Lattice

generatelattice(param::Parameter) generates a Lattice from the parameter.

• "Lattice"
  • The name of the lattice
• "L"
  • Length along each dimension

If you want to use a lattice/bravairs/unitcell you defined, the following optional parameters must be set:

• "LatticeDict"
• "BravaisDict"
• "UnitcellDict"

Pre-defined lattices

• "chain lattice"
• "bond-alternating chain lattice"
• "square lattice"
• "triangular lattice"
• "honeycomb lattice"
• "ladder"
• "cubic lattice"
• "fully connected lattice"

Define your lattice

A lattice can be defined by combining a Bravais lattice (lattice basic vector) and a unit cell (sublattice structure). A lattice, a Bravais lattice, and a unit cell are represented by an instance of P = Dict{Symbol, Any}.

Lattice

• :name => String
• :dimenstion => Integer
• :bravais => String
• :unitcell => String
• :parameters => Vector{Tuple{Symbol, Any}}
  • To overwrite the default value of parameters of a Bravais lattice
  • An element of a value is a tuple of parameter_name :: Symbol and new_default_value :: Any.
  • ex. [(:a, sqrt(3.0))]
• :periodic => Vector{Bool}
  • To specify the boundary condition (BC) for each dimension, periodic BC if true and open BC if false.

Bravais lattice

• :name => String
• :dimension => Integer
• :parameters => Vector{Tuple{Symbol, Any}}
  • parameter of the lattice vector
  • An element of a value is a tuple of parameter_name :: Symbol and default_value :: Any.
  • ex. [(:a, 1.0)]
• :basis => Expr
  • parameterized lattice basic vector
  • Type of a value is Expr of an dim×dim Matrix
  • ex. :( [a 0.0; 0.0 a] )

Unit cell

• :name => String
• :dimension => Integer
• :sites => Vector{P}
• :bonds => Vector{P}

A site is an instance of Dict{Symbol, Any} having the following items:

• :id => Integer
  • The site index in a unitcell (1-origin)
• :sitetype => Integer
  • The site type (1-origin)
• :coord => Vector{Float64}
  • The fractional coordinate of the site

A bond is an instance of Dict{Symbol, Any} having the following items:

• :bondtype => Integer
  • The bond type (1-origin)
• :source => P
  • One end (site) of a bond
  • The value is a P having the following items:
    • :id => Integer : the site index in a unitcell
    • :offset => Vector{Integer} : the coordinate of the unitcell
• :target => P
  • Another end (site) of a bond