Class to solve the eigenproblem of a translational invariant leads and calculate the group velocities. More...

Inheritance diagram for EigenProblemLead:

[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 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	display (message, nosilent)
	Displays output messages on the screen. More...

function	EigenProblemLead (Opt, param, varargin)
	Constructor of the class. 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	Group_Velocity ()
	Calculates the group velocities corresponding to the propagating states. The calculated group velocities are stored within the class. More...

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

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

function	MomentumDependentHamiltonian (ka, qb)
	Construct a momentum dependent (Fourier-transformed) Hamiltonian. More...

function	qDependentHamiltonians ()
	Construct a K0 and K1 Hamiltonians (transformed to the grand canonical potential) for a given subspace of the transverse momentum number q. More...

function	qDependentOverlaps ()
	Construct a S0 and S1 overlap matrices for a given subspace of the transverse momentum number q. More...

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

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

function	saveLeads ()
	Save Lead Hamiltonians into a file 'Hamiltoni_Lead_' + num2str(Hanyadik_Lead) + '.mat'. 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	SVD_transform ()
	Regularize the Hamiltonians of the lead by SVD regularization. More...

function	SVDdecompozition (K1)
	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 by a unitary transformation. More...

function	Write (MemberName, input)
	Sets the value of an attribute in the class. 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	ExceedIteration ()
	Throws an "iteration exceeded" warning. More...

Protected Member Functions
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	Initialize ()
	Initializes object properties. More...

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

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

Protected Attributes
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	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_H1_skew_left
	The matrix of the Peierls phases in the skew coupling matrix in the left direction between the unit cells. More...

Property	fazis_mtx_H1_skew_right
	The matrix of the Peierls phases in the skew coupling matrix in the right direction 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	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 left direction between Hamiltonians H0 for transverse calculations. More...

Property	H1_skew_right
	The skew coupling in the right direction 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	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_skew_left
	K1_skew_left = H1_skew_left - E*S1_skew_left. More...

Property	K1_skew_right
	K1_skew_right = H1_skew_right - E*S1_skew_right. 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	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	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	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	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	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	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_skew_left
	The overlap integrals for the skew coupling in the left direction between Hamiltonians H0 for transverse calculations. More...

Property	S1_skew_right
	The overlap integrals for the skew coupling in the right direction between Hamiltonians H0 for transverse calculations. 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	sort_tolerance
	A real number corresponding to the tolerance used to sort the left and right moving (decaying) modes. 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...

Private Member Functions
function	Determine_Degenerate_k_subspaces ()
	Determine the degenerate k subspaces for which the current operator needs to be diagonalized. More...

function	Extend_Wavefncs ()
	Extend the reduced wave functions to the original basis before the SVD regularization (Eq (45) in PRB 78 035407) This function is in a development stage. More...

function	NormalizeModes ()
	Renormalizes the wave functions with the overlap integrals (Eq (9) in PRB 78 035407. More...

Detailed Description

Class to solve the eigenproblem of a translational invariant leads and calculate the group velocities.

Available

EQuUs v4.8 or later

Definition at line 26 of file EigenProblemLead.m.

Constructor & Destructor Documentation

◆ EigenProblemLead()

function EigenProblemLead::EigenProblemLead	(	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 identical to SVDregularizationLead.SVDregularizationLead.

Returns: An instance of the class

Member Function Documentation

◆ AddPotential()

function EigenProblemLead::AddPotential ( V )

Adds on-site potential to the Hamiltonian H0.

Parameters

V	The potential calculated on the sites.

◆ 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

◆ 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.

◆ Clear()

function EigenProblemLead::Clear ( MemberName )

Clears the value of an attribute in the class.

Parameters

MemberName The name of the attribute to be cleared.

◆ CreateClone()

function EigenProblemLead::CreateClone ( varargin )

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_Degenerate_k_subspaces()

function EigenProblemLead::Determine_Degenerate_k_subspaces ( )

private

Determine the degenerate k subspaces for which the current operator needs to be diagonalized.

◆ Determine_Open_Channels()

function EigenProblemLead::Determine_Open_Channels ( )

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

◆ 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.

◆ 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.

◆ Extend_Wavefncs()

function EigenProblemLead::Extend_Wavefncs ( )

private

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

◆ 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.

◆ Group_Velocity()

function EigenProblemLead::Group_Velocity ( )

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

◆ Initialize()

function EigenProblemLead::Initialize ( )

protected

Initializes object properties.

◆ InputParsing()

function CreateLeadHamiltonians::InputParsing ( varargin )

protectedinherited

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.

◆ 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

◆ 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.

◆ MomentumDependentHamiltonian()

function CreateLeadHamiltonians::MomentumDependentHamiltonian	(	ka	,
		qb
	)

inherited

Construct a momentum dependent (Fourier-transformed) Hamiltonian.

Parameters

ka	The longitudinal momentum times the lattice constant.
qb	The transverse momentum times the transverse lattice constant.

Returns: Return with the momentum dependent Hamiltonian.

◆ NormalizeModes()

function EigenProblemLead::NormalizeModes ( )

private

Renormalizes the wave functions with the overlap integrals (Eq (9) in PRB 78 035407.

◆ qDependentHamiltonians()

function CreateLeadHamiltonians::qDependentHamiltonians ( )

inherited

Construct a K0 and K1 Hamiltonians (transformed to the grand canonical potential) for a given subspace of the transverse momentum number q.

Returns: [1] the transverse momentum dependent Hamiltonian of the unit cell.; [2] the transverse momentum dependent Hamiltonian of the coupling boeween the unit cells.; [3] the transverse momentum dependent Hamiltonian of the coupling boeween the unit cells in the opposite direction.

◆ qDependentOverlaps()

function CreateLeadHamiltonians::qDependentOverlaps ( )

inherited

Construct a S0 and S1 overlap matrices for a given subspace of the transverse momentum number q.

Returns: [1] the transverse momentum dependent overlap matrix of the unit cell.; [2] the transverse momentum dependent overlap matrix of the coupling between the unit cells.; [3] the transverse momentum dependent overlap matrix of the coupling boeween the unit cells in the opposite direction.

◆ Read()

function EigenProblemLead::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 EigenProblemLead::Reset ( )

Resets all elements in the object.

◆ saveLeads()

function CreateLeadHamiltonians::saveLeads ( )

inherited

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

◆ setM()

function CreateLeadHamiltonians::setM ( )

protectedinherited

Updates the number of sites in the cross section.

◆ 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 CreateLeadHamiltonians::ShiftLead ( Energy )

inherited

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

Parameters

Energy The enrgy value.

◆ SVD_transform()

function SVDregularizationLead::SVD_transform ( )

inherited

Regularize the Hamiltonians of the lead by SVD regularization.

◆ SVDdecompozition()

function SVDregularizationLead::SVDdecompozition ( K1 )

inherited

Calculates the SVD decomposition of the matrix H1.

Parameters

The	transverse momentum dependent coulping between the unit cell (K1 is transverse momentum dependent, only if skew coupling H1_skew_right or H1_skew_left and the transverse momentum q are not empty).

◆ szetvalaszto()

function EigenProblemLead::szetvalaszto ( tolerance )

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 EigenProblemLead::TrukkosSajatertekek ( E )

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

The calculated wave numbers are stored by attribute expk.

Parameters

E	The energy value used in the calculations.

◆ Unitary_Transform()

function EigenProblemLead::Unitary_Transform ( Umtx )

Transforms the effective Hamiltonians by a unitary transformation.

Parameters

Umtx	The matrix of the unitary transformation.

◆ Write()

function EigenProblemLead::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.

Member Data Documentation

◆ coordinates

Property CreateLeadHamiltonians::coordinates

protectedinherited

An instance of the structure coordinates.

Definition at line 58 of file CreateLeadHamiltonians.m.

◆ csoportseb

Property EigenProblemLead::csoportseb

protected

The unsorted group velocities.

Definition at line 46 of file EigenProblemLead.m.

◆ d_modusmtx_m

Property EigenProblemLead::d_modusmtx_m

protected

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

protected

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

protected

Logical matrix containing the degenerate k subspaces.

Definition at line 85 of file EigenProblemLead.m.

◆ E

Property EigenProblemLead::E

protected

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

Definition at line 88 of file EigenProblemLead.m.

◆ expk

Property EigenProblemLead::expk

protected

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

Definition at line 43 of file EigenProblemLead.m.

◆ expk_m

Property EigenProblemLead::expk_m

protected

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

protected

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 118 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 121 of file CreateLeadHamiltonians.m.

◆ fazis_mtx_H1_skew_left

Property CreateLeadHamiltonians::fazis_mtx_H1_skew_left

protectedinherited

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

Definition at line 130 of file CreateLeadHamiltonians.m.

◆ fazis_mtx_H1_skew_right

Property CreateLeadHamiltonians::fazis_mtx_H1_skew_right

protectedinherited

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

Definition at line 127 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 124 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 145 of file CreateLeadHamiltonians.m.

◆ H0

Property CreateLeadHamiltonians::H0

protectedinherited

The Hamiltonian of a unit cell.

Definition at line 79 of file CreateLeadHamiltonians.m.

◆ H00

Property CreateLeadHamiltonians::H00

protectedinherited

Obsolete.

Definition at line 88 of file CreateLeadHamiltonians.m.

◆ H1

Property CreateLeadHamiltonians::H1

protectedinherited

The coupling Hamiltonian between the unit cells.

Definition at line 82 of file CreateLeadHamiltonians.m.

◆ H1_skew_left

Property CreateLeadHamiltonians::H1_skew_left

protectedinherited

The skew coupling in the left direction between Hamiltonians H0 for transverse calculations.

Definition at line 97 of file CreateLeadHamiltonians.m.

◆ H1_skew_right

Property CreateLeadHamiltonians::H1_skew_right

protectedinherited

The skew coupling in the right direction between Hamiltonians H0 for transverse calculations.

Definition at line 94 of file CreateLeadHamiltonians.m.

◆ H1_transverse

Property CreateLeadHamiltonians::H1_transverse

protectedinherited

The transverse coupling between the slabs for transverse calculations.

Definition at line 91 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 85 of file CreateLeadHamiltonians.m.

◆ HamiltoniansCreated

Property CreateLeadHamiltonians::HamiltoniansCreated

protectedinherited

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

Definition at line 133 of file CreateLeadHamiltonians.m.

◆ HamiltoniansDecimated

Property CreateLeadHamiltonians::HamiltoniansDecimated

protectedinherited

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

Definition at line 136 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.

◆ 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_skew_left

Property CreateLeadHamiltonians::K1_skew_left

protectedinherited

K1_skew_left = H1_skew_left - E*S1_skew_left.

Definition at line 76 of file CreateLeadHamiltonians.m.

◆ K1_skew_right

Property CreateLeadHamiltonians::K1_skew_right

protectedinherited

K1_skew_right = H1_skew_right - E*S1_skew_right.

Definition at line 73 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.

◆ 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.

◆ 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 142 of file CreateLeadHamiltonians.m.

◆ modusmtx

Property EigenProblemLead::modusmtx

protected

The unsorted right-sided eigenstates.

Definition at line 37 of file EigenProblemLead.m.

◆ modusmtx_left

Property EigenProblemLead::modusmtx_left

protected

The unsorted left-sided eigenstates.

Definition at line 40 of file EigenProblemLead.m.

◆ modusmtx_m

Property EigenProblemLead::modusmtx_m

protected

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

protected

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

protected

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

protected

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

Definition at line 67 of file EigenProblemLead.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.

◆ open_channels

Property EigenProblemLead::open_channels

protected

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 139 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.

◆ q

Property CreateLeadHamiltonians::q

protectedinherited

The tranverse momentum for transverse computations.

Definition at line 52 of file CreateLeadHamiltonians.m.

◆ retarted

Property EigenProblemLead::retarted

protected

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 100 of file CreateLeadHamiltonians.m.

◆ S1

Property CreateLeadHamiltonians::S1

protectedinherited

The overlap integrals between the unit cells.

Definition at line 103 of file CreateLeadHamiltonians.m.

◆ S1_skew_left

Property CreateLeadHamiltonians::S1_skew_left

protectedinherited

The overlap integrals for the skew coupling in the left direction between Hamiltonians H0 for transverse calculations.

Definition at line 115 of file CreateLeadHamiltonians.m.

◆ S1_skew_right

Property CreateLeadHamiltonians::S1_skew_right

protectedinherited

The overlap integrals for the skew coupling in the right direction between Hamiltonians H0 for transverse calculations.

Definition at line 112 of file CreateLeadHamiltonians.m.

◆ S1_transverse

Property CreateLeadHamiltonians::S1_transverse

protectedinherited

The overlap integrals between the slabs for transverse calculations.

Definition at line 109 of file CreateLeadHamiltonians.m.

◆ S1adj

Property CreateLeadHamiltonians::S1adj

protectedinherited

The adjungate of the overlap integrals between the unit cells.

Definition at line 106 of file CreateLeadHamiltonians.m.

◆ sort_tolerance

Property EigenProblemLead::sort_tolerance

protected

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.

◆ 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 148 of file CreateLeadHamiltonians.m.

◆ vcsop_m

Property EigenProblemLead::vcsop_m

protected

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

protected

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.

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

EigenProblemLead.m

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Available

Constructor & Destructor Documentation

◆ EigenProblemLead()

Member Function Documentation

◆ AddPotential()

◆ ApplyOverlapMatrices()

◆ BadInputType()

◆ BadInputTypeNoDefault()

◆ Calc_Effective_Hamiltonians()

◆ CalcSpektrum()

◆ Clear()

◆ CreateClone()

◆ CreateHamiltonians()

◆ Decimate_Hamiltonians()

◆ Determine_Degenerate_k_subspaces()

◆ Determine_Open_Channels()

◆ display()

◆ ExceedIteration()

◆ Extend_Wavefnc()

◆ Extend_Wavefncs()

◆ Get_Effective_Coordinates()

◆ Get_Effective_Hamiltonians()

◆ Get_Effective_Overlaps()

◆ Get_Neff()

◆ Get_V()

◆ getOpt()

◆ Group_Velocity()

◆ Initialize()

◆ InputParsing()

◆ is_SVD_needed()

◆ isSuperconducting()

◆ MomentumDependentHamiltonian()

◆ NormalizeModes()

◆ qDependentHamiltonians()

◆ qDependentOverlaps()

◆ Read()

◆ Reset()

◆ saveLeads()

◆ setM()

◆ ShiftCoordinates()

◆ ShiftLead()

◆ SVD_transform()

◆ SVDdecompozition()

◆ szetvalaszto()

◆ Transform2BdG()

◆ Transform2Spin()

◆ TrukkosSajatertekek()

◆ Unitary_Transform()

◆ Write()

Member Data Documentation

◆ coordinates

◆ csoportseb

◆ d_modusmtx_m

◆ d_modusmtx_p

◆ degenerate_k_subspaces

◆ E

◆ expk

◆ expk_m

◆ expk_p

◆ fazis_mtx_H0

◆ fazis_mtx_H1

◆ fazis_mtx_H1_skew_left

◆ fazis_mtx_H1_skew_right

◆ fazis_mtx_H1t

◆ GaugeTransformationApplied

◆ H0

◆ H00

◆ H1

◆ H1_skew_left

◆ H1_skew_right

◆ H1_transverse

◆ H1adj

◆ HamiltoniansCreated

◆ HamiltoniansDecimated