API usage

You can call a function in this library as follows:

import libtetrabz

Total energy, charge density, occupations

$$\begin{array}{r}\sum _n{\int }_{\mathrm{B}\mathrm{Z}}\frac{d^{3}k}{V_{\mathrm{B}\mathrm{Z}}}\theta ({\epsilon }_{\mathrm{F}}-{\epsilon }_{nk})X_{nk}\end{array}$$

wght = libtetrabz.occ(bvec, eig)

Parameters

bvec = numpy.array([[b0x, b0y, b0z], [b1x, b1y, b1z], [b2x, b2y, b2z]])

Reciprocal lattice vectors (arbitrary unit). Because they are used to choose the direction of tetrahedra, only their ratio is used.

eig = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

The energy eigenvalue ${\epsilon }_{nk}$ in arbitrary unit. Where ng0, ng1, ng2 are the number of grid for each direction of the reciprocal lattice vectors and nb is the number of bands.

Return

wght = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

The integration weights.

Fermi energy and occupations

$$\begin{array}{r}\sum _n{\int }_{\mathrm{B}\mathrm{Z}}\frac{d^{3}k}{V_{\mathrm{B}\mathrm{Z}}}\theta ({\epsilon }_{\mathrm{F}}-{\epsilon }_{nk})X_{nk}\end{array}$$

ef, wght, iteration = libtetrabz.fermieng(bvec, eig, nelec)

Parameters

bvec = numpy.array([[b0x, b0y, b0z], [b1x, b1y, b1z], [b2x, b2y, b2z]])

Reciprocal lattice vectors (arbitrary unit). Because they are used to choose the direction of tetrahedra, only their ratio is used.

eig = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

The energy eigenvalue ${\epsilon }_{nk}$ in arbitrary unit. Where ng0, ng1, ng2 are the number of grid for each direction of the reciprocal lattice vectors and nb is the number of bands.

nelec = # float

The number of electrons.

Return

ef = # float

The Fermi energy. Unit is the same as eig.

wght = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

The integration weights.

Partial density of states

$$\begin{array}{r}\sum _n{\int }_{\mathrm{B}\mathrm{Z}}\frac{d^{3}k}{V_{\mathrm{B}\mathrm{Z}}}\delta (\omega -{\epsilon }_{nk})X_{nk}(\omega )\end{array}$$

wght = libtetrabz.dos(bvec, eig, e0)

Parameters

bvec = numpy.array([[b0x, b0y, b0z], [b1x, b1y, b1z], [b2x, b2y, b2z]])

Reciprocal lattice vectors (arbitrary unit). Because they are used to choose the direction of tetrahedra, only their ratio is used.

eig = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

The energy eigenvalue ${\epsilon }_{nk}$ in arbitrary unit. Where ng0, ng1, ng2 are the number of grid for each direction of the reciprocal lattice vectors and nb is the number of bands.

e0 = numpy.empty(ne, dtype=numpy.float_)

The energy point $\omega$ in the same unit of eig. Where ne is the number of energy points.

Return

wght = numpy.empty([ng0, ng1, ng2, nb, ne], dtype=numpy.float_)

The integration weights.

Integrated density of states

$$\begin{array}{r}\sum _n{\int }_{\mathrm{B}\mathrm{Z}}\frac{d^{3}k}{V_{\mathrm{B}\mathrm{Z}}}\theta (\omega -{\epsilon }_{nk})X_{nk}(\omega )\end{array}$$

wght = libtetrabz.intdos(bvec, eig, e0)

Parameters

bvec = numpy.array([[b0x, b0y, b0z], [b1x, b1y, b1z], [b2x, b2y, b2z]])

Reciprocal lattice vectors (arbitrary unit). Because they are used to choose the direction of tetrahedra, only their ratio is used.

eig = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

The energy eigenvalue ${\epsilon }_{nk}$ in arbitrary unit. Where ng0, ng1, ng2 are the number of grid for each direction of the reciprocal lattice vectors and nb is the number of bands.

e0 = numpy.empty(ne, dtype=numpy.float_)

The energy point $\omega$ in the same unit of eig. Where ne is the number of energy points.

Return

wght = numpy.empty([ng0, ng1, ng2, nb, ne], dtype=numpy.float_)

The integration weights.

Nesting function and Fr&oumlhlich parameter

$$\begin{array}{r}\sum _{n{n}^{\prime }}{\int }_{\mathrm{B}\mathrm{Z}}\frac{d^{3}k}{V_{\mathrm{B}\mathrm{Z}}}\delta ({\epsilon }_{\mathrm{F}}-{\epsilon }_{nk})\delta ({\epsilon }_{\mathrm{F}}-{\epsilon }_{n^{\prime }k}^{\prime })X_{n{n}^{\prime }k}\end{array}$$

wght = libtetrabz.dbldelta(bvec, eig1, eig2)

Parameters

bvec = numpy.array([[b0x, b0y, b0z], [b1x, b1y, b1z], [b2x, b2y, b2z]])

Reciprocal lattice vectors (arbitrary unit). Because they are used to choose the direction of tetrahedra, only their ratio is used.

eig1 = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

The energy eigenvalue ${\epsilon }_{nk}$ in arbitrary unit. Where ng0, ng1, ng2 are the number of grid for each direction of the reciprocal lattice vectors and nb is the number of bands.

eig2 = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

Another energy eigenvalue ${\epsilon }_{nk}^{\prime }$ in the same unit of eig1. Typically it is assumed to be ${\epsilon }_{nk+q}$.

Return

wght = numpy.empty([ng0, ng1, ng2, nb, nb], dtype=numpy.float_)

The integration weights.

A part of DFPT calculation

$$\begin{array}{r}\sum _{n{n}^{\prime }}{\int }_{\mathrm{B}\mathrm{Z}}\frac{d^{3}k}{V_{\mathrm{B}\mathrm{Z}}}\theta ({\epsilon }_{\mathrm{F}}-{\epsilon }_{nk})\theta ({\epsilon }_{nk}-{\epsilon }_{n^{\prime }k}^{\prime })X_{n{n}^{\prime }k}\end{array}$$

wght = libtetrabz.dblstep(bvec, eig1, eig2)

Parameters

bvec = numpy.array([[b0x, b0y, b0z], [b1x, b1y, b1z], [b2x, b2y, b2z]])

Reciprocal lattice vectors (arbitrary unit). Because they are used to choose the direction of tetrahedra, only their ratio is used.

eig1 = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

The energy eigenvalue ${\epsilon }_{nk}$ in arbitrary unit. Where ng0, ng1, ng2 are the number of grid for each direction of the reciprocal lattice vectors and nb is the number of bands.

eig2 = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

Another energy eigenvalue ${\epsilon }_{nk}^{\prime }$ in the same unit of eig1. Typically it is assumed to be ${\epsilon }_{nk+q}$.

Return

wght = numpy.empty([ng0, ng1, ng2, nb, nb], dtype=numpy.float_)

The integration weights.

Static polarization function

$$\begin{array}{r}\sum _{n{n}^{\prime }}{\int }_{\mathrm{B}\mathrm{Z}}\frac{d^{3}k}{V_{\mathrm{B}\mathrm{Z}}}\frac{\theta ({\epsilon }_{\mathrm{F}}-{\epsilon }_{nk})\theta ({\epsilon }_{n^{\prime }k}^{\prime }-{\epsilon }_{\mathrm{F}})}{{\epsilon }_{n^{\prime }k}^{\prime }-{\epsilon }_{nk}}{X}_{n{n}^{\prime }k}\end{array}$$

wght = libtetrabz.polstat(bvec, eig1, eig2)

Parameters

bvec = numpy.array([[b0x, b0y, b0z], [b1x, b1y, b1z], [b2x, b2y, b2z]])

Reciprocal lattice vectors (arbitrary unit). Because they are used to choose the direction of tetrahedra, only their ratio is used.

eig1 = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

The energy eigenvalue ${\epsilon }_{nk}$ in arbitrary unit. Where ng0, ng1, ng2 are the number of grid for each direction of the reciprocal lattice vectors and nb is the number of bands.

eig2 = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

Another energy eigenvalue ${\epsilon }_{nk}^{\prime }$ in the same unit of eig1. Typically it is assumed to be ${\epsilon }_{nk+q}$.

Return

wght = numpy.empty([ng0, ng1, ng2, nb, nb], dtype=numpy.float_)

The integration weights.

Phonon linewidth

$$\begin{array}{r}\sum _{n{n}^{\prime }}{\int }_{\mathrm{B}\mathrm{Z}}\frac{d^{3}k}{V_{\mathrm{B}\mathrm{Z}}}\theta ({\epsilon }_{\mathrm{F}}-{\epsilon }_{nk})\theta ({\epsilon }_{n^{\prime }k}^{\prime }-{\epsilon }_{\mathrm{F}})\delta ({\epsilon }_{n^{\prime }k}^{\prime }-{\epsilon }_{nk}-\omega )X_{n{n}^{\prime }k}(\omega )\end{array}$$

wght = libtetrabz.fermigr(bvec, eig1, eig2, e0)

Parameters

bvec = numpy.array([[b0x, b0y, b0z], [b1x, b1y, b1z], [b2x, b2y, b2z]])

Reciprocal lattice vectors (arbitrary unit). Because they are used to choose the direction of tetrahedra, only their ratio is used.

eig1 = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

The energy eigenvalue ${\epsilon }_{nk}$ in arbitrary unit. Where ng0, ng1, ng2 are the number of grid for each direction of the reciprocal lattice vectors and nb is the number of bands.

eig2 = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

Another energy eigenvalue ${\epsilon }_{nk}^{\prime }$ in the same unit of eig1. Typically it is assumed to be ${\epsilon }_{nk+q}$.

e0 = numpy.empty(ne, dtype=numpy.float_)

The energy point $\omega$ in the same unit of eig. Where ne is the number of energy points.

Return

wght = numpy.empty([ng0, ng1, ng2, nb, nb, ne], dtype=numpy.float_)

The integration weights.

Polarization function (complex frequency)

$$\begin{array}{r}\sum _{n{n}^{\prime }}{\int }_{\mathrm{B}\mathrm{Z}}\frac{d^{3}k}{V_{\mathrm{B}\mathrm{Z}}}\frac{\theta ({\epsilon }_{\mathrm{F}}-{\epsilon }_{nk})\theta ({\epsilon }_{n^{\prime }k}^{\prime }-{\epsilon }_{\mathrm{F}})}{{\epsilon }_{n^{\prime }k}^{\prime }-{\epsilon }_{nk}+i\omega }{X}_{n{n}^{\prime }k}(\omega )\end{array}$$

wght = libtetrabz.polcmplex(bvec, eig1, eig2, e0)

Parameters

bvec = numpy.array([[b0x, b0y, b0z], [b1x, b1y, b1z], [b2x, b2y, b2z]])

Reciprocal lattice vectors (arbitrary unit). Because they are used to choose the direction of tetrahedra, only their ratio is used.

eig1 = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

The energy eigenvalue ${\epsilon }_{nk}$ in arbitrary unit. Where ng0, ng1, ng2 are the number of grid for each direction of the reciprocal lattice vectors and nb is the number of bands.

eig2 = numpy.empty([ng0, ng1, ng2, nb], dtype=numpy.float_)

Another energy eigenvalue ${\epsilon }_{nk}^{\prime }$ in the same unit of eig1. Typically it is assumed to be ${\epsilon }_{nk+q}$.

e0 = numpy.empty(ne, dtype=numpy.complex_)

The energy point $\omega$ in the same unit of eig. Where ne is the number of energy points.

Return

wght = numpy.empty([ng0, ng1, ng2, nb, nb, ne], dtype=numpy.complex)

The integration weights.