InteractionElPhWan Class Reference

Class to handle the coupling between electron and phonons. More...

#include <interaction_elph.h>

Public Member Functions
	InteractionElPhWan (const Crystal &crystal_, const Eigen::Tensor< std::complex< double >, 5 > &couplingWannier_, const Eigen::MatrixXd &wsR1Vectors_, const Eigen::VectorXd &wsR1VectorsDegeneracies_, const Eigen::MatrixXd &wsR2Vectors_, const Eigen::VectorXd &wsR2VectorsDegeneracies_, const int &phaseConvention, const PhononH0 &phononH0_)
	Main constructor. More...
void	resetK1 ()
	~InteractionElPhWan ()
	Almost empty constructor. More...
void	calcCouplingSquared (const Eigen::MatrixXcd &eigvec1, const std::vector< Eigen::MatrixXcd > &eigvecs2, const std::vector< Eigen::MatrixXcd > &eigvecs3, const std::vector< Eigen::Vector3d > &q3Cs, const Eigen::Vector3d &k1C, const std::vector< Eigen::VectorXcd > &polarData)
	Computes the values of the el-ph coupling strength for transitions of type k1,q3 -> k2, where k1 is one fixed wavevector, and k2,q3 are wavevectors running in lists of wavevectors. More...
void	oldCalcCouplingSquared (const Eigen::MatrixXcd &eigvec1, const std::vector< Eigen::MatrixXcd > &eigvecs2, const std::vector< Eigen::MatrixXcd > &eigvecs3, const Eigen::Vector3d &k1C, const std::vector< Eigen::Vector3d > &k2Cs, const std::vector< Eigen::Vector3d > &q3Cs)
void	cacheElPh (const Eigen::MatrixXcd &eigvec1, const Eigen::Vector3d &k1C)
	Computes a partial Fourier transform over the k1/R_el variables. More...
Eigen::Tensor< double, 3 > &	getCouplingSquared (const int &ik2)
	Get the coupling for the values of the wavevectors triplet (k1,k2,q3), where k1 is the wavevector used at calcCoupling Squared(), k2 (at index ik2) is the wavevector of the scattered electron in the final state, and q3 = k2 - k1 is the phonon wavevector. More...
Eigen::Tensor< std::complex< double >, 3 >	getPolarCorrection (const Eigen::Vector3d &q3, const Eigen::MatrixXcd &ev1, const Eigen::MatrixXcd &ev2, const Eigen::MatrixXcd &ev3)
	Add polar correction to the electron-phonon coupling. More...
double	getDeviceMemoryUsage ()
	Estimate the memory in bytes, occupied by the kokkos Views containing the coupling tensor to be interpolated. More...
Eigen::VectorXi	getCouplingDimensions ()
	Auxiliary function to return the shape of the electron-phonon tensor. More...
int	estimateNumBatches (const int &nk2, const int &nb1)
	Estimate the number of batches that the list of k2 wavevectors must be split into, in order to fit in memory. More...
Eigen::VectorXcd	polarCorrectionPart1 (const Eigen::Vector3d &q3, const Eigen::MatrixXcd &ev3)
Eigen::MatrixXcd	precomputeQDependentPolar (BaseBandStructure &phBandStructure, const bool useMinusQ=false)
	precompute the q-dependent part of the polar correction More...

Static Public Member Functions
static InteractionElPhWan	parse (Context &context, Crystal &crystal, PhononH0 &phononH0_)
	Static method to initialize the class by parsing a file. More...
static Eigen::Tensor< std::complex< double >, 3 >	getPolarCorrectionStatic (const Eigen::Vector3d &q3, const Eigen::MatrixXcd &ev1, const Eigen::MatrixXcd &ev2, const Eigen::MatrixXcd &ev3, const double &volume, const Eigen::Matrix3d &reciprocalUnitCell, const Eigen::Matrix3d &epsilon, const Eigen::Tensor< double, 3 > &bornCharges, const Eigen::MatrixXd &atomicPositions, const Eigen::Vector3i &qCoarseMesh, const int dimensionality)
static Eigen::VectorXcd	polarCorrectionPart1Static (const Eigen::Vector3d &q3, const Eigen::MatrixXcd &ev3, const double &volume, const Eigen::Matrix3d &reciprocalUnitCell, const Eigen::Matrix3d &epsilon, const Eigen::Tensor< double, 3 > &bornCharges, const Eigen::MatrixXd &atomicPositions, const Eigen::Vector3i &qCoarseMesh, const int dimensionality)
static Eigen::Tensor< std::complex< double >, 3 >	polarCorrectionPart2 (const Eigen::MatrixXcd &ev1, const Eigen::MatrixXcd &ev2, const Eigen::VectorXcd &x)

Static Public Attributes
static const int	GiustinoPhaseConvention = 0
static const int	JdftxPhaseConvention = 1
static const int	spinNonPolarized = 1
static const int	spinPolarizedOrSOC = 2

Detailed Description

Currently implements the calculation of the diagram for the interaction k + q -> k'. Use the static method to initialize an instance of this class. Then, use calc + get to compute and retrieve the values of the electron-phonon interaction strength in Bloch space |g|^2.

This class starts from the interaction matrix elements in real space Wannier representation and mostly does: 1) a double Fourier transform on phonon and electron coordinates; 2) multiply by phonon/electron eigenvectors/rotation matrices; 3) for polar materials, adds the long-range Frohlich interaction.

Constructor & Destructor Documentation

InteractionElPhWan()

InteractionElPhWan::InteractionElPhWan	(	const Crystal &	crystal_,
		const Eigen::Tensor< std::complex< double >, 5 > &	couplingWannier_,
		const Eigen::MatrixXd &	wsR1Vectors_,
		const Eigen::VectorXd &	wsR1VectorsDegeneracies_,
		const Eigen::MatrixXd &	wsR2Vectors_,
		const Eigen::VectorXd &	wsR2VectorsDegeneracies_,
		const int &	phaseConvention,
		const PhononH0 &	phononH0_
	)

Parameters

crystal_	object describing the crystal unit cell.
couplingWannier_	matrix elements of the electron phonon interaction. A tensor of shape (iw1,iw2,imode,rPh,rEl), where iw1 iw2 are indices on Wannier functions, imode is a phonon mode index in real space, rPh is an index on phonon Bravais lattice vectors, and rEl is an index on electronic Bravais Lattice vectors. Built such that the iw2 Wannier functions are set in the origin (k2 doesn't contribute to the Fourier transform).
wsR1Vectors_	list of Bravais lattice vectors used in the electronic Fourier transform of the coupling.
wsR1VectorsWeights_	weights (degeneracies) of the lattice vectors used in the electronic Fourier transform of the coupling.
wsR2Vectors_	list of Bravais lattice vectors used in the phonon Fourier transform of the coupling.
wsR2VectorsWeights_	weights (degeneracies) of the lattice vectors used in the phonon Fourier transform of the coupling.
phaseConvention_	whether to use g(Re,Rp) = convention = 0 or g(Re,Re') = convention = 1, as used by JDFTx
phononH0_	the phonon dynamical matrix object. Used for adding the polar interaction.

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~InteractionElPhWan()

InteractionElPhWan::~InteractionElPhWan

(

)

Used to fake the existence of a coupling with the constant relaxation time approximation.

Parameters

crystal_

a Crystal object Copy constructor Assignment operator Destructor

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Member Function Documentation

cacheElPh()

void InteractionElPhWan::cacheElPh	(	const Eigen::MatrixXcd &	eigvec1,
		const Eigen::Vector3d &	k1C
	)

Parameters

k1C	values of the k1 cartesian coordinates over which the Fourier transform is computed.
eigvec1	Wannier rotation matrix U at point k1.

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calcCouplingSquared()

void InteractionElPhWan::calcCouplingSquared	(	const Eigen::MatrixXcd &	eigvec1,
		const std::vector< Eigen::MatrixXcd > &	eigvecs2,
		const std::vector< Eigen::MatrixXcd > &	eigvecs3,
		const std::vector< Eigen::Vector3d > &	q3Cs,
		const Eigen::Vector3d &	k1C,
		const std::vector< Eigen::VectorXcd > &	polarData
	)

It is assumed that the relation (k2 = k1 + q3) holds.

The call to this function must be preceded by a call to cacheElPh(), which does a precomputation at fixed value of k1. If not, results will be wrong. Hence, structure a code calling this functions as: for k1: cacheElPh(k1) for k2: k3 = k2 - k1 calcCouplingSquared(k2,k3)

Note: this method must be used in conjunction with getCouplingSquared, which is used to return the values computed here.

Parameters

el1Eigenvec	electron eigenvector matrix U_{mb}(k1), where U is obtained by diagonalizing the Wannier Hamiltonian.
el2Eigenvecs	vector of electron eigenvectors matrix U_{mb}(k2), where U is obtained by diagonalizing the Wannier Hamiltonian at a bunch of k2 wavevectors.
phEigvecs	phonon eigenvectors, in matrix form, for a bunch of wavevectors q3
q3s	list of phonon wavevectors.
k1C	the electron wavevector last used by cacheElPh (only used when phaseConvention) = 1, as here we need to reconstruct k2

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estimateNumBatches()

int InteractionElPhWan::estimateNumBatches	(	const int &	nk2,
		const int &	nb1
	)

Parameters

nk2	total number of k2 wavevectors to be split in batches.
nb1	number of bands at the k1 wavevector.

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getCouplingDimensions()

Eigen::VectorXi InteractionElPhWan::getCouplingDimensions

(

)

Returns

(numWannier,numWannier,numPhModes,numElVectors,numPhVectors)

getCouplingSquared()

Eigen::Tensor< double, 3 > & InteractionElPhWan::getCouplingSquared

(

const int &

ik2

)

Note: this method only works AFTER calcCouplingSquared has been called.

Parameters

ik2	index of the 2nd wavevector, aligned with the list of wavevectors passed to calcCouplingSquared().

Returns

g2: a tensor of shape (nb1,nb2,numPhBands=3*numAtoms) with the values of the coupling squared |g(ik1,ik2,iq3)|^2 for the el-ph transition k1,q3 -> k2

getDeviceMemoryUsage()

double InteractionElPhWan::getDeviceMemoryUsage

(

)

Returns

a memory estimate in bytes

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getPolarCorrection()

Eigen::Tensor< std::complex< double >, 3 > InteractionElPhWan::getPolarCorrection	(	const Eigen::Vector3d &	q3,
		const Eigen::MatrixXcd &	ev1,
		const Eigen::MatrixXcd &	ev2,
		const Eigen::MatrixXcd &	ev3
	)

Parameters

q3	phonon wavevector, in cartesian coordinates
ev1	eigenvector (rotation matrix U) at k
ev2	eigenvector (rotation matrix U) at k'
ev3	phonon eigenvector at q = k'-k

Returns

g^L: the long-range (Frohlich) component of the el-ph interaction, as a tensor of shape (nb1,nb2,numPhBands)

parse()

InteractionElPhWan InteractionElPhWan::parse ( Context &  context, Crystal &  crystal, PhononH0 &  phononH0_  )

static

Parameters

fileName	name of the file containing the coupling matrix elements in real space, and the information on the lattice vectors and degeneracies.
crystal	object describing the crystal unit cell.

Returns

intElPh: an instance of InteractionElPh.

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precomputeQDependentPolar()

Eigen::MatrixXcd InteractionElPhWan::precomputeQDependentPolar	(	BaseBandStructure &	phBandStructure,
		const bool	useMinusQ = false
	)

Parameters

phbandstructure

the bandstructure object containing all q-points for which this precomputation should occur

Returns

polarData: the q-dependent part of the polar correction

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