ElectronH0Fourier Class Reference

Class for a Fourier-like interpolation of an electronic band structure. More...

#include <electron_h0_fourier.h>

Inheritance diagram for ElectronH0Fourier:

Collaboration diagram for ElectronH0Fourier:

Public Member Functions
	ElectronH0Fourier (Crystal &crystal_, const Points &coarsePoints_, const FullBandStructure &coarseBandStructure_, double cutoff)
	Constructor of the Fourier interpolation This class stores a copy of the electronic band structure on the coarse grid. More...
Particle	getParticle () override
	Method to return that the underlying is that of an electronic Fermion.
int	getNumBands () override
	Get the total number of bands available at ech wavevector.
std::tuple< Eigen::VectorXd, Eigen::MatrixXcd >	diagonalize (Point &point) override
	get the electronic energies (in Ry) at a single k-point. More...
std::tuple< Eigen::VectorXd, Eigen::MatrixXcd >	diagonalizeFromCoordinates (Eigen::Vector3d &wavevector) override
	Diagonalize the Harmonic Hamiltonian at an arbitrary wavevector. More...
Eigen::Tensor< std::complex< double >, 3 >	diagonalizeVelocity (Point &point) override
	get the electron velocities (in atomic units) at a single k-point. More...
Eigen::Tensor< std::complex< double >, 3 >	diagonalizeVelocityFromCoordinates (Eigen::Vector3d &coordinates) override
FullBandStructure	populate (Points &fullPoints, const bool &withVelocities, const bool &withEigenvectors, const bool isDistributed=false) override
	This method constructs an electron band structure. More...
void	trimBands (Context &context, const double &minEn, const double &maxEn)
virtual StridedComplexView3D	kokkosBatchedBuildBlochHamiltonian (const DoubleView2D &cartesianCoordinates) override
virtual std::tuple< DoubleView2D, StridedComplexView3D, ComplexView4D >	kokkosBatchedDiagonalizeWithVelocities (const DoubleView2D &cartesianCoordinates) override
std::tuple< DoubleView2D, StridedComplexView3D >	kokkosBatchedDiagonalizeFromCoordinates (const DoubleView2D &cartesianCoordinates, const bool withMassScaling=true) override
Public Member Functions inherited from HarmonicHamiltonian
void	kokkosBatchedTreatDegenerateVelocities (const DoubleView2D &cartesianCoordinates, const DoubleView2D &resultEnergies, ComplexView4D &resultVelocities, const double &threshold)
virtual int	estimateBatchSize (const bool &withVelocity)
	Estimate how many k-points we can compute on the GPU in one batch. More...

Protected Member Functions
void	setPositionVectors ()
Eigen::VectorXcd	getLagrangeMultipliers (Eigen::VectorXd energies)
Eigen::VectorXcd	getCoefficients (Eigen::VectorXd energies)
std::complex< double >	getStarFunction (Eigen::Vector3d &wavevector, int &iR)
Eigen::Vector3cd	getDerivativeStarFunction (Eigen::Vector3d &wavevector, int &iR)
double	getRoughnessFunction (const Eigen::Vector3d &position) const
double	getEnergyFromCoordinates (Eigen::Vector3d &wavevector, int &bandIndex)
Eigen::Vector3d	getGroupVelocityFromCoordinates (Eigen::Vector3d &wavevector, int &bandIndex)

Protected Attributes
Crystal &	crystal
FullBandStructure	coarseBandStructure
Points	coarsePoints
Particle	particle
Eigen::MatrixXcd	expansionCoefficients
int	numBands
double	cutoff
int	numDataPoints
int	numPositionVectors = 0
double	minDistance = 10.
Eigen::VectorXd	positionDegeneracies
Eigen::MatrixXd	positionVectors
Eigen::Vector3d	refWavevector
const double	coefficient1 = 0.75
const double	coefficient2 = 0.75

Detailed Description

Takes the information on the band structure computed on a uniform coarse grid of k-points, and interpolates it to finer grids with a plane wave based method.

Constructor & Destructor Documentation

ElectronH0Fourier()

ElectronH0Fourier::ElectronH0Fourier	(	Crystal &	crystal_,
		const Points &	coarsePoints_,
		const FullBandStructure &	coarseBandStructure_,
		double	cutoff
	)

Parameters

crystal	the crystal used in the band structure calculation
coarseBandStructure	values of the electronic bands over a full grid of k-points, provided by an external (DFT) code.
cutoff	a parameter used to define the number of coefficients in the plane-wave interpolation. It should be an integer >1. This parameter controls that the interpolation is generated using a grid of lattice vectors which is of size 2*Grid(i)*cutoff, where i is the direction index and grid(i) is the size of the wavevector coarse grid.

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Member Function Documentation

diagonalize()

std::tuple< Eigen::VectorXd, Eigen::MatrixXcd > ElectronH0Fourier::diagonalize ( Point &  point )

overridevirtual

Energies don't have any reference value, and must be used in connection with a chemical potential.

Parameters

k	a point object with the wavevector. Must have the cartesian coordinates of the wavevector.

Returns

tuple(energies, eigenvectors): the energies are a double vector of size (numBands). Eigenvectors of size (numBands,numBands), but are simply set to zero, since there is no diagonalization happening here.

Implements HarmonicHamiltonian.

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diagonalizeFromCoordinates()

std::tuple< Eigen::VectorXd, Eigen::MatrixXcd > ElectronH0Fourier::diagonalizeFromCoordinates ( Eigen::Vector3d &  k )

overridevirtual

Same as diagonalize(), but the wavevector coordinates are explicitly passed in input.

Parameters

point

the wavevector in cartesian coordinates.

Returns

eigenvalues: the values of quasiparticle energies, a double vector of size numBands.

eigenvectors: a complex matrix of size (numBands,numBands) with the eigenvectors, ordered in columns, computed at the input wavevector.

Implements HarmonicHamiltonian.

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diagonalizeVelocity()

Eigen::Tensor< std::complex< double >, 3 > ElectronH0Fourier::diagonalizeVelocity ( Point &  point )

overridevirtual

Parameters

k	a Point object with the wavevector coordinates.

Returns

velocity(numBands,numBands,3): values of the velocity operator for this state, in atomic units. Note that the off-diagonal matrix elements are set to zero, because this kind of interpolation, at the moment, doesn't have any information on the off-diagonal elements.

Implements HarmonicHamiltonian.

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populate()

FullBandStructure ElectronH0Fourier::populate ( Points &  fullPoints, const bool &  withVelocities, const bool &  withEigenvectors, const bool  isDistributed = false  )

overridevirtual

Parameters

points	the object with the list/mesh of wavevectors
withVelocities	if true, compute the electron velocity operator.
withEigenvectors	can only be false, as there are no eigenvectors with this kind of interpolation.

Returns

FullBandStructure: the band structure object containing the complete electronic band structure.

Implements HarmonicHamiltonian.

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