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--- documentation:language_reference:objects:tightbinding:properties:start [2024/09/16 14:08] – Sina Shokri
+++ documentation:language_reference:objects:tightbinding:properties:start [2024/09/18 18:08] (current) – Sina Shokri
@@ Line 6: / Line 6: @@
   * Name: a string
   * Cell: {a,b,c} defining the unit cell of the system. a, b and c are vectors of length 3 and define the uni-cell vectors.
-  * Atoms: a list of atoms, their positions within the unit cell and their atomic shells (spin-orbitals). Each element has the format {Atom.Name, Atom.Position, {Atom.Shells}}.
+  * ReciprocalCell: {a,b,c} the reciprocal cell, satisfying the condition $\vec{r}\cdot\vec{g}=2\pi$, where $\vec{r}$ are the unit-cell vectors and $\vec{g}$ are the reciprocal-cell vectors.
-  * Hopping: A list of local and non-local hoppings among spin-orbitals. Each element has the format {spinOrb1, spinOrb1, {a,b,c}, $\{\{t_{\downarrow, \downarrow},t_{\downarrow, \uparrow}\},\{t_{\uparrow, \downarrow}, t_{\uparrow, \uparrow}\}\}$}, where here {a,b,c} is the distance between the two atoms and $\{\{t_{\downarrow, \downarrow},t_{\downarrow, \uparrow}\},\{t_{\uparrow, \downarrow}, t_{\uparrow, \uparrow}\}\}$ defines the hopping matrix elements (in second-quantization language: $ \Sigma t_{\sigma, \sigma'} a^{\dagger}_{\sigma} a_{\sigma'} $)
+  * Atoms: a list of atoms, their positions within the unit cell and their atomic shells (spin-orbitals). Each element has the format {Atom.Name, Atom.Position, {Atom.Shells}}. The Atom.Shells can be a list of atomic shell with arbitrary number of orbitals, including or not including spin. For example: {"H", {0,0,0}, { {"s", {"^{dn}", "^{up}"}, {"p",  {"_y^{dn}", "_y^{up}", "_z^{dn}", "_z^{up}", "_x^{dn}", "_x^{up}"} } } } } .
-  * Units: {“2Pi”, “Angstrom”, “Absolute”}
+  * NAtoms: number of atoms in //TB.Atoms//
-  * NF: number of fermionic modes
+  * 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'} $)
+  * Units: {Units[1], Units[2], Units[3]} (see below)
+  * NF: number of fermionic modes
-The //Units// property is a list of three strings with the following contributions:
+The //Units// property is a list of three strings with the following components:
-  * Units[1]: Sets the scaling for the reciprocal lattice, e.g., $\vec{r}\cdot\vec{g}=2\pi$ for "2Pi" or $\vec{r}\cdot\vec{g}=1$ for "NoPi".
+  * Units[1]: Sets the scaling for the reciprocal lattice, e.g., $\vec{r}\cdot\vec{g}=2\pi$ for "2Pi" or $\vec{r}\cdot\vec{g}=1$ for "NoPi". (standard value "2Pi")
-  * Units[2]: Defines the unit of measurement as "Angstrom", "Bohr", or "nanometer".
+  * Units[2]: Defines the unit of measurement as "Angstrom", "Bohr", or "nanometer". (standard value "Angstrom")
-  * Units[3]: Selects "Absolute" or "Relative" for the definition of atom positions.
+  * Units[3]: Selects "Absolute" or "Relative" for the definition of atom positions. (standard value "Absolute")
-Once a Tight Binding object is created, all properties can be assigned except //NF//, which is determined by the number of orbitals defined in //Atoms//.
+For creating a tight-binding object, one needs to define at least the properties //TB.Cell//, //TB.Atoms// and //TB.Hopping//. The rest of the properties will be either automatically calculated or will be set with standard values (//TB.Name// and //TB.Units//). See also //[[documentation:language_reference:functions:NewTightBinding|NewTightBinding()]]//.
 ===== Example =====
 ###
-description text
+Two simple examples (with and without spin):
 ###
 ==== Input ====
 <code Quanty Example.Quanty>
--- some example code
+-- 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>
-text produced as 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:
+
+HTB.Hopping:
+Hopping
+HTB.Units:
+{ 2Pi , Angstrom , Absolute }
+HTB.NF:
+
+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:
+
+HTB.Hopping:
+Hopping
+HTB.Units:
+{ 2Pi , Angstrom , Absolute }
+HTB.NF:
+
+HTB.Hk:
+Hk
+HTB.ReciprocalCell:
+{ { 3.6275987284684 , -2.0943951023932 , 0 } ,
+  { 0 , 4.1887902047864 , 0 } ,
+  { 0 , 0 , 6.2831853071796 } }
 </file>

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