BerryCurvature

Calculate energy eigenvalue and Berry curvature of a matrix Hamiltonian

Usage

$ ./eigen.o INPUT_FILE
$ ./berry.o INPUT_FILE

The default name of the input file (used when missing the argument INPUT_FILE) is input.dat (defined in initialize.cpp).

Input file

Input file is a formatted text file, according to the following rules. Several space letters are put between each value. In each line, you can write down some comments after arguments. No blank row should be put between each section.

Parameters section (ll.1-(1+N_params))

The first line of this section represents the number of parameters (N_params) and successive N_params rows represent the name and value of the parameters. You can't use, as names of parameters,kx, ky, kz, I, PI, cos, sin, cis, exp, sqrt, cosh, sinh, conj and any string starting from _ (underscore) or including +, -, *, /, . because they have specific meaning in interpretation of matrix elements.

2 #Number of parameters
a 3.0  #Name and value of the first parameter
b -2.0 #The second parameter

Equations section (ll.(2+N_params)-(2+N_params+N_eqns))

The first line of this section represents the number of equations (N_eqns) and successive N_eqns rows represent the name and value of the equations. You can use any representations other than the name of the equation itself. Be careful not to cause circular reference.

Actually, the function of equations includes that of parameters.

2 #Number of equations
func1 kx+I*ky #Name and value of the first equation
func2 kx-I*ky #The second equation

Matrix section (ll.(3+N_params+N_eqns)-(3+N_params+N_eqns+N))

The first line of this section represents the size of the Hamiltonian matrix (N) and successive N rows represent the rows of the matrix.

4 #Size of the Hamiltonian matrix
a+b     0         kz        kx-I*ky   #The first row
0       a-b       kx+I*ky   (-1)*kz   #The second row
kz      kx-I*ky   (-1)*a+b  0         #The third row
kx+I*ky (-1)*kz   0         (-1)*a-b  #The fourth row

• Several space letters are put between each matrix element and no space letter is put in one matrix element.
• You can use parameters (defined in the parameters section), kx, ky, kz (coordinates of a wave vector), I (the imaginary unit), PI (pi), real numbers (x.yy format is ok, x.yye+01 is not), +, -, *, / (binary operators), (, ) (parentheses), cos (cosine), sin (sine), cis (cos+I*sin), exp (exponential), sqrt (square root), cosh (hyperbolic cosine), sinh (hyperbolic sine), and conj (complex conjugate) when you specity matrix elements.
  • When you use negative real numbers, you must enclose the number by parentheses to distinguish it from a minus operator (see the above example).
• Since Hamiltonian matrix should be Hermite, only upper triangular part and diagonal component are used in diagonalization procedure. However you probably should write down also lower trianglular part so that the Hamiltonian matrix is clearly Hermite.

k basis vectors section (ll. (4+N_params+N_eqns+N)-(6+N_params+N_eqns+N))

This section has been newly added in Dec. 2020. These three lines in this section define three basis vectors for k range designation. As the following example does, the equation format is allowed, although using kx, ky, and kz is prohibited (definitely causes meaningless result).

0      (-4)*PI/(sqrt(3)*a) 0      #kx, ky, and kz components of the first basis vector b_1
2*PI/a (-2)*PI/(sqrt(3)*a) 0      #The second basis vector b_2
0      0                   2*PI/c #The third basis vector b_3

k range section for eigenvalue calculation (ll.(7+N_params+N_eqns+N)-(9+N_params+N_eqns+N))

These three lines in this section represent k range of calculation in the format of b₁, b₂, and b₃ components.

0  0 0  #b_1 range (double start, double stop, int split)
-1 1 10 #b_2 range
-2 2 20 #b_3 range

This program split the range [start, stop] into split pieces and calculation is done in split+1 points.

 [Index of k point] 1    2    3   --- n-1     n 
 [Index of piece]   | #1 | #2 |   ---  | #n-1 | 
 [Value of k point] i   i+d  i+2d --- f-d     f 
i=start, f=stop, d=(stop-start)/split, n=split+1

If split is zero, calculation is done in case of k=start.

k range section for Berry curvature calculation (ll.(10+N_params+N_eqns+N)-(12+N_params+N_eqns+N))

The format is the same as above k range section.

Delta k section (l.(13+N_params+N_eqns+N), only for Berry curvature calculation)

This section has only one row, representing Δk (used in difference approximation). The equation format is allowed, although using kx, ky, and kz is prohibited (definitely causes meaningless result).

0.001*2*PI/a #Delta k