ElPhQeToPhoebeApp Class Reference

Main driver for the transport calculation.

#include <elph_qe_to_phoebe_app.h>

Inheritance diagram for ElPhQeToPhoebeApp:

Collaboration diagram for ElPhQeToPhoebeApp:

Public Member Functions
void	run (Context &context) override
	Executes the program contained in this class.
void	checkRequirements (Context &context) override
	Check that user provided all necessary input.
void	postProcessingWannier (Context &context, Crystal &crystal, PhononH0 &phononH0, Points &kPoints, Points &qPoints, int numQEBands, int numModes, int numIrrQPoints, int numElectrons, int numSpin, const Eigen::MatrixXd &energies, const Eigen::MatrixXd &kGridFull, const Eigen::Vector3i &kMesh, const Eigen::Vector3i &qMesh, bool runTests=false)
	This is the driver for converting QE data to Phoebe data for Wannier interpolation of the el-ph coupling. More...

Static Public Member Functions
static std::tuple< Eigen::Vector3i, Eigen::Vector3i, Eigen::MatrixXd, Eigen::MatrixXd, Eigen::MatrixXd, int, int, int, int >	readQEPhoebeHeader (Crystal &crystal, const std::string &phoebePrefixQE)
	In this function, we read the header file produced by the patched QE version. More...
Static Public Member Functions inherited from App
static std::unique_ptr< App >	loadApp (const std::string &choice)
	Factory method, used to load the desired subclass. More...

Protected Member Functions
Eigen::Tensor< std::complex< double >, 5 >	BlochToWannierEfficient (Context &context, const Eigen::MatrixXd &energies, const Eigen::MatrixXd &kGridFull, const int &numIrrQPoints, const int &numQEBands, const Eigen::MatrixXd &elBravaisVectors, const Eigen::MatrixXd &phBravaisVectors, const Eigen::Tensor< std::complex< double >, 3 > &uMatrices, Points &kPoints, Points &qPoints, Crystal &crystal, PhononH0 &phononH0)
std::tuple< Eigen::Tensor< std::complex< double >, 5 >, Eigen::Tensor< std::complex< double >, 3 >, Eigen::MatrixXd >	readGFromQEFile (Context &context, const int &numModes, const int &numBands, const int &numWannier, Points &kPoints, Points &qPoints, const Eigen::MatrixXd &kGridFull, const int &numIrrQPoints, const int &numQEBands, const Eigen::MatrixXd &energies)
	Reads the electron-phonon coupling computed by QE on a coarse grid. More...
std::tuple< Eigen::Tensor< std::complex< double >, 5 >, Eigen::Tensor< std::complex< double >, 3 >, Eigen::MatrixXd, Eigen::MatrixXd >	readChunkGFromQE (const int &iqIrr, Context &context, Points &kPoints, const int &numModes, const int &numQEBands, const Eigen::VectorXi &ikMap)
void	epaPostProcessing (Context &context, Eigen::MatrixXd &elEnergies, Points &kPoints, Points &qPoints, const int &numElectrons, const int &numSpin, const int &numModes, const int &numIrrQPoints, const int &numQEBands, const Eigen::MatrixXd &kGridFull)
	Main driver for generating the EPA coupling. More...

Static Protected Member Functions
static Eigen::Tensor< std::complex< double >, 5 >	blochToWannier (const Eigen::MatrixXd &elBravaisVectors, const Eigen::MatrixXd &phBravaisVectors, Eigen::Tensor< std::complex< double >, 5 > &gFull, const Eigen::Tensor< std::complex< double >, 3 > &uMatrices, const Eigen::Tensor< std::complex< double >, 3 > &phEigenvectors, Points &kPoints, Points &qPoints, Crystal &crystal, PhononH0 &phononH0)
	Transform the electron-phonon coupling computed by QE from the Bloch to the Wannier representation. More...
static Eigen::Tensor< std::complex< double >, 3 >	setupRotationMatrices (const std::string &wannierPrefix, Points &fullPoints)
	Returns the rotation that moves the wave-function from the (entangled) Bloch representation to the disentangled Wannier representation. More...
static int	computeOffset (const Eigen::MatrixXd &energies, const std::string &wannierPrefix)
	This method compares the energies computed by qe2wannier90 and the energies of quantum espresso pw.x, to compute the offset between the two sets (wannier90 may skip some core states).
static void	testElectronicTransform (Points &kPoints, const std::string &wannierPrefix, const Eigen::MatrixXd &elBravaisVectors, const Eigen::Tensor< std::complex< double >, 3 > &uMatrices, const Eigen::VectorXd &elDegeneracies, ElectronH0Wannier &electronH0)
	Test that the transform Wannier To Bloch of the electronic Hamiltonian returns the original results computed by QE/Wannier90 on a coarse grid. More...
static void	testPhononTransform (Crystal &crystal, PhononH0 &phononH0, Points &qPoints, const Eigen::Tensor< std::complex< double >, 3 > &phEigenvectors, const Eigen::MatrixXd &phBravaisVectors, const Eigen::VectorXd &phDegeneracies, const Eigen::MatrixXd &phEnergies)
	Test that the transform Wannier To Bloch of the phonon harmonic Hamiltonian returns the original results computed by QE on a coarse grid. More...
static void	testBackTransform (Context &context, PhononH0 &phononH0, Points &kPoints, Points &qPoints, ElectronH0Wannier &electronH0, Crystal &crystal, Eigen::Tensor< std::complex< double >, 5 > &gFull)
	Test that the transform Wannier To Bloch of the electron-phonon coupling returns the original results computed by QE on a coarse grid, and that it is correctly computed tby the class InteractionElPh. More...
static void	writeWannierCoupling (Context &context, Eigen::Tensor< std::complex< double >, 5 > &gWannier, const int &numFilledWannier, const int &numSpin, const int &numModes, const int &numWannier, const Eigen::VectorXd &phDegeneracies, const Eigen::VectorXd &elDegeneracies, const Eigen::MatrixXd &phBravaisVectors, const Eigen::MatrixXd &elBravaisVectors, const Eigen::Vector3i &qMesh, const Eigen::Vector3i &kMesh)
	This function writes the el-ph coupling to file. More...
Static Protected Member Functions inherited from App
static void	throwErrorIfUnset (const std::string &x, const std::string &name)
static void	throwErrorIfUnset (const std::vector< std::string > &x, const std::string &name)
static void	throwErrorIfUnset (const double &x, const std::string &name)
static void	throwErrorIfUnset (const Eigen::VectorXi &x, const std::string &name)
static void	throwErrorIfUnset (const Eigen::Vector3i &x, const std::string &name)
static void	throwErrorIfUnset (const Eigen::VectorXd &x, const std::string &name)
static void	throwErrorIfUnset (const Eigen::MatrixXd &x, const std::string &name)
static void	throwErrorIfUnset (const Eigen::Tensor< double, 3 > &x, const std::string &name)
static void	throwWarningIfUnset (const std::string &x, const std::string &name)

Protected Attributes
std::vector< std::string >	choices

Member Function Documentation

blochToWannier()

Eigen::Tensor< std::complex< double >, 5 > ElPhQeToPhoebeApp::blochToWannier ( const Eigen::MatrixXd &  elBravaisVectors, const Eigen::MatrixXd &  phBravaisVectors, Eigen::Tensor< std::complex< double >, 5 > &  gFull, const Eigen::Tensor< std::complex< double >, 3 > &  uMatrices, const Eigen::Tensor< std::complex< double >, 3 > &  phEigenvectors, Points &  kPoints, Points &  qPoints, Crystal &  crystal, PhononH0 &  phononH0  )

staticprotected

Follows roughly the procedure described in [PRB 76, 165108 (2007)]. This is the expensive function of this app.

Parameters

elBravaisVectors	list of Bravais lattice vectors for the electronic Fourier transform
phBravaisVectors	list of Bravais lattice vectors for the phonon Fourier transform
gFull	electron-phonon coupling in the Bloch space, with size gFull(nBands, nBands, nModes, nKPoints, nQPoints), where in the notation of [PRB 76, 165108 (2007)], is g(i,j,nu,k,q) = g_{i,j,nu}(k,q)
uMatrices	the matrices for the rotation to the maximally localized basis set of Wannier functions. Has size U(nBands,nWannier,k). Note that there can be more bands than Wannier functions due to the disentanglement procedure of Wannier90.
phEigenvectors	tensor (nu,mu,q) with the phonon eigenvectors, where the first index is the index on cartesian and atomic basis, the second is the index on phonon modes, and the third is on q-points.
kPoints	FullPoints class of k-points.
qPoints	FullPoints class of q-points.
crystal	class describing the crystal unit cell.
phononH0	class with the Phonon harmonic Hamiltonian.

Returns

g: the electron-phonon coupling in the Wannier representation. in the notation of [PRB 76, 165108 (2007)], is g(n,m,mu,R_p,R_e) = g_{m,n,mu}(R_e,R_p). Note that the first index refers to what must be Fourier transformed to k, whereas PRB refers that to the band at k+q.

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epaPostProcessing()

void ElPhQeToPhoebeApp::epaPostProcessing ( Context &  context, Eigen::MatrixXd &  elEnergies, Points &  kPoints, Points &  qPoints, const int &  numElectrons, const int &  numSpin, const int &  numModes, const int &  numIrrQPoints, const int &  numQEBands, const Eigen::MatrixXd &  kGridFull  )

protected

UNTESTED!

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postProcessingWannier()

void ElPhQeToPhoebeApp::postProcessingWannier	(	Context &	context,
		Crystal &	crystal,
		PhononH0 &	phononH0,
		Points &	kPoints,
		Points &	qPoints,
		int	numQEBands,
		int	numModes,
		int	numIrrQPoints,
		int	numElectrons,
		int	numSpin,
		const Eigen::MatrixXd &	energies,
		const Eigen::MatrixXd &	kGridFull,
		const Eigen::Vector3i &	kMesh,
		const Eigen::Vector3i &	qMesh,
		bool	runTests = false
	)

Parameters

context	class with user input values.
crystal	class describing crystal unit cell.
phononH0	class with the phonon harmonic Hamiltonian.
kPoints	coarse grid of k-points used by QE.
qPoints	coarse grid of q-points used by QE. Equal to kPoints.
numQEBands	number of Kohn-Sham states used by QE.
numModes	number of phonon modes = 3*numAtoms.
numIrrQPoints	number of irreducible q-points computed by QE.
numElectrons	number of electrons in the crystal unit cell.
numSpin	number of spin components used by QE.
energies	matrix with electronic energies.
kGridFull	list of k-point cartesian coordinates in Bohr^-1.
kMesh	mesh of k-points used by QE.
qMesh	mesh of q-points used by QE.
runTests	if true (*default False) runs some sanity checks.

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readGFromQEFile()

std::tuple< Eigen::Tensor< std::complex< double >, 5 >, Eigen::Tensor< std::complex< double >, 3 >, Eigen::MatrixXd > ElPhQeToPhoebeApp::readGFromQEFile ( Context &  context, const int &  numModes, const int &  numBands, const int &  numWannier, Points &  kPoints, Points &  qPoints, const Eigen::MatrixXd &  kGridFull, const int &  numIrrQPoints, const int &  numQEBands, const Eigen::MatrixXd &  energies  )

protected

Note: numQEBands != numBands. The first is the number of bands computes in QE, while the latter is the number of bands passed to Wannier90.

Note: we pass kGridFull because we need to align the list of kPoints used by QE with the "list" of kPoints of Phoebe.

Parameters

context	class with user input.
numModes	number of phonon modes.
numBands	number of bands used in QE
numWannier	number of Wannier functions
kPoints	FullPoints class with kPoints
qPoints	FullPoints class with qPoints
kGridFull	list of kPoints in cartesian coordinates in QE
numIrrQPoints	number of irreducible qPoints used by QE
numQEBands	number of KS bands used by QE.
energies	matrix with electronic energies

Returns

tuple with:

• gFull: electron-phonon coupling in the Bloch space, with size gFull(nBands, nBands, nModes, nKPoints, nQPoints), where in the notation of [PRB 76, 165108 (2007)], is g(i,j,nu,k,q) = g_{i,j,nu}(k,q)
• complex tensor (nu,mu,q) with the phonon eigenvectors, where the first index is the index on cartesian and atomic basis, the second is the index on phonon modes, and the third is on q-points.
• MatrixXd(nb,nq) containing phonon energies

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readQEPhoebeHeader()

std::tuple< Eigen::Vector3i, Eigen::Vector3i, Eigen::MatrixXd, Eigen::MatrixXd, Eigen::MatrixXd, int, int, int, int > ElPhQeToPhoebeApp::readQEPhoebeHeader ( Crystal &  crystal, const std::string &  phoebePrefixQE  )

static

The header contains some global and/or electronic information coming from Quantum-ESPRESSO.

Parameters

crystal	class with the crystal info,
phoebePrefixQE	prefix of file, e.g. "si" corresponds to the file "si.phoebe.****.dat"

Returns

tuple: with elements:

• Eigen::Vector3i: mesh of q-points
• Eigen::Vector3i: mesh of k-points
• Eigen::MatrixXd(3,nk): kPoint cartesian coordinates in Bohr^-1
• Eigen::MatrixXd(3,nq): qPoint cartesian coordinates in Bohr^-1
• Eigen::Matrix(nb,nk): electronic energies
• int : number of irreducible q-points.
• numQEBands: number of KS states used by QE in the ph.x run
• numElectrons: number of electrons in the unit cell (KS states>= electrons)
• numSpin: number of spin components.

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setupRotationMatrices()

Eigen::Tensor< std::complex< double >, 3 > ElPhQeToPhoebeApp::setupRotationMatrices ( const std::string &  wannierPrefix, Points &  fullPoints  )

staticprotected

Parameters

wannierPrefix	path with the prefix used for the Wannier90 calculation (e.g. "si" or "./si")
fullPoints	coarse grid of wavevectors. Must be aligned with the grid used in Wannier90 or an error will be raised.

Returns

U: tensor of shape (numBands, numWannier, numPoints), where the wavevector index is aligned with fullPoints. If no disentanglement was used in Wannier90, numWannier = numBands, otherwise, numBands > numWannier due to the disentanglement. See Wannier90 docs.

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testBackTransform()

void ElPhQeToPhoebeApp::testBackTransform ( Context &  context, PhononH0 &  phononH0, Points &  kPoints, Points &  qPoints, ElectronH0Wannier &  electronH0, Crystal &  crystal, Eigen::Tensor< std::complex< double >, 5 > &  gFull  )

staticprotected

This is the important test of el-ph Wannier interpolation We compute the band structure Read the el-ph interaction from file Check that the el-ph coupling, interpolated on the same initial grid, is the same of the el-ph coupling read from QE.

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testElectronicTransform()

void ElPhQeToPhoebeApp::testElectronicTransform ( Points &  kPoints, const std::string &  wannierPrefix, const Eigen::MatrixXd &  elBravaisVectors, const Eigen::Tensor< std::complex< double >, 3 > &  uMatrices, const Eigen::VectorXd &  elDegeneracies, ElectronH0Wannier &  electronH0  )

staticprotected

This is a simple test: 1) Fourier Transform the electronic Hamiltonian to Wannier representation Here I use the U matrices from file 2) FT back to Bloch representation, using the U matrices from ElectronH0 on the original grid of k-points If everything works, I expect to find the same electronic energies Phases of rotation matrices in the back-FT will be random.

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testPhononTransform()

void ElPhQeToPhoebeApp::testPhononTransform ( Crystal &  crystal, PhononH0 &  phononH0, Points &  qPoints, const Eigen::Tensor< std::complex< double >, 3 > &  phEigenvectors, const Eigen::MatrixXd &  phBravaisVectors, const Eigen::VectorXd &  phDegeneracies, const Eigen::MatrixXd &  phEnergies  )

staticprotected

Like the test above, we 1) FT to real space phonon basis representation. Since these are force constants, they should be real. 2) FT back to Bloch space and check that we find the same results.

We also verify that the eigenvectors are normalized by masses Note that the test works fine for non-polar systems.

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writeWannierCoupling()

void ElPhQeToPhoebeApp::writeWannierCoupling ( Context &  context, Eigen::Tensor< std::complex< double >, 5 > &  gWannier, const int &  numFilledWannier, const int &  numSpin, const int &  numModes, const int &  numWannier, const Eigen::VectorXd &  phDegeneracies, const Eigen::VectorXd &  elDegeneracies, const Eigen::MatrixXd &  phBravaisVectors, const Eigen::MatrixXd &  elBravaisVectors, const Eigen::Vector3i &  qMesh, const Eigen::Vector3i &  kMesh  )

staticprotected

There are three modes of writing file. 1) plain text file. The slowest option, but we allow the user to not use the HDF5 file format. 2) HDF5 v1 (default and preferred). The el-ph tensor is written to a single dataspace. if compiled with parallel HDf5, the write operation is done in parallel. Note that we do the write operation in bunches of siez ~2Gb. This is done to avoid a limitation of the MPI library, which has problem when offsets to the tensor become > max(INT_32). 3) HDF5 v2. The el-ph tensor is split along the R_e index into different datasets. This format has been introduced because we suspect the HDF5 library has limitations when the electron-phonon tensor is very large. We suspect this happens when the tensor size > max(UINT_32).

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