Density Class Reference

A class to calculate the onsite desnity useful for self-consistent calculations. More...

Inheritance diagram for Density:

Public Member Functions
function	Density (Opt, varargin)
	Constructor of the class. More...
function	DensityCalc (varargin)
	Calculates the onsite desnity using the method in Nanotechnology 25 (2014), 465201. More...
function	DensityCalcSmall (num_occupied_states)
	determine the number of sites in the calculations to preallocate memory More...
function	diagInv (A)
	Calculates the diagonal part of the inverse of a sparse matrix. More...
function	display (message, nosilent)
	Displays output messages on the screen. More...
function	DOSCalc (Evec, varargin)
	Calculates the onsite desnity of states. More...
function	eig (A, B)
	Calculates the generalized eigenvalue problem based on the zggev and dggev LAPACK functions. More...
function	Fermi (E)
	A function of the Fermi-Dirac statistics. More...
function	getBandWidth ()
	creating site indexes corresponding to the elements of the density vector More...
function	getOpt ()
	Retrives the structure containing the calculation parameters. More...
function	getProgramName ()
	Gets the name of the package. More...
function	getProgramShortName ()
	Gets the short name of the package. More...
function	getVersion ()
	Gets the current version of the package. More...
function	IsDeployedMKL ()
	Checks whether the MKL component is deployed. More...
function	LocalDOSCalc (Energy, varargin)
	preallocate memory for Densitysurf More...
function	partialInv (A, sizeInv)
	Calculates a partial inverse of a sparse matrix. More...
function	SetEnergy (newE, varargin)
	Sets the energy for the calculations. More...
function	setTemperature (T)
	Sets the temperature for the calculations. More...
function	xmlread (filename)
	Function to load XML files (based on xerces libraries), providing octave compatibility. More...
function	xmlwrite (filename, DOM)
	Function to export XML files (based on xerces libraries), providing octave compatibility. More...

Static Public Member Functions
static function	BadInputType (variable, type)
	Throws a "bad input type" warning, with using the default value. More...
static function	BadInputTypeNoDefault (variable, type)
	Throws a "bad input type" warning without setting it to default. More...
static function	checkMEXfile (fncname)
	Checks the presence of a given MEX file. More...
static function	ExceedIteration ()
	Throws an "iteration exceeded" warning. More...
static function	inv_SVD (A)
	Inverts badly conditioned matrix A with SVD regularization. More...
static function	isOctave ()
	Checks whether the running environment is matlab or octave. More...
static function	SimphsonInt (y, h)
	Simphson integral: y is a vector of function values at equal distant points: y_i = f(x_i), x_i-x_{i-1}=h. More...

Public Attributes
Property	BandWidth
	An instance of structure BandWidth. More...
Property	DOSdata
	DOSvec
	Array of the density of states values. More...
	Evec
	Array of the enrgy points. More...
Property	gfininvfromHamiltonian
	logical value. Set true for calculate the Greens function of the scattering region from Hamiltonian, or false (default) otherwise. More...
Property	junction
	An instance of class NTerminal (or its subclass) representing the junction. More...
Property	scatterPotential
	Function handle pot = f(#coordinates) for the additional potential to be applied in the scattering region. More...
Property	useSelfEnergy
	logical value. Set true (default) for solve the Dyson equation with the self energies, or false otherwise. More...
Property	varargin
	cell array of optional parameters. (For details see InputParsing) More...

Protected Member Functions
function	complexDensity (junction_loc, JustScatter)
	Calculates the density at a complex energy. More...
function	complexSpectral (junction_loc, JustScatter)
	setting the current energy More...
function	create_Hamiltonians (varargin)
	Creates the Hamiltonians of the system. More...
function	create_scatter (varargin)
	cerating Hamiltonian of the scattering region More...
function	InputParsing (varargin)
	Parses the optional parameters for the class constructor. More...

Protected Attributes
Property	beta
	More...
Property	DeployedMKL
	True if MKL component is built, false otherwise. More...
Property	k_B
	Boltzmann constant in eV/K. More...
Property	MaxSize
	Maximal size of full matrixes to be handled. More...
Property	mu
	The Chemical potential in the same unit as other energy scales in the Hamiltonians. More...
Property	Opt
	An instance of structure Opt. More...
Property	ProgramName
	Name of the package. More...
Property	ProgramShortName
	Short name of the package. More...
Property	T
	The temperature in Kelvin. More...
Property	T_treshold
	treshold temperature (makes difference between T=0 and T>0) More...
Property	version
	The current version of the package. More...

Detailed Description

A class to calculate the onsite desnity useful for self-consistent calculations.

Available

EQuUs v4.9 or later

Definition at line 26 of file Density.m.

Constructor & Destructor Documentation

Density()

function Density::Density	(	Opt	,
		varargin
	)

Constructor of the class.

Parameters

Opt	An instance of structure Opt.
varargin	Cell array of optional parameters. For details see InputParsing.

Returns

An instance of the class

Member Function Documentation

BadInputType()

static function Messages::BadInputType ( variable  , type    )

staticinherited

Throws a "bad input type" warning, with using the default value.

Parameters

variable	A string conatining the name of the variable.
type	A string describing the desired type.

BadInputTypeNoDefault()

static function Messages::BadInputTypeNoDefault ( variable  , type    )

staticinherited

Throws a "bad input type" warning without setting it to default.

Parameters

variable	A string conatining the name of the variable.
type	A string describing the desired type.

checkMEXfile()

static function CommonFunctions::checkMEXfile ( fncname  )

staticinherited

Checks the presence of a given MEX file.

Parameters

fncname

The name of the function.

Returns

Returns true if the MEX file is present, false otherwise.

complexDensity()

function Density::complexDensity ( junction_loc  , JustScatter    )

protected

Calculates the density at a complex energy.

Parameters

junction_loc	An instance of class NTerminal or its subclass describing the junction.
JustScatter	Logical value. True if only an isolated scattering center should be considered in the self-consistent calculations, false otherwise.

complexSpectral()

function DOS::complexSpectral ( junction_loc  , JustScatter    )

protectedinherited

setting the current energy

creating the Hamiltonian of the scattering region evaluating the energy resolved density creating the data structure of the local density of states Calculates the spectral function at a complex energy

Parameters

junction_loc	An instance of class NTerminal or its subclass representing the junction.
JustScatter	logical value. True if only an isolated scattering center should be considered in the calculations, false otherwise.

Returns

spectral_function The calculted spectral function and a data structure containing geometry data of the junction.

create_Hamiltonians()

function DOS::create_Hamiltonians ( varargin  )

protectedinherited

Creates the Hamiltonians of the system.

Parameters

varargin

Cell array of optional parameters:.

create_scatter()

function DOS::create_scatter ( varargin  )

protectedinherited

cerating Hamiltonian of the scattering region

creating the Lead Hamiltonians Creates the Hamiltonian of the scattering center

Parameters

varargin

Cell array of optional parameters:.

DensityCalc()

function Density::DensityCalc

(

varargin

)

Calculates the onsite desnity using the method in Nanotechnology 25 (2014), 465201.

Parameters

varargin	Cell array of optional parameters:
'Edb'	The number of the energy points over the contour integral.
'DeltaPhi'	A parameter to control the incident angle of the integration contour near the real axis. (Default value is $$\Delta\Phi=0.5\pi$$.
'Evec'	The complex energy points in case of custom integration path. (Overrides all other optional parameters.)
'Emin'	The minimum of the energy array.
'JustScatter'	Logical value. True if only an isolated scattering center should be considered in the self-consistent calculations, false otherwise.

Returns

An array of the calculated density and a structure describing the geometry of the sites.

DensityCalcSmall()

function Density::DensityCalcSmall

(

num_occupied_states

)

determine the number of sites in the calculations to preallocate memory

preallocate memory for Densitysurf creating function handles for parallel for setting the current energy creating the Hamiltonian of the scattering region evaluating the energy resolved density closing the parallel pool calculating the contour integrals Calculates the onsite desnity using the method in Nanotechnology 25 (2014), 465201. This method is usable for small isolated scattering centers for which an exact diagonalization can be performed

Parameters

num_occupied_states

Number of occupied states

Returns

An array of the calculated density and a structure describing the geometry of the sites.

diagInv()

function CommonFunctions::diagInv ( A  )

inherited

Calculates the diagonal part of the inverse of a sparse matrix.

If MKL component is advised to build.

Parameters

A	A sparse matrix to be inverted

Returns

Returns the diagonal elements of the inverse

display()

function Messages::display ( message  , nosilent    )

inherited

Displays output messages on the screen.

Parameters

message	String containing the message to be displayed
nosilent	Set true to override the silent option given in Opt.Silent.

DOSCalc()

function DOS::DOSCalc ( Evec  , varargin    )

inherited

Calculates the onsite desnity of states.

Parameters

Evec	One-dimensional array of the energy points.
varargin	Cell array of optional parameters:
'JustScatter'	Logical value. Set true to omit the contacts from the system

eig()

function CommonFunctions::eig ( A  , B    )

inherited

Calculates the generalized eigenvalue problem based on the zggev and dggev LAPACK functions.

Parameters

A	A square matrix on the left side.
B	A square matrix on the right side.

Returns

Returns the calculated generalized eigenvalues and the right and left sided eigenvectors.

ExceedIteration()

static function Messages::ExceedIteration ( )

staticinherited

Throws an "iteration exceeded" warning.

Fermi()

function FermiDirac::Fermi ( E  )

inherited

A function of the Fermi-Dirac statistics.

Parameters

E	The energy value in eV (scalar or an array of energy values).

Returns

Returns with the occupation number (numbers).

getBandWidth()

function Density::getBandWidth

(

)

creating site indexes corresponding to the elements of the density vector

Determines the band width of the leads and of the scattering region.

Returns

ret An instance of structure BandWidth containing the bandwidths.

getOpt()

function Messages::getOpt ( )

inherited

Retrives the structure containing the calculation parameters.

Returns

Return an instance of structure Opt.

getProgramName()

function CommonFunctions::getProgramName ( )

inherited

Gets the name of the package.

Returns

Returns the name of the package.

getProgramShortName()

function CommonFunctions::getProgramShortName ( )

inherited

Gets the short name of the package.

Returns

Returns the short name of the package.

getVersion()

function CommonFunctions::getVersion ( )

inherited

Gets the current version of the package.

Returns

Returns the current version of the package.

InputParsing()

function Density::InputParsing ( varargin  )

protected

Parses the optional parameters for the class constructor.

Parameters

varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'T'	The absolute temperature in Kelvins.
'silent'	Set true to suppress output messages.
'scatterPotential'	A function handle y=f( #coordinates coords ) or y=f( CreateHamiltonians CreateH, E ) of the potential across the junction.
'useSelfEnergy'	Logical value. Set true (default) to solve the Dyson equation with the self energies of the leads, or false to use the surface Green operators.
'gfininvfromHamiltonian'	Logical value. Set true calculate the surface Greens function of the scattering region from the Hamiltonaian of the scattering region, or false (default) to calculate it by the fast way (see Phys. Rev. B 90, 125428 (2014) for details).
'junction'	An instance of a class NTerminal or its subclass describing the junction.

inv_SVD()

static function CommonFunctions::inv_SVD ( A  )

staticinherited

Inverts badly conditioned matrix A with SVD regularization.

Parameters

A	A square matrix to be inverted.

Returns

Returns the calculated inverse.

IsDeployedMKL()

function CommonFunctions::IsDeployedMKL ( )

inherited

Checks whether the MKL component is deployed.

Returns

Returns with true if MKL component is deployed, false otherwise.

isOctave()

static function CommonFunctions::isOctave ( )

staticinherited

Checks whether the running environment is matlab or octave.

Returns

Returns true if running environment is octave, false otherwise.

LocalDOSCalc()

function DOS::LocalDOSCalc ( Energy  , varargin    )

inherited

preallocate memory for Densitysurf

creating function handles for parallel for setting the current energy creating the Hamiltonian of the scattering region evaluating the energy resolved density closing the parallel pool Calculates the local desnity of states for a given energy.

Parameters

Energy	The energy value in the units of the Hamiltonians
varargin	Cell array of optional parameters:
'JustScatter'	Logical value. Set true to omit the contacts from the system

Returns

Returns with the calculated local DOS. (An instance of structure LocalDOS)

partialInv()

function CommonFunctions::partialInv ( A  , sizeInv    )

inherited

Calculates a partial inverse of a sparse matrix.

If MKL component is not developed, the backslash operator is used insted.

Parameters

A	A sparse matrix to be inverted
sizeInv	The size of partial inverse to be calculated.

Returns

Returns the calculated partial inverse

SetEnergy()

function UtilsBase::SetEnergy ( newE  , varargin    )

inherited

Sets the energy for the calculations.

Parameters

newE	The value of the energy in the same units as the Hamiltonian.
varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'junction'	An instance of class NTerminal (or its derived class) representing the junction.

setTemperature()

function FermiDirac::setTemperature ( T  )

inherited

Sets the temperature for the calculations.

Parameters

T	The temperature in Kelvin (scalar or an array)

SimphsonInt()

static function CommonFunctions::SimphsonInt ( y  , h    )

staticinherited

Simphson integral: y is a vector of function values at equal distant points: y_i = f(x_i), x_i-x_{i-1}=h.

Parameters

y	Function values to be integrated
h	Increment between the x_i points.

xmlread()

function CommonFunctions::xmlread ( filename  )

inherited

Function to load XML files (based on xerces libraries), providing octave compatibility.

Parameters

filename

Absolute path to the file to be opened. (In matlab relative path is sufficient)

Returns

The loaded document object model (see http://www.mathworks.com/help/matlab/ref/xmlread.html#outputarg_DOMnode for details.)

xmlwrite()

function CommonFunctions::xmlwrite ( filename  , DOM    )

inherited

Function to export XML files (based on xerces libraries), providing octave compatibility.

Parameters

filename	Absolute path to the file to be opened. (In matlab relative path is sufficient)
DOM	The loaded document object model (see http://www.mathworks.com/help/matlab/ref/xmlread.html#outputarg_DOMnode for details.)

Member Data Documentation

BandWidth

Property UtilsBase::BandWidth

inherited

An instance of structure BandWidth.

Definition at line 36 of file UtilsBase.m.

beta

Property FermiDirac::beta

protectedinherited

Definition at line 38 of file FermiDirac.m.

DeployedMKL

Property CommonFunctions::DeployedMKL

protectedinherited

True if MKL component is built, false otherwise.

Definition at line 32 of file CommonFunctions.m.

DOSdata

Property DOS::DOSdata

inherited

Definition at line 34 of file DOS.m.

DOSvec

DOS::DOSvec

inherited

Array of the density of states values.

Definition at line 198 of file structures.m.

Evec

DOS::Evec

inherited

Array of the enrgy points.

Definition at line 200 of file structures.m.

gfininvfromHamiltonian

Property UtilsBase::gfininvfromHamiltonian

inherited

logical value. Set true for calculate the Greens function of the scattering region from Hamiltonian, or false (default) otherwise.

Definition at line 45 of file UtilsBase.m.

junction

Property UtilsBase::junction

inherited

An instance of class NTerminal (or its subclass) representing the junction.

Definition at line 33 of file UtilsBase.m.

k_B

Property FermiDirac::k_B

protectedinherited

Boltzmann constant in eV/K.

Definition at line 32 of file FermiDirac.m.

MaxSize

Property CommonFunctions::MaxSize

protectedinherited

Maximal size of full matrixes to be handled.

Definition at line 44 of file CommonFunctions.m.

mu

Property FermiDirac::mu

protectedinherited

The Chemical potential in the same unit as other energy scales in the Hamiltonians.

Definition at line 44 of file FermiDirac.m.

Opt

Property Messages::Opt

protectedinherited

An instance of structure Opt.

Definition at line 31 of file Messages.m.

ProgramName

Property CommonFunctions::ProgramName

protectedinherited

Name of the package.

Definition at line 38 of file CommonFunctions.m.

ProgramShortName

Property CommonFunctions::ProgramShortName

protectedinherited

Short name of the package.

Definition at line 41 of file CommonFunctions.m.

scatterPotential

Property UtilsBase::scatterPotential

inherited

Function handle pot = f(#coordinates) for the additional potential to be applied in the scattering region.

Definition at line 42 of file UtilsBase.m.

T

Property FermiDirac::T

protectedinherited

The temperature in Kelvin.

Definition at line 35 of file FermiDirac.m.

T_treshold

Property FermiDirac::T_treshold

protectedinherited

treshold temperature (makes difference between T=0 and T>0)

Definition at line 41 of file FermiDirac.m.

useSelfEnergy

Property UtilsBase::useSelfEnergy

inherited

logical value. Set true (default) for solve the Dyson equation with the self energies, or false otherwise.

Definition at line 39 of file UtilsBase.m.

varargin

Property UtilsBase::varargin

inherited

cell array of optional parameters. (For details see InputParsing)

Definition at line 48 of file UtilsBase.m.

version

Property CommonFunctions::version

protectedinherited

The current version of the package.

Definition at line 35 of file CommonFunctions.m.

---

The documentation for this class was generated from the following file:

• Density.m