A class to calculate the Keldysh lesser and greater Green functions and self energies of a translational invariant lead. More...

Inheritance diagram for Lead_Keldysh:

[legend]

Public Member Functions
function	AddPotential (V)
	Adds on-site potential to the Hamiltonian H0. More...

function	ApplyOverlapMatrices (E)
	Applies the overlap matrices to the Hamiltonians: K = H-ES. More...

function	Calc_Effective_Hamiltonians (E)
	Calculates the effective Hamiltonians according to Eq (48) of of PRB 78, 035407. More...

function	CalcSpektrum (varargin)
	Calculates the band structure of the lead. More...

function	Clear (MemberName)
	Clears the value of an attribute in the class. More...

function	CreateClone (varargin)
	Creates a clone of the present Lead object. More...

function	CreateClone ()
	Creates a clone of the present object. More...

function	CreateHamiltonians (varargin)
	Creates the Hamiltonians H_0 and H_1 of the lead. More...

function	Decimate_Hamiltonians ()
	Decimates the Hamiltonians (if the singular sites are predefined). More...

function	Determine_Open_Channels ()
	Determines the open channels in the lead. The data are storen within the attribute open_channels. 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	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	FiniteGreenFunction (z1, z2, varargin)
	Eq (20), (17) and (36) in PRB 78 035407 g00 = inv(Normamtx) More...

function	Gamma ()
	Calculates the effective coupling of the lead to the scattering region according to Eq (3) in Eur. More...

function	Get_Effective_Coordinates ()
	Gets the coordinates of the sites of the effective Hamiltonians. More...

function	Get_Effective_Hamiltonians ()
	Gets the effective Hamiltonians K0_eff, K1_eff, K1adj_eff according to Eq (48) of of PRB 78, 035407. More...

function	Get_Effective_Overlaps ()
	Gets the effective Hamiltonians S0_eff, S1_eff, S1adj_eff according to Eq (48) of of PRB 78, 035407. More...

function	Get_Neff ()
	Gets the effective number of sites after the elimination of the singular values. More...

function	Get_V ()
	Gets the total transformation U related to the SVD transformation. 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	Group_Velocity ()
	Calculates the group velocities corresponding to the propagating states. The calculated group velocities are stored within the class. More...

function	InfGreenFunction (z1, z2, varargin)
	Calculates the Green function of the infinite lead for eregy E between slabs z1 and z2. More...

function	is_SVD_needed ()
	Decides whether SVD regularization is needed or not. More...

function	IsDeployedMKL ()
	Checks whether the MKL component is deployed. More...

function	isSuperconducting ()
	Test, whether the lead is in the superconducting phase or not. More...

function	Lead_Keldysh (Opt, param, varargin)
	Constructor of the class. More...

function	LesserSelfEnergy ()
	Calculates the lesser self energy of a semi-infinite lead for energy E according to Eq (41) in Adv. More...

function	LesserSurfaceGreenFunction (varargin)
	Calculates the lesser Green function of a semi-infinite lead for eregy E. The calculated Green function is stored by the attribute lessergsurf. More...

function	MomentumDependentHamiltonian (k, q)
	Construct a momentum dependent (Fourier-transformed) Hamiltonian. More...

function	NormamtxSzamolo ()
	right SGF Eq (33) in PRB 78, 035407 (2008) g00 = inv(Normamtx) More...

function	partialInv (A, sizeInv)
	Calculates a partial inverse of a sparse matrix. More...

function	Read (MemberName)
	Query for the value of an attribute in the class. More...

function	Reset ()
	Resets all elements in the class. More...

function	saveLeads ()
	Save Lead Hamiltonians into a file 'Hamiltoni_Lead_' + num2str(Hanyadik_Lead) + '.mat'. More...

function	SelfEnergy ()
	Calculates the retarded self energy of the semi-infinite lead according to Eq (36) of Ref PRB 78, 035407 (2008). More...

function	setTemperature (T)
	Sets the temperature in the calculations. More...

function	ShiftCoordinates (shift)
	Shifts the coordinates of the sites by an integer multiple of the lattice vector Coordinates.a. More...

function	ShiftLead (Energy)
	Shifts the on-site energies in the leads by a given energy. More...

function	SurfaceGreenFunction (varargin)
	Calculates the surface Green function of a semi-infinite lead for eregy E. More...

function	SVD_transform ()
	Regularize the Hamiltonians of the lead by SVD regularization. More...

function	SVDdecompozition ()
	Calculates the SVD decomposition of the matrix H1. More...

function	szetvalaszto (tolerance)
	Sorts the left and right propagating (decaying) modes. More...

function	Transform2BdG ()
	Transforms the Hamiltonians and the overlap matrices into the BdG model in the Nambu space representation according to New Journal of Physics 9 (2007) 278. More...

function	Transform2Spin ()
	Transforms the Hamiltonians and the overlap matrices to include electron spin. More...

function	TrukkosSajatertekek (E)
	Calculates the wave numbers corresponding to the propagating states at given energy. More...

function	Unitary_Transform (Umtx)
	Transforms the effective Hamiltonians and the calculated surface Green operator and selfenergy by a unitary transformation. More...

function	Write (MemberName, input)
	Sets the value of an attribute in the class. 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...

Protected Member Functions
function	calcDualModes ()
	Calculates the dual modes. The dual modes is stored by attributes d_modusmtx_m and d_modusmtx_p. More...

function	CalcDualModesEigenvec (modusmtx)
	Calculates the dual modes by inverting the right-sided eigenvectors. More...

function	CalcDualModesEigenvecWithLeftModes (modusmtx_left, vcsop)
	Calculates the dual modes using the left-sided eigenvectors. More...

function	Extend_Wavefnc (wavefnc_reduced, expk)
	Extend a reduced wave function to the original basis before the SVD regularization (Eq (45) in PRB 78 035407. More...

function	GinfCalcWithDualModes (z1, z2, z1points, z2points)
	Calculates the Green function of the infinite ribbon with dual modes. More...

function	GinfCalcWithLeftModes (z1, z2, z1points, z2points)
	Calculates the Green function of the infinite ribbon with with the left-sided modes. More...

function	GsurfSzamoloWithDualModes ()
	Calculates the surface Green function with dual modes. The calculated Green function is stored by attribute gsurf. More...

function	GsurfSzamoloWithLeftModes ()
	Calculates the surface Green function with the left-sided modes according to Eq (33) in PRB 78, 035407 (2008). The calculated Green function is stored by attribute gsurf. More...

function	Initialize ()
	Initializes class attributes. More...

function	InputParsing (varargin)
	Parses the optional parameters for the class constructor. More...

function	NormamtxSzamoloWithDualModes ()
	Calculates the normalization matrix to calculate the Green function using the dual modes. The calculated normalization matrix is stored by attribute Normamtx. More...

function	NormamtxSzamoloWithLeftModes ()
	Calculates the normalization matrix to calculate the Green function using the left-sided modes. The calculated normalization matrix is stored by attribute Normamtx. More...

function	SelfEnergyCalcWithDualModes ()
	Calculates the self energy with dual modes according to Eqs (17) and (36) in PRB 78 035407. More...

function	SelfEnergyCalcWithLeftModes ()
	Eq (17) and (36) in PRB 78 035407 g00 = inv(Normamtx) More...

function	setM ()
	Updates the number of sites in the cross section. More...

Protected Attributes
Property	beta
	$\beta = 1/(k_BT)$ More...

Property	bias
	The bias on the lead in units of the energy unit in the elements of the Hamiltonian. More...

Property	coordinates
	An instance of the structure coordinates. More...

Property	csoportseb
	The unsorted group velocities. More...

Property	d_modusmtx_m
	The dual basis of the right-sided wave functions of the eigenstates, that propagates or decays in the negative direction. More...

Property	d_modusmtx_p
	The dual basis of the right-sided wave functions of the eigenstates, that propagates or decays in the positive direction. More...

Property	degenerate_k_subspaces
	Logical matrix containing the degenerate k subspaces. More...

Property	DeployedMKL
	True if MKL component is built, false otherwise. More...

Property	E
	The energy value for which the TrukkosSajatertekek eigenvalue problem was solved. More...

Property	expk
	The unsorted wave numbers in form exp(1i*k). More...

Property	expk_m
	The wave numbers of the eigenstates in form exp(1i*k), that propagates or decays in the negative direction. More...

Property	expk_p
	The wave numbers of the eigenstates, that propagates or decays in the positive direction. More...

Property	fazis_mtx_H0
	The matrix of the Peierls phases in the unit cell. More...

Property	fazis_mtx_H1
	The matrix of the Peierls phases in the coupling matrix between the unit cells. More...

Property	fazis_mtx_H1t
	The matrix of the Peierls phases in the transverse coupling matrix between the unit cells. More...

Property	GaugeTransformationApplied
	A logical value. True if a gauge transformation was incorporated into the Hamiltonians or false otherwise. More...

Property	gfin
	The matrix of the retarded surface Greens function of a finite ribbon. More...

Property	gfininv
	The inverse of the retarded surface Greens function of a finite ribbon. More...

Property	ginf
	The matrix of the retarded Greens function of the infinite ribbon. More...

Property	GinfCalc
	Function handle to calculate the retarded infinite Greens function. More...

Property	gsurf
	The matrix of the surface Greens function of the semi-infinite ribbon. More...

Property	gsurfinv
	The inverse of the retarded surface Greens function. More...

Property	H0
	The Hamiltonian of a unit cell. More...

Property	H00
	Obsolete. More...

Property	H1
	The coupling Hamiltonian between the unit cells. More...

Property	H1_skew_left
	The skew coupling (in the positive direction) between Hamiltonians H0 for transverse calculations. More...

Property	H1_skew_right
	The skew upward (in the negative direction) coupling between Hamiltonians H0 for transverse calculations. More...

Property	H1_transverse
	The transverse coupling between the slabs for transverse calculations. More...

Property	H1adj
	The coupling Hamiltonian between the unit cells in the opposite direction as H1. (For complex energies they differ from each other.) More...

Property	HamiltoniansCreated
	A logical value. True if the Hamiltonians were created, false otherwise. More...

Property	HamiltoniansDecimated
	A logical value. True if the Hamiltonians were decimated, false otherwise. More...

Property	Hanyadik_Lead
	The id number of the current lead. More...

Property	invNormamtx
	The inverse of the normalization matrix. More...

Property	is_SVD_transformed
	true if the Hamiltonians were SVD transformed, false otherwise More...

Property	K0
	K0=H0-E*S0, see Eq (4) of PRB 78, 035407. More...

Property	K1
	K1=H1-E*S1, see Eq (4) of PRB 78, 035407. More...

Property	K1_transverse
	K1_transverse=H1_transverse-E*S1_transverse. More...

Property	K1adj
	K1adj=H1adj-E*S1', see Eq (4) of PRB 78, 035407. More...

Property	k_B
	Boltzmann constant in eV/K. More...

Property	kulso_szabfokok
	List of sites in the unit cell that should be kept after decimation. More...

Property	Lead_Orientation
	The orientation of the lead. Set +1 is the "incoming" direction of the propagating states is defined in the +x or +y direction, and "-1" otherwise. More...

Property	lessergfin
	The matrix of the lesser surface Greens function of a finite ribbon. More...

Property	lesserginf
	The matrix of the lesser Greens function of the infinite ribbon. More...

Property	lessergsurf
	The matrix of the lesser surface Greens function of the semi-infinite ribbon. More...

Property	lesserSigma
	The lesser self-energy of the semi-infinite ribbon. More...

Property	M
	The number of the sites in the cross section. More...

Property	MagneticFieldApplied
	A logical value. True if magnetic field was applied in the Hamiltonians, false otherwise. More...

Property	MaxSize
	Maximal size of full matrixes to be handled. More...

Property	modusmtx
	The unsorted right-sided eigenstates. More...

Property	modusmtx_left
	The unsorted left-sided eigenstates. More...

Property	modusmtx_m
	The right-sided wave functions of the eigenstates, that propagates or decays in the negative direction. More...

Property	modusmtx_m_left
	The left-sided wave functions of the eigenstates, that propagates or decays in the negative direction. More...

Property	modusmtx_p
	The right sided wave functions of the eigenstates, that propagates or decays in the positive direction. More...

Property	modusmtx_p_left
	The left-sided wave numbers of the eigenstates, that propagates or decays in the positive direction. More...

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

Property	Neff
	Effective number of sites after the elimination of the singular values. More...

Property	next_SVD_cycle
	Somethimes it is needed to perform another SVD cycle to regularize the H1 matrix. More...

Property	Normamtx
	The normalization matrix in the Greens function. More...

Property	open_channels
	A structure open_channels containing info on the open channels. More...

Property	Opt
	An instance of structure Opt. More...

Property	OverlapApplied
	A logical value. True if the overlap integrals were applied, false otherwise. More...

Property	param
	An instance of the structure param. More...

Property	params
	An instance of the structure lead_param. More...

Property	ProgramName
	Name of the package. More...

Property	ProgramShortName
	Short name of the package. More...

Property	q
	The tranverse momentum for transverse computations. More...

Property	retarted
	true for calculating the retarded Green function, or false for the advanced Green function. More...

Property	S
	S matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407. More...

Property	S0
	The overlap integrals of a unit cell. More...

Property	S1
	The overlap integrals between the unit cells. More...

Property	S1_transverse
	The overlap integrals between the slabs for transverse calculations. More...

Property	S1adj
	The adjungate of the overlap integrals between the unit cells. More...

Property	SelfEnergyCalc
	function handle to calculate the self energy More...

Property	Sigma
	The retarded self-energy of the semi-infinite ribbon. More...

Property	sort_tolerance
	A real number corresponding to the tolerance used to sort the left and right moving (decaying) modes. More...

Property	T
	The temperature in Kelvin. More...

Property	T_treshold
	treshold temperature (makes difference between T=0 and T>0) More...

Property	tolerance
	SVD tolerance to identify singular values. More...

Property	U
	U matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407. More...

Property	V
	V matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407. More...

Property	varargin
	list of optional parameters (see http://www.mathworks.com/help/matlab/ref/varargin.html for details) More...

Property	vcsop_m
	The group velocities of the eigenstates, that propagates or decays in the negative direction. More...

Property	vcsop_p
	The group velocities of the eigenstates in form exp(1i*k), that propagates or decays in the positive direction. More...

Property	version
	The current version of the package. More...

Detailed Description

A class to calculate the Keldysh lesser and greater Green functions and self energies of a translational invariant lead.

The notations and the structure of the Hamiltonian is defined accroding to the following image:

Available

EQuUs v4.9 or later

Definition at line 29 of file Lead_Keldysh.m.

Constructor & Destructor Documentation

◆ Lead_Keldysh()

function Lead_Keldysh::Lead_Keldysh	(	Opt	,
		param	,
		varargin
	)

Constructor of the class.

Parameters

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

Returns: An instance of the class

Member Function Documentation

◆ AddPotential()

function Lead::AddPotential ( V )

inherited

Adds on-site potential to the Hamiltonian H0.

Parameters

V	The potential calculated on the sites. The normalization matrix is set to empty.

◆ ApplyOverlapMatrices()

function CreateLeadHamiltonians::ApplyOverlapMatrices ( E )

inherited

Applies the overlap matrices to the Hamiltonians: K = H-ES.

Parameters

E	The energy value.

◆ 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.

◆ Calc_Effective_Hamiltonians()

function SVDregularizationLead::Calc_Effective_Hamiltonians ( E )

inherited

Calculates the effective Hamiltonians according to Eq (48) of of PRB 78, 035407.

Parameters

E	The energy value

◆ calcDualModes()

function Lead::calcDualModes ( )

protectedinherited

Calculates the dual modes. The dual modes is stored by attributes d_modusmtx_m and d_modusmtx_p.

◆ CalcDualModesEigenvec()

function Lead::CalcDualModesEigenvec ( modusmtx )

protectedinherited

Calculates the dual modes by inverting the right-sided eigenvectors.

Parameters

modusmtx The right-sided eigenvectors.

Returns: Returns with the calculated dual modes.

◆ CalcDualModesEigenvecWithLeftModes()

function Lead::CalcDualModesEigenvecWithLeftModes	(	modusmtx_left	,
		vcsop
	)

protectedinherited

Calculates the dual modes using the left-sided eigenvectors.

Parameters

modusmtx_left	The left-sided eigenvectors.
vcsop	The group velocities.

Returns: Returns with the calculated dual modes

◆ CalcSpektrum()

function CreateLeadHamiltonians::CalcSpektrum ( varargin )

inherited

Calculates the band structure of the lead.

Parameters

varargin	Cell array of optional parameters:
'toPlot'	Set 1 in order to plot the calculated spectrum, 0 (default) otherwise
'ka_min'	The lower bound of the wave numbers. (Default is -pi.)
'ka_max'	The upper bound of the wave numbers. (Default is pi.)
'ka_num'	The number of wave number points involved in the calculations. (Default is 300.)
'ka_vec'	One dimensional array of the k-pints. (Overrides previous attributes related to the k-vector array.)
'center'	The calculated energy eigenvalues are centered around this value. (Default is 0.001.)
'db'	The number of the calculated eigenvalues.
'offset'	Offset value to shift the spectrum along the energy axis.
'calcWaveFnc'	Logical value. Set true to calculate also the wave functions, or false (default) otherwise.

Returns: [1] ka_num x 2 array of the calculated spactrum. In the first column are the k-points, whil ein the second columns are the calculated energy points.; [2] The calculated wave functions stored in a structure WaveFnc.

◆ 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.

◆ Clear()

function Lead_Keldysh::Clear ( MemberName )

Clears the value of an attribute in the class.

Parameters

MemberName The name of the attribute to be cleared.

◆ CreateClone() [1/2]

function Lead_Keldysh::CreateClone ( varargin )

Creates a clone of the present Lead object.

Returns: Returns with the cloned object.

Parameters

varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'empty'	Set true to create an empty clone, or false (default) to clone all atributes.

◆ CreateClone() [2/2]

function EigenProblemLead::CreateClone ( )

inherited

Creates a clone of the present object.

Returns: Returns with the cloned class.

Parameters

varargin	Cell array of optional parameters:
'empty'	Set true to create an empty class, or false (default) to copy all the attributes.

Returns: Returns with an instance of the cloned class.

◆ CreateHamiltonians()

function CreateLeadHamiltonians::CreateHamiltonians ( varargin )

inherited

Creates the Hamiltonians H_0 and H_1 of the lead.

The created Hamiltonians are stored by within the object.

Parameters

varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'toSave'	Logical value. If true, the created Hamiltonians are saved into a file 'Hamiltoni_Lead_' + num2str(Hanyadik_Lead) + '.mat'.
'CustomHamiltonian'	An instance of class Custom_Hamiltonians describing external source of Hamiltonians.

◆ Decimate_Hamiltonians()

function SVDregularizationLead::Decimate_Hamiltonians ( )

inherited

Decimates the Hamiltonians (if the singular sites are predefined).

◆ Determine_Open_Channels()

function EigenProblemLead::Determine_Open_Channels ( )

inherited

Determines the open channels in the lead. The data are storen within the attribute open_channels.

◆ 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.

◆ 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.

◆ Extend_Wavefnc()

function SVDregularizationLead::Extend_Wavefnc	(	wavefnc_reduced	,
		expk
	)

protectedinherited

Extend a reduced wave function to the original basis before the SVD regularization (Eq (45) in PRB 78 035407.

Parameters

wavefnc_reduced	The reduced wavefunction of the effective system
expk	e^(i*k)

Returns: A matrix conatining the extended wave functions.

◆ 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).

◆ FiniteGreenFunction()

function Lead::FiniteGreenFunction	(	z1	,
		z2	,
		varargin
	)

inherited

Eq (20), (17) and (36) in PRB 78 035407 g00 = inv(Normamtx)

Calculates the Green function of a finite piece of the lead for eregy E between slabs z1 and z2. The calculated Greens function is stored by attribute gfin.

Parameters

z1	The index of the first slab.
z2	The index of the second slab.
varargin	Optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'onlygfininv'	If true, only the inverse of the Green function is calculated. (Default value is false)

Returns: Return with the Green function of the infinite lead between the given slabs.

◆ Gamma()

function Lead::Gamma ( )

inherited

Calculates the effective coupling of the lead to the scattering region according to Eq (3) in Eur.

Phys. J. B 53, 537-549 (2006)

Returns: Return with the matrix of the effective coupling.

◆ Get_Effective_Coordinates()

function SVDregularizationLead::Get_Effective_Coordinates ( )

inherited

Gets the coordinates of the sites of the effective Hamiltonians.

(Has sense if the singular sites were given directly)

Returns: [1] A class Coordinates containing the coordinates of the sites of the effective Hamiltonian

◆ Get_Effective_Hamiltonians()

function SVDregularizationLead::Get_Effective_Hamiltonians ( )

inherited

Gets the effective Hamiltonians K0_eff, K1_eff, K1adj_eff according to Eq (48) of of PRB 78, 035407.

Returns: [1] The effective Hamiltonian of one unit cell; [2] The effective coupling between unit cells K1_eff; [3] The adjungate of the effective coupling between unit cells K1adj_eff

◆ Get_Effective_Overlaps()

function SVDregularizationLead::Get_Effective_Overlaps ( )

inherited

Gets the effective Hamiltonians S0_eff, S1_eff, S1adj_eff according to Eq (48) of of PRB 78, 035407.

Returns: [1] The effective overlap matrix of one unit cell S0_eff; [2] The effective overlap matrix between unit cells S1_eff; [3] The adjungate of the effective overlap matrix between unit cells S1adj_eff

◆ Get_Neff()

function SVDregularizationLead::Get_Neff ( )

inherited

Gets the effective number of sites after the elimination of the singular values.

Returns: Returns with the effective number of sites

◆ Get_V()

function SVDregularizationLead::Get_V ( )

inherited

Gets the total transformation U related to the SVD transformation.

Returns: Returns with the total transformation U

◆ 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.

◆ GinfCalcWithDualModes()

function Lead::GinfCalcWithDualModes	(	z1	,
		z2	,
		z1points	,
		z2points
	)

protectedinherited

Calculates the Green function of the infinite ribbon with dual modes.

The calculated Greens function is stored by attribute ginf.

Parameters

z1	The index of the first slab.
z2	The index of the second slab.
z1points	Site indexes in the slab at z1.
z2points	Site indexes in the slab at z2.

Returns: Return with the Greens function of the infinite lead between the given slabs.

◆ GinfCalcWithLeftModes()

function Lead::GinfCalcWithLeftModes	(	z1	,
		z2	,
		z1points	,
		z2points
	)

protectedinherited

Calculates the Green function of the infinite ribbon with with the left-sided modes.

The calculated Greens function is stored by attribute ginf.

Parameters

z1	The index of the first slab.
z2	The index of the second slab.
z1points	Site indexes in the slab at z1.
z2points	Site indexes in the slab at z2.

Returns: Return with the Greens function of the infinite lead between the given slabs.

◆ Group_Velocity()

function EigenProblemLead::Group_Velocity ( )

inherited

Calculates the group velocities corresponding to the propagating states. The calculated group velocities are stored within the class.

◆ GsurfSzamoloWithDualModes()

function Lead::GsurfSzamoloWithDualModes ( )

protectedinherited

Calculates the surface Green function with dual modes. The calculated Green function is stored by attribute gsurf.

◆ GsurfSzamoloWithLeftModes()

function Lead::GsurfSzamoloWithLeftModes ( )

protectedinherited

Calculates the surface Green function with the left-sided modes according to Eq (33) in PRB 78, 035407 (2008). The calculated Green function is stored by attribute gsurf.

◆ InfGreenFunction()

function Lead::InfGreenFunction	(	z1	,
		z2	,
		varargin
	)

inherited

Calculates the Green function of the infinite lead for eregy E between slabs z1 and z2.

The calculated Greens function is stored by attribute ginf.

Parameters

z1	The index of the first slab.
z2	The index of the second slab.
varargin	Optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'z1points'	Array of sites in the slab z1 to include in the calculations. By default each site in the given slab is included.
'z2points'	Array of sites in the slab z2 to include in the calculations. By default each site in the given slab is included.

Returns: Return with the Green function of the infinite lead between the given slabs.

◆ Initialize()

function Lead_Keldysh::Initialize ( )

protected

Initializes class attributes.

◆ InputParsing()

function Lead_Keldysh::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):
'Hanyadik_Lead'	The ID number of the current lead. Set to empty (default) for using parameters of the scatter region.
'Lead_Orientation'	Orientation of the lead. Set +1 (default) is the "incoming" direction of the propagating states is defined in the +x or +y direction, and "-1" otherwise.
'q'	The transverse momentum. Set to empty (default) for computations without transverse momentums.
'T'	The absolute temperature in Kelvins.

◆ 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.

◆ is_SVD_needed()

function SVDregularizationLead::is_SVD_needed ( )

inherited

Decides whether SVD regularization is needed or not.

Returns: Returns with true if SVD regularization is needed, false otherwise

◆ 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.

◆ isSuperconducting()

function CreateLeadHamiltonians::isSuperconducting ( )

inherited

Test, whether the lead is in the superconducting phase or not.

Returns: True if the lead is superconducting, false otherwise.

◆ LesserSelfEnergy()

function Lead_Keldysh::LesserSelfEnergy ( )

Calculates the lesser self energy of a semi-infinite lead for energy E according to Eq (41) in Adv.

Nat. Sci.: Nanosci. Nanotechnol. 5 (2014) 033001. The calculated lesser self energy is stored by attribute lesserSigma.

Returns: Returns with the calculated self energy.

◆ LesserSurfaceGreenFunction()

function Lead_Keldysh::LesserSurfaceGreenFunction ( varargin )

Calculates the lesser Green function of a semi-infinite lead for eregy E. The calculated Green function is stored by the attribute lessergsurf.

◆ MomentumDependentHamiltonian()

function CreateLeadHamiltonians::MomentumDependentHamiltonian	(	k	,
		q
	)

inherited

Construct a momentum dependent (Fourier-transformed) Hamiltonian.

Parameters

k	The longitudinal momentum times the lattice constant.
q	The transverse momentum times the lattice constant.

Returns: Return with the momentum dependent Hamiltonian.

◆ NormamtxSzamolo()

function Lead::NormamtxSzamolo ( )

inherited

right SGF Eq (33) in PRB 78, 035407 (2008) g00 = inv(Normamtx)

left SGF Eq (33) in PRB 78, 035407 (2008) g00 = inv(Normamtx) The normalization matrix to calculate the Green function. The calculated normalization matrix is stored by attribute Normamtx.

◆ NormamtxSzamoloWithDualModes()

function Lead::NormamtxSzamoloWithDualModes ( )

protectedinherited

Calculates the normalization matrix to calculate the Green function using the dual modes. The calculated normalization matrix is stored by attribute Normamtx.

◆ NormamtxSzamoloWithLeftModes()

function Lead::NormamtxSzamoloWithLeftModes ( )

protectedinherited

Calculates the normalization matrix to calculate the Green function using the left-sided modes. The calculated normalization matrix is stored by attribute Normamtx.

◆ 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

◆ Read()

function Lead_Keldysh::Read ( MemberName )

Query for the value of an attribute in the class.

Parameters

MemberName The name of the attribute to be set.

Returns: Returns with the value of the attribute.

◆ Reset()

function Lead_Keldysh::Reset ( )

Resets all elements in the class.

◆ saveLeads()

function CreateLeadHamiltonians::saveLeads ( )

inherited

Save Lead Hamiltonians into a file 'Hamiltoni_Lead_' + num2str(Hanyadik_Lead) + '.mat'.

◆ SelfEnergy()

function Lead::SelfEnergy ( )

inherited

Calculates the retarded self energy of the semi-infinite lead according to Eq (36) of Ref PRB 78, 035407 (2008).

The calculated self energy is stored by attribure Sigma.

Returns: Returns with the calculated self energy.

◆ SelfEnergyCalcWithDualModes()

function Lead::SelfEnergyCalcWithDualModes ( )

protectedinherited

Calculates the self energy with dual modes according to Eqs (17) and (36) in PRB 78 035407.

Returns: Return with the self energy.

◆ SelfEnergyCalcWithLeftModes()

function Lead::SelfEnergyCalcWithLeftModes ( )

protectedinherited

Eq (17) and (36) in PRB 78 035407 g00 = inv(Normamtx)

Calculates the self energy with the left-sided modes according to Eqs (20), (17) and (36) in PRB 78 035407

Returns: Return with the self energy.

◆ setM()

function CreateLeadHamiltonians::setM ( )

protectedinherited

Updates the number of sites in the cross section.

◆ setTemperature()

function Lead_Keldysh::setTemperature ( T )

Sets the temperature in the calculations.

Parameters

T	The value of the temperature in Kelvins.

◆ ShiftCoordinates()

function CreateLeadHamiltonians::ShiftCoordinates ( shift )

inherited

Shifts the coordinates of the sites by an integer multiple of the lattice vector Coordinates.a.

Parameters

shift Integer by which the coordinates are shifted.

◆ ShiftLead()

function Lead::ShiftLead ( Energy )

inherited

Shifts the on-site energies in the leads by a given energy.

The normalization matrix is set to empty.

Parameters

Energy The enrgy value.

◆ 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.

◆ SurfaceGreenFunction()

function Lead::SurfaceGreenFunction ( varargin )

inherited

Calculates the surface Green function of a semi-infinite lead for eregy E.

The calculated Green function is stored in attribute gsurf.

Parameters

varargin	Optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'OnlyInverse'	If true (default), only the inverse of the Green function is calculated.
'CalcInverse'	If true (default), the inverse of the Green function is also calculated.

◆ SVD_transform()

function SVDregularizationLead::SVD_transform ( )

inherited

Regularize the Hamiltonians of the lead by SVD regularization.

◆ SVDdecompozition()

function SVDregularizationLead::SVDdecompozition ( )

inherited

Calculates the SVD decomposition of the matrix H1.

◆ szetvalaszto()

function EigenProblemLead::szetvalaszto ( tolerance )

inherited

Sorts the left and right propagating (decaying) modes.

Parameters

tolerance The tolerance to be used during the sort.

◆ Transform2BdG()

function CreateLeadHamiltonians::Transform2BdG ( )

inherited

Transforms the Hamiltonians and the overlap matrices into the BdG model in the Nambu space representation according to New Journal of Physics 9 (2007) 278.

It is assumed, that the Hamiltonian is already transfromed to the grand canonical operator: $\hat{H} \rightarrow \hat{H} - E_F\hat{N}$

◆ Transform2Spin()

function CreateLeadHamiltonians::Transform2Spin ( )

inherited

Transforms the Hamiltonians and the overlap matrices to include electron spin.

◆ TrukkosSajatertekek()

function Lead::TrukkosSajatertekek ( E )

inherited

Calculates the wave numbers corresponding to the propagating states at given energy.

The calculated wave numbers are stored in attribute expk. The normalization matrix is set to empty.

Parameters

E	The energy value used in the calculations.

◆ Unitary_Transform()

function Lead::Unitary_Transform ( Umtx )

inherited

Transforms the effective Hamiltonians and the calculated surface Green operator and selfenergy by a unitary transformation.

Parameters

Umtx	The matrix of the unitary transformation.

◆ Write()

function Lead_Keldysh::Write	(	MemberName	,
		input
	)

Sets the value of an attribute in the class.

Parameters

MemberName	The name of the attribute to be set.
input	The value to be set.

◆ 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

◆ beta

Property FermiDirac::beta

protectedinherited

$\beta = 1/(k_BT)$

Definition at line 38 of file FermiDirac.m.

◆ bias

Property Lead_Keldysh::bias

protected

The bias on the lead in units of the energy unit in the elements of the Hamiltonian.

Definition at line 49 of file Lead_Keldysh.m.

◆ coordinates

Property CreateLeadHamiltonians::coordinates

protectedinherited

An instance of the structure coordinates.

Definition at line 58 of file CreateLeadHamiltonians.m.

◆ csoportseb

Property EigenProblemLead::csoportseb

protectedinherited

The unsorted group velocities.

Definition at line 46 of file EigenProblemLead.m.

◆ d_modusmtx_m

Property EigenProblemLead::d_modusmtx_m

protectedinherited

The dual basis of the right-sided wave functions of the eigenstates, that propagates or decays in the negative direction.

Definition at line 76 of file EigenProblemLead.m.

◆ d_modusmtx_p

Property EigenProblemLead::d_modusmtx_p

protectedinherited

The dual basis of the right-sided wave functions of the eigenstates, that propagates or decays in the positive direction.

Definition at line 73 of file EigenProblemLead.m.

◆ degenerate_k_subspaces

Property EigenProblemLead::degenerate_k_subspaces

protectedinherited

Logical matrix containing the degenerate k subspaces.

Definition at line 85 of file EigenProblemLead.m.

◆ DeployedMKL

Property CommonFunctions::DeployedMKL

protectedinherited

True if MKL component is built, false otherwise.

Definition at line 32 of file CommonFunctions.m.

◆ E

Property EigenProblemLead::E

protectedinherited

The energy value for which the TrukkosSajatertekek eigenvalue problem was solved.

Definition at line 88 of file EigenProblemLead.m.

◆ expk

Property EigenProblemLead::expk

protectedinherited

The unsorted wave numbers in form exp(1i*k).

Definition at line 43 of file EigenProblemLead.m.

◆ expk_m

Property EigenProblemLead::expk_m

protectedinherited

The wave numbers of the eigenstates in form exp(1i*k), that propagates or decays in the negative direction.

Definition at line 52 of file EigenProblemLead.m.

◆ expk_p

Property EigenProblemLead::expk_p

protectedinherited

The wave numbers of the eigenstates, that propagates or decays in the positive direction.

Definition at line 49 of file EigenProblemLead.m.

◆ fazis_mtx_H0

Property CreateLeadHamiltonians::fazis_mtx_H0

protectedinherited

The matrix of the Peierls phases in the unit cell.

Definition at line 106 of file CreateLeadHamiltonians.m.

◆ fazis_mtx_H1

Property CreateLeadHamiltonians::fazis_mtx_H1

protectedinherited

The matrix of the Peierls phases in the coupling matrix between the unit cells.

Definition at line 109 of file CreateLeadHamiltonians.m.

◆ fazis_mtx_H1t

Property CreateLeadHamiltonians::fazis_mtx_H1t

protectedinherited

The matrix of the Peierls phases in the transverse coupling matrix between the unit cells.

Definition at line 112 of file CreateLeadHamiltonians.m.

◆ GaugeTransformationApplied

Property CreateLeadHamiltonians::GaugeTransformationApplied

protectedinherited

A logical value. True if a gauge transformation was incorporated into the Hamiltonians or false otherwise.

Definition at line 127 of file CreateLeadHamiltonians.m.

◆ gfin

Property Lead::gfin

protectedinherited

The matrix of the retarded surface Greens function of a finite ribbon.

Definition at line 57 of file Lead.m.

◆ gfininv

Property Lead::gfininv

protectedinherited

The inverse of the retarded surface Greens function of a finite ribbon.

Definition at line 60 of file Lead.m.

◆ ginf

Property Lead::ginf

protectedinherited

The matrix of the retarded Greens function of the infinite ribbon.

Definition at line 54 of file Lead.m.

◆ GinfCalc

Property Lead::GinfCalc

protectedinherited

Function handle to calculate the retarded infinite Greens function.

Definition at line 39 of file Lead.m.

◆ gsurf

Property Lead::gsurf

protectedinherited

The matrix of the surface Greens function of the semi-infinite ribbon.

Definition at line 48 of file Lead.m.

◆ gsurfinv

Property Lead::gsurfinv

protectedinherited

The inverse of the retarded surface Greens function.

Definition at line 51 of file Lead.m.

◆ H0

Property CreateLeadHamiltonians::H0

protectedinherited

The Hamiltonian of a unit cell.

Definition at line 73 of file CreateLeadHamiltonians.m.

◆ H00

Property CreateLeadHamiltonians::H00

protectedinherited

Obsolete.

Definition at line 82 of file CreateLeadHamiltonians.m.

◆ H1

Property CreateLeadHamiltonians::H1

protectedinherited

The coupling Hamiltonian between the unit cells.

Definition at line 76 of file CreateLeadHamiltonians.m.

◆ H1_skew_left

Property CreateLeadHamiltonians::H1_skew_left

protectedinherited

The skew coupling (in the positive direction) between Hamiltonians H0 for transverse calculations.

Definition at line 91 of file CreateLeadHamiltonians.m.

◆ H1_skew_right

Property CreateLeadHamiltonians::H1_skew_right

protectedinherited

The skew upward (in the negative direction) coupling between Hamiltonians H0 for transverse calculations.

Definition at line 88 of file CreateLeadHamiltonians.m.

◆ H1_transverse

Property CreateLeadHamiltonians::H1_transverse

protectedinherited

The transverse coupling between the slabs for transverse calculations.

Definition at line 85 of file CreateLeadHamiltonians.m.

◆ H1adj

Property CreateLeadHamiltonians::H1adj

protectedinherited

The coupling Hamiltonian between the unit cells in the opposite direction as H1. (For complex energies they differ from each other.)

Definition at line 79 of file CreateLeadHamiltonians.m.

◆ HamiltoniansCreated

Property CreateLeadHamiltonians::HamiltoniansCreated

protectedinherited

A logical value. True if the Hamiltonians were created, false otherwise.

Definition at line 115 of file CreateLeadHamiltonians.m.

◆ HamiltoniansDecimated

Property CreateLeadHamiltonians::HamiltoniansDecimated

protectedinherited

A logical value. True if the Hamiltonians were decimated, false otherwise.

Definition at line 118 of file CreateLeadHamiltonians.m.

◆ Hanyadik_Lead

Property CreateLeadHamiltonians::Hanyadik_Lead

protectedinherited

The id number of the current lead.

Definition at line 43 of file CreateLeadHamiltonians.m.

◆ invNormamtx

Property Lead::invNormamtx

protectedinherited

The inverse of the normalization matrix.

Definition at line 45 of file Lead.m.

◆ is_SVD_transformed

Property SVDregularizationLead::is_SVD_transformed

protectedinherited

true if the Hamiltonians were SVD transformed, false otherwise

Definition at line 37 of file SVDregularizationLead.m.

◆ K0

Property CreateLeadHamiltonians::K0

protectedinherited

K0=H0-E*S0, see Eq (4) of PRB 78, 035407.

Definition at line 61 of file CreateLeadHamiltonians.m.

◆ K1

Property CreateLeadHamiltonians::K1

protectedinherited

K1=H1-E*S1, see Eq (4) of PRB 78, 035407.

Definition at line 64 of file CreateLeadHamiltonians.m.

◆ K1_transverse

Property CreateLeadHamiltonians::K1_transverse

protectedinherited

K1_transverse=H1_transverse-E*S1_transverse.

Definition at line 70 of file CreateLeadHamiltonians.m.

◆ K1adj

Property CreateLeadHamiltonians::K1adj

protectedinherited

K1adj=H1adj-E*S1', see Eq (4) of PRB 78, 035407.

Definition at line 67 of file CreateLeadHamiltonians.m.

◆ k_B

Property FermiDirac::k_B

protectedinherited

Boltzmann constant in eV/K.

Definition at line 32 of file FermiDirac.m.

◆ kulso_szabfokok

Property CreateLeadHamiltonians::kulso_szabfokok

protectedinherited

List of sites in the unit cell that should be kept after decimation.

Definition at line 55 of file CreateLeadHamiltonians.m.

◆ Lead_Orientation

Property CreateLeadHamiltonians::Lead_Orientation

protectedinherited

The orientation of the lead. Set +1 is the "incoming" direction of the propagating states is defined in the +x or +y direction, and "-1" otherwise.

Definition at line 40 of file CreateLeadHamiltonians.m.

◆ lessergfin

Property Lead_Keldysh::lessergfin

protected

The matrix of the lesser surface Greens function of a finite ribbon.

Definition at line 43 of file Lead_Keldysh.m.

◆ lesserginf

Property Lead_Keldysh::lesserginf

protected

The matrix of the lesser Greens function of the infinite ribbon.

Definition at line 40 of file Lead_Keldysh.m.

◆ lessergsurf

Property Lead_Keldysh::lessergsurf

protected

The matrix of the lesser surface Greens function of the semi-infinite ribbon.

Definition at line 37 of file Lead_Keldysh.m.

◆ lesserSigma

Property Lead_Keldysh::lesserSigma

protected

The lesser self-energy of the semi-infinite ribbon.

Definition at line 46 of file Lead_Keldysh.m.

◆ M

Property CreateLeadHamiltonians::M

protectedinherited

The number of the sites in the cross section.

Definition at line 46 of file CreateLeadHamiltonians.m.

◆ MagneticFieldApplied

Property CreateLeadHamiltonians::MagneticFieldApplied

protectedinherited

A logical value. True if magnetic field was applied in the Hamiltonians, false otherwise.

Definition at line 124 of file CreateLeadHamiltonians.m.

◆ MaxSize

Property CommonFunctions::MaxSize

protectedinherited

Maximal size of full matrixes to be handled.

Definition at line 44 of file CommonFunctions.m.

◆ modusmtx

Property EigenProblemLead::modusmtx

protectedinherited

The unsorted right-sided eigenstates.

Definition at line 37 of file EigenProblemLead.m.

◆ modusmtx_left

Property EigenProblemLead::modusmtx_left

protectedinherited

The unsorted left-sided eigenstates.

Definition at line 40 of file EigenProblemLead.m.

◆ modusmtx_m

Property EigenProblemLead::modusmtx_m

protectedinherited

The right-sided wave functions of the eigenstates, that propagates or decays in the negative direction.

Definition at line 64 of file EigenProblemLead.m.

◆ modusmtx_m_left

Property EigenProblemLead::modusmtx_m_left

protectedinherited

The left-sided wave functions of the eigenstates, that propagates or decays in the negative direction.

Definition at line 70 of file EigenProblemLead.m.

◆ modusmtx_p

Property EigenProblemLead::modusmtx_p

protectedinherited

The right sided wave functions of the eigenstates, that propagates or decays in the positive direction.

Definition at line 61 of file EigenProblemLead.m.

◆ modusmtx_p_left

Property EigenProblemLead::modusmtx_p_left

protectedinherited

The left-sided wave numbers of the eigenstates, that propagates or decays in the positive direction.

Definition at line 67 of file EigenProblemLead.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.

◆ Neff

Property SVDregularizationLead::Neff

protectedinherited

Effective number of sites after the elimination of the singular values.

Definition at line 55 of file SVDregularizationLead.m.

◆ next_SVD_cycle

Property SVDregularizationLead::next_SVD_cycle

protectedinherited

Somethimes it is needed to perform another SVD cycle to regularize the H1 matrix.

Definition at line 52 of file SVDregularizationLead.m.

◆ Normamtx

Property Lead::Normamtx

protectedinherited

The normalization matrix in the Greens function.

Definition at line 42 of file Lead.m.

◆ open_channels

Property EigenProblemLead::open_channels

protectedinherited

A structure open_channels containing info on the open channels.

Definition at line 82 of file EigenProblemLead.m.

◆ Opt

Property Messages::Opt

protectedinherited

An instance of structure Opt.

Definition at line 31 of file Messages.m.

◆ OverlapApplied

Property CreateLeadHamiltonians::OverlapApplied

protectedinherited

A logical value. True if the overlap integrals were applied, false otherwise.

Definition at line 121 of file CreateLeadHamiltonians.m.

◆ param

Property CreateLeadHamiltonians::param

protectedinherited

An instance of the structure param.

Definition at line 37 of file CreateLeadHamiltonians.m.

◆ params

Property CreateLeadHamiltonians::params

protectedinherited

An instance of the structure lead_param.

Definition at line 49 of file CreateLeadHamiltonians.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.

◆ q

Property CreateLeadHamiltonians::q

protectedinherited

The tranverse momentum for transverse computations.

Definition at line 52 of file CreateLeadHamiltonians.m.

◆ retarted

Property EigenProblemLead::retarted

protectedinherited

true for calculating the retarded Green function, or false for the advanced Green function.

Definition at line 34 of file EigenProblemLead.m.

◆ S

Property SVDregularizationLead::S

protectedinherited

S matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407.

Definition at line 43 of file SVDregularizationLead.m.

◆ S0

Property CreateLeadHamiltonians::S0

protectedinherited

The overlap integrals of a unit cell.

Definition at line 94 of file CreateLeadHamiltonians.m.

◆ S1

Property CreateLeadHamiltonians::S1

protectedinherited

The overlap integrals between the unit cells.

Definition at line 97 of file CreateLeadHamiltonians.m.

◆ S1_transverse

Property CreateLeadHamiltonians::S1_transverse

protectedinherited

The overlap integrals between the slabs for transverse calculations.

Definition at line 103 of file CreateLeadHamiltonians.m.

◆ S1adj

Property CreateLeadHamiltonians::S1adj

protectedinherited

The adjungate of the overlap integrals between the unit cells.

Definition at line 100 of file CreateLeadHamiltonians.m.

◆ SelfEnergyCalc

Property Lead::SelfEnergyCalc

protectedinherited

function handle to calculate the self energy

Definition at line 36 of file Lead.m.

◆ Sigma

Property Lead::Sigma

protectedinherited

The retarded self-energy of the semi-infinite ribbon.

Definition at line 63 of file Lead.m.

◆ sort_tolerance

Property EigenProblemLead::sort_tolerance

protectedinherited

A real number corresponding to the tolerance used to sort the left and right moving (decaying) modes.

Definition at line 79 of file EigenProblemLead.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.

◆ tolerance

Property SVDregularizationLead::tolerance

protectedinherited

SVD tolerance to identify singular values.

Definition at line 49 of file SVDregularizationLead.m.

◆ U

Property SVDregularizationLead::U

protectedinherited

U matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407.

Definition at line 40 of file SVDregularizationLead.m.

◆ V

Property SVDregularizationLead::V

protectedinherited

V matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407.

Definition at line 46 of file SVDregularizationLead.m.

◆ varargin

Property CreateLeadHamiltonians::varargin

protectedinherited

list of optional parameters (see http://www.mathworks.com/help/matlab/ref/varargin.html for details)

Definition at line 130 of file CreateLeadHamiltonians.m.

◆ vcsop_m

Property EigenProblemLead::vcsop_m

protectedinherited

The group velocities of the eigenstates, that propagates or decays in the negative direction.

Definition at line 58 of file EigenProblemLead.m.

◆ vcsop_p

Property EigenProblemLead::vcsop_p

protectedinherited

The group velocities of the eigenstates in form exp(1i*k), that propagates or decays in the positive direction.

Definition at line 55 of file EigenProblemLead.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:

Lead_Keldysh.m

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Available

Constructor & Destructor Documentation

◆ Lead_Keldysh()

Member Function Documentation

◆ AddPotential()

◆ ApplyOverlapMatrices()

◆ BadInputType()

◆ BadInputTypeNoDefault()

◆ Calc_Effective_Hamiltonians()

◆ calcDualModes()

◆ CalcDualModesEigenvec()

◆ CalcDualModesEigenvecWithLeftModes()

◆ CalcSpektrum()

◆ checkMEXfile()

◆ Clear()

◆ CreateClone() [1/2]

◆ CreateClone() [2/2]

◆ CreateHamiltonians()

◆ Decimate_Hamiltonians()

◆ Determine_Open_Channels()

◆ diagInv()

◆ display()

◆ eig()

◆ ExceedIteration()

◆ Extend_Wavefnc()

◆ Fermi()

◆ FiniteGreenFunction()

◆ Gamma()

◆ Get_Effective_Coordinates()

◆ Get_Effective_Hamiltonians()

◆ Get_Effective_Overlaps()

◆ Get_Neff()

◆ Get_V()

◆ getOpt()

◆ getProgramName()

◆ getProgramShortName()

◆ getVersion()

◆ GinfCalcWithDualModes()

◆ GinfCalcWithLeftModes()

◆ Group_Velocity()

◆ GsurfSzamoloWithDualModes()

◆ GsurfSzamoloWithLeftModes()

◆ InfGreenFunction()

◆ Initialize()

◆ InputParsing()

◆ inv_SVD()

◆ is_SVD_needed()

◆ IsDeployedMKL()

◆ isOctave()

◆ isSuperconducting()

◆ LesserSelfEnergy()

◆ LesserSurfaceGreenFunction()

◆ MomentumDependentHamiltonian()

◆ NormamtxSzamolo()

◆ NormamtxSzamoloWithDualModes()

◆ NormamtxSzamoloWithLeftModes()

◆ partialInv()

◆ Read()

◆ Reset()

◆ saveLeads()

◆ SelfEnergy()

◆ SelfEnergyCalcWithDualModes()

◆ SelfEnergyCalcWithLeftModes()

◆ setM()

◆ setTemperature()

◆ ShiftCoordinates()

◆ ShiftLead()

◆ SimphsonInt()

◆ SurfaceGreenFunction()

◆ SVD_transform()

◆ SVDdecompozition()

◆ szetvalaszto()

◆ Transform2BdG()

◆ Transform2Spin()

◆ TrukkosSajatertekek()