTB.Name:")
print(HTB.Name)
    
print("\nHTB.Cell:")
print(HTB.Cell)
    
print("\nHTB.Atoms:")
print(HTB.Atoms)

print("\nHTB.NAtoms:")
print(HTB.NAtoms)
    
print("\nHTB.Hopping:")
print(HTB.Hopping)
    
print("\nHTB.Units:")
print(HTB.Units)
    
print("\nHTB.NF:")
print(HTB.NF)

print("\nHTB.Hk:")
print(HTB.Hk)

print("\nHTB.ReciprocalCell:")
print(HTB.ReciprocalCell)
</code>

==== Result ====
<file Quanty_Output>
HTB.Name:
dichalcogenide tight binding

HTB.Cell:
{ { 1.7320508075689 , 0 , 0 } , 
  { 0.86602540378444 , 1.5 , 0 } , 
  { 0 , 0 , 1 } }

HTB.Atoms:
{ { A , 
  { 0 , 0 , 0 } , 
  { { p , 
  { 0 } } } } , 
  { B , 
  { 1.7320508075689 , 1 , 0 } , 
  { { p , 
  { 0 } } } } }

HTB.NAtoms:
2

HTB.Hopping:
Hopping

HTB.Units:
{ 2Pi , Angstrom , Absolute }

HTB.NF:
2

HTB.Hk:
Hk

HTB.ReciprocalCell:
{ { 3.6275987284684 , -2.0943951023932 , 0 } , 
  { 0 , 4.1887902047864 , 0 } , 
  { 0 , 0 , 6.2831853071796 } }
HTB.Name:
dichalcogenide tight binding (with spin)

HTB.Cell:
{ { 1.7320508075689 , 0 , 0 } , 
  { 0.86602540378444 , 1.5 , 0 } , 
  { 0 , 0 , 1 } }

HTB.Atoms:
{ { A , 
  { 0 , 0 , 0 } , 
  { { p , 
  { ^{dn} , ^{up} } } } } , 
  { B , 
  { 1.7320508075689 , 1 , 0 } , 
  { { p , 
  { ^{dn} , ^{up} } } } } }

HTB.NAtoms:
2

HTB.Hopping:
Hopping

HTB.Units:
{ 2Pi , Angstrom , Absolute }

HTB.NF:
4

HTB.Hk:
Hk

HTB.ReciprocalCell:
{ { 3.6275987284684 , -2.0943951023932 , 0 } , 
  { 0 , 4.1887902047864 , 0 } , 
  { 0 , 0 , 6.2831853071796 } }
</file>

===== Table of contents =====
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